- Growth and Exhaustible Resources
- Rational Individual Choice and Consequentialism
- Game Theory and Consequentialism
- Consequentialist Social Choice and Utilitarian Ethical Theory
- Social Choice: General
- Social Choice with Interpersonal Comparisons
- Social Choice with Individual and Group Rights
- Distributional Objectives in Welfare Economics
- General Equilibrium Theory
- Gains from Trade and Migration
- Widespread Externalities and the
*f*-Core - Equilibrium in Incomplete Markets
- Private Information and Incentive Constraints
- Cost–Benefit Analysis, Policy Reform, and Welfare Measurement
- Welfare, Information and Uncertainty
- Miscellaneous Work in Welfare Economics and Ethics
- Continuum of Random Variables
- Empirics, Statistics, Experiments, and Other Topics

**Agreeable Plans with Many Capital
Goods** *Review of Economic Studies* **42** (1975),
1–14.

**Abstract:**

In planning capital accumulation, only an interim plan, or overture,
needs to be chosen initially. “Agreeable” plans exploit
this fact; they lead to accumulation paths which are nearly optimal,
provided that the time-horizon is long and is known far enough in
advance. An earlier treatment of one-good models is extended to
models with many capital goods. It is shown that, in many cases, an
“insensitive path” — the limit of finite-horizon
optimal paths — is agreeable. Also, with a convex technology
and a strictly concave welfare function, if an agreeable plan exists,
it must be insensitive and also unique.

**JSTOR link for paper**

**
Maximin Paths of Heterogeneous Capital Accumulation
and the Instability of Paradoxical Steady States**
(with Edwin Burmeister) *Econometrica* **45**
(1977), 853–870.

**Abstract:**

If there exist heterogeneous capital goods, a steady state may be
“paradoxical” in the sense that increasing the rate of
interest above the Golden Rule level may lead to an increase in
consumption or utility, rather than to the decrease which always
occurs in one-sector models. It is shown that, in many cases, a path
of capital accumulation which maximizes the minimum consumption or
utility level is unlikely to converge to a paradoxical steady state of
this kind.

**JSTOR link for paper**

**Uniformly Optimal Infinite Horizon
Plans** (with John F. Kennan) *International Economic
Review* **20** (1979), 283–296.

**Abstract:**

A plan is defined to be uniformly optimal if, for all positive epsilon
and all long enough time horizons, it is uniformly not
epsilon-inferior to all alternative plans. It is shown that uniformly
optimal plans are “agreeable” in a strong sense. In some
cases, too, finite horizon optimal plans may converge to a uniformly
optimal plan as the horizon tends to infinity. It is also shown that,
in most cases where it is known that an optimal plan exists, any
optimal plan is uniformly optimal.

**JSTOR link for paper**

**On Hartwick’s Rule for Constant Utility
and Regular Maximin Paths of Capital Accumulation and Resource Depletion**
(with Avinash K. Dixit and Michael Hoel) *Review
of Economic Studies* **47** (1980), 551–6.

**Abstract:**

Hartwick’s rule of investing resource rents in an economy with
producible capital and exhaustible resources becomes, in a general
model of heterogeneous stocks, a rule whereby the total value of net
investment (resource depletion counting negative) is equal to zero. It
is shown that holding the discounted present value of net investment
constant is necessary and sufficient for a competitive path to give
constant utility. With free disposal, it is shown that, provided the
Hartwick rule yields a path that does not exhibit “stock
reversal,” it must be a maximin path.

**JSTOR link for paper**

**On Endogenizing Long-Run Growth**
(with Andrés Rodríguez-Clare) *Scandinavian Journal of
Economics* **95** (1993), 391–425; also in
T.M. Andersen and K.O. Moene (eds.) *Endogenous Growth*
(Oxford: Blackwell, 1993), pp. 1–35.

**Abstract:**

This assessment of recent theoretical work on endogenous growth
identifies three different engines of long-run growth: (i) the
asymptotic average product of capital is positive; (ii) labor
productivity increases as an external effect of capital accumulation;
(iii) there are feedback effects on the cost of accumulating knowledge
or innovating. A general model encompassing all three is considered,
and then used to review different proposed determinants of long-run
growth rates. The contribution of endogenous growth theory has been to
create a framework in which to explain why economic institutions and
policies can have long-run effects on growth rates.

**PDF version of preprint**

**Changing Tastes and Coherent Dynamic
Choice** *Review of Economic Studies* **43** (1976),
159–173; reprinted in K.J. Lancaster (ed.) *Consumer
Theory* (Cheltenham, UK: Edward Elgar, 1999) ch. 23,
pp. 367–381.

**Abstract**:

Changes of taste can be exogenous or endogenous. Both kinds can be
handled by the general notion of a dynamic choice function defined on
a decision tree. A general dynamic choice function is inconsistent in
the sense that actual choices are likely to depart from planned
choices. Then the agent may be naive or sophisticated. But then he
is likely to be “incoherent” — in particular, his
choices will not correspond to a preference relation. Under special
assumptions, naive and sophisticated choice are coherent if and only
if they coincide, which happens when tastes are “essentially
consistent”; otherwise, both are incoherent.

**JSTOR link for paper**

**Total Discounted Demands and
Long-Period Preferences** *Economic Record* **52** (1976),
26–35.

**Abstract**:

Suppose a consumer’s tastes are not changing secularly, but
merely fluctuating over short periods. Suppose the consumer predicts
his fluctuating tastes. Suppose prices remain constant. Then the
consumer’s present discounted demand vector maximizes a fixed
long period utility function. But when some taste fluctuations are
unforeseen, then in general, a long period average demand vector
maximizes a long period utility function only if the short run Engel
curves are linear and have constant slopes that are independent of the
taste fluctuations.

**Endogenous Tastes and Stable
Long-Run Choice** *Journal of Economic Theory* **13**
(1976), 329–340.

**Abstract**:

Suppose that short-run preferences depend upon consumption one period
earlier. Then there is an acyclic long-run strict preference relation
iff, for every finite set, every conservative choice sequence
converges. If long-run preferences are acyclic, then a unique
long-run choice from a compact set is globally stable. If the
long-run choice set includes multiple choices, there is a weaker
stability property. Under special assumptions there results are
extended to cases when the short-run consumption set is endogenous,
and when more previous periods affect the present.

**ScienceDirect link for paper**

**Dynamic Restrictions on Metastatic
Choice** *Economica* **44** (1977), 337–350.

**Abstract**:

Economists customarily reduce dynamic decision problems to the choice
of a single policy, which lasts for all time. This
“metastatic” approach ignores the possibilities for changing
the original choice. Can metastatic choices always be expanded into
consistent dynamic choices when these possibilities are allowed for,
and regardless of what the structure of the dynamic decision problem
is? For an individual, such an expansion is possible if and only if
his choice function corresponds to an ordering. For social choices
depending on individuals’ choices, the expansion is always
possible if and only if Arrow’s condition of independence of
irrelevant alternatives is satisfied.

**JSTOR link for paper**

**Consequentialist Foundations for
Expected Utility** *Theory and Decision* **25** (1988),
25–78.

**Abstract**:

Behaviour norms are considered for decision trees which allow both
objective probabilities and uncertain states of the world with unknown
probabilities. Terminal nodes have consequences in a given domain.
Behaviour is required to be consistent in subtrees. Consequentialist
behaviour, by definition, reveals a consequence choice function
independent of the structure of the decision tree. It implies that
behaviour reveals a revealed preference ordering satisfying both the
independence axiom and a novel form of sure-thing principle.
Continuous consequentialist behaviour must be expected utility
maximizing. Other familiar assumptions then imply additive utilities,
subjective probabilities, and Bayes’ rule.

**PDF version of preprint**

**Consequentialism, Structural
Rationality and Game Theory** in K.J. Arrow,
E. Colombatto, M. Perlman, and C. Schmidt (eds.) *The
Rational Foundations of Economic Behaviour* (IEA Conference Volume
No. 114) (London: Macmillan, 1996) ch. 2,
pp. 25–42.

**Abstract**:

Previous work on consequentialism (especially in *Theory and
Decision* 1988, pp. 25–78) has provided some
justification for regarding an agent’s behaviour as
“structurally rational” if and only if there are subjective
probabilities, and expected utility is maximized. The key axiom is
that rational behaviour should be explicable as the choice of good
consequences. This and other axioms will be re-assessed critically,
together with their logical implications. Their applicability to
behaviour in *n*-person games will also be discussed. The paper
concludes with some discussion of modelling bounded rationality.

**PDF version of preprint**

**Subjectively Expected State-Independent
Utility on State-Dependent Consequence Domains** in
M.J. Machina and B. Munier (eds.) *Beliefs, Interactions,
and Preferences in Decision Making* (Dordrecht: Kluwer Academic,
1999), pp. 7–21.

**Abstract**:

The standard decision theories of Savage and of Anscombe and Aumann
both postulate that the domain of consequences is state independent.
But this hypothesis makes no sense when, for instance, there is a risk
of death or serious injury. The paper considers one possible way of
deriving subjective probabilities and utilities in this case also.
Moreover, the utilities will be state independent in the sense of
giving equal value to any consequence that happens to occur in more
than one state dependent consequence domain. The key is to consider
decision trees having “hypothetical” probabilities attached
to states of nature, and even to allow hypothetical choices of these
probabilities.

**PDF file of preprint**

**Schumpeterian Innovation in Modelling
Decisions, Games, and Economic Behaviour** *History of Economic
Ideas* XV (2007), 179–195.

**Abstract**:

Von Neumann's standard paradigm of a game in extensive form and
Kolmogorov's standard model of a stochastic process both rely on
constructing a fixed state space large enough to include all possible
future eventualities. This allows a typical single-person decision
problem to be represented as a decision tree. Yet not all
eventualities can be foreseen. Also, any practical decision model must
limit the state space rather severely. In this way the standard
paradigm excludes not only Schumpeter's ideas regarding
entrepreneurship, innovation and development, but also Shackle's
“unexpected events”. This paper proposes an alternative
approach using “decision jungles” with an evolving state
space.

**PDF file of reprint**

**
Rationality and Dynamic Consistency under Risk and Uncertainty** (with Horst Zank)
in Mark J. Machina and W. Kip Viscusi (eds.)
*Handbook of the Economics of Risk and Uncertainty, Vol 1*
(Oxford: North Holland, 2014) ch. 2, pp. 41–97.

**Abstract**:

For choice with deterministic consequences, the standard rationality hypothesis
is ordinality — i.e., maximization of a weak preference ordering.
For choice under risk (resp. uncertainty), preferences are assumed to be represented
by the objectively (resp. subjectively) expected value
of a von Neumann–Morgenstern utility function.
For choice under risk, this implies a key independence axiom;
under uncertainty, it implies some version of Savage's sure thing principle.
This chapter investigates the extent
to which ordinality, independence, and the sure thing principle
can be derived from more fundamental axioms concerning behaviour in decision trees.
Following Cubitt (1996), these principles include
dynamic consistency, separability, and reduction of sequential choice,
which can be derived in turn from one consequentialist hypothesis
applied to continuation subtrees as well as entire decision trees.
Examples of behavior violating these principles are also reviewed,
as are possible explanations of why such violations are often observed in experiments.

**PDF file of preprint**

**How Restrictive Are Information
Partitions?** (January 2005 revision).

**Abstract:**

Recently, several game theorists have questioned whether information
partitions are appropriate. Bacharach (2005) has considered in
particular more general information patterns which may not even
correspond to a knowledge operator. Such patterns arise when agents
lack perfect discrimination, as in Luce’s (1956) example of
intransitive indifference. Yet after extending the state space to
include what the agent knows, a modified information partition can
still be constructed in a straightforward manner. The required
modification introduces an extra set of impossible states into the
partition. This allows a natural represention of the agent’s
knowledge that some extended states are impossible.

**PDF file of preprint**

**The Core and Equilibrium through
the Looking-Glass** *Australian Economic Papers* **16**
(1977), 211–218; **Voluntary Contracts and Jam in the Far
Future** *Australian Economic Papers* **17** (1978),
363–364.

**Abstract:**

In a game in extensive form, a natural subgame arises at each node of
the game tree, with the players’ strategies restricted to ensure
that node is attained. A solution to the game may not be consistent
with the solutions to these subgames. The core of the simplest
possible two-period exchange economy is not consistent with the core
of the second-period economy. Considering just equilibria of the
normal form of the game, as the core does, neglects this aspect of a
dynamic game, which arises whenever players cannot (unlike the White
Queen in *Through the Looking Glass*) “remember” the
future as well as the past.

**Aspects of Rationalizable Behavior**
in K. Binmore, A.P. Kirman, and P. Tani (eds.)
*Frontiers of Game Theory* (Cambridge, Mass.: M.I.T Press, 1993),
ch. 14, pp. 277–305.

**Abstract:**

Equilibria in games involve common “rational” expectations,
which are supposed to be endogenous. Apart from being more plausible,
and requiring less common knowledge, rationalizable strategies may be
better able than equilibria to capture the essential intuition behind
both correlated strategies and forward induction. A version of
Pearce’s “cautious” rationalizability allowing
correlation between other players’ strategies is, moreover,
equivalent to an iterated procedure for removing all strictly, and
some weakly dominated strategies. Finally, as the effect of forward
induction in subgames helps to show, the usual description of a normal
form game may be seriously inadequate, since other considerations may
render implausible some otherwise rationalizable strategies.

**PDF file of preprint**

**Elementary Non-Archimedean
Representations of Probability for Decision Theory and Games** in
P. Humphreys (ed.) *Patrick Suppes: Scientific Philosopher,
Vol. I: Probability and Probabilistic Causality* (Kluwer
Academic Publishers, 1994), ch. 2, pp. 25–59.

**Abstract:**

A fundamental problem in extensive form game theory is that, in order
to tell whether a player has a better strategy than in a presumed
equilibrium, one must know the other players’ equilibrium
reactions to a counterfactual deviation with prior probability zero.
Past work by Selten and Myerson has considered
“trembling-hand” strategies. Here one particular space of
“extended” probabilities is proposed and characterized in
the following four equivalent ways: (i) as complete conditional
probability systems considered by Rényi, Myerson, and others;
(ii) as lexicographic hierarchies of probabilities considered by
Blume, Brandenburger and Dekel; (iii) as extended logarithmic
likelihood ratios considered by McClennan; and (iv) as certain
“canonical rational probability functions” which represent
trembles directly. However, one wants to describe adequately the
joint probability distributions determined by compound lotteries, and
also to distinguish all pairs of probability distributions over the
consequences of decisions that, according to the
“consequentialist” axioms of decision theory, should not be
indifferent. To achieve this, it is shown that an extension to
general rational probability functions is needed.

**PDF file of preprint**

**Consequentialism and Bayesian
Rationality in Normal Form Games** in W. Leinfellner and
E. Köhler (eds.) *Game Theory, Experience, Rationality.
Foundations of Social Sciences, Economics and Ethics. In honor of John
C. Harsanyi*. (*Vienna Circle Institute Yearbook 5*)
(Kluwer Academic Publishers, 1998), pp. 187–196.

**Abstract:**

The consequentialist hypothesis requires the set of possible
consequences of behaviour in any single-person decision tree to depend
only on the feasible set of consequences. This implies that behaviour
reveals a consequence choice function. Previous work has applied this
hypothesis to dynamically consistent behaviour in an (almost)
unrestricted domain of finite decision trees. Provided that behaviour
is continuous as objective probabilities vary, there is state
independence, and also Anscombe and Aumann’s reversal of order
axiom is satisfied, then behaviour must be “Bayesian
rational” in the sense of maximizing subjective expected utility.
Moreover, null events are excluded, so strictly positive subjective
probabilities must be attached to all states of the world.

For
agents playing a multi-person game, it is not immediately clear that
single-person decision theory can be applied because, as Mariotti
(1996) has pointed out, changing the decision problem faced by any one
player typically changes the entire game and so changes other
players’ likely choices in the game. Nevertheless, by applying
the consequentialist hypothesis to particular variations of any given
game, the force of these objections can be considerably blunted. For
any one player *i*, the variations involve a positive probability
that the game changes to another in which player *i* faces an
arbitrary finite decision tree. However, only player *i* knows
whether the game has changed. Also, if the game does change, then only
player *i* has any choice to make, and only player *i* is
affected by whatever decision is taken. In effect, player *i* is
then betting on the other players’ strategy choices in the
original game. Moreover, there is no reason for these choices to
change because, outside the original game, the other players have no
reason to care what happens.

In this way, Bayesian rational
behaviour in normal form games can be given a consequentialist
justification. There is a need, however, to attach strictly positive
probabilities to all other players’ strategies which are not
ruled out as completely impossible and so irrelevant to the game. This
suggests that strictly positive probabilities should be attached to
all other players’ rationalizable strategies, at least —
i.e., to all those that are not removed by iterative deletion of
strictly dominated strategies.

**PDF
file of preprint**

**Consequentialism, Non-Archimedean
Probabilities, and Lexicographic Expected Utility** in
C. Bicchieri, R. Jeffrey and B. Skyrms (eds.) *The
Logic of Strategy* (Oxford University Press, 1999), ch. 2,
pp. 39–66.

**Abstract:**

Earlier work (Hammond, 1988a, b) on dynamically consistent
“consequentialist” behaviour in decision trees was unable to
treat zero probability events satisfactorily. Here the rational
probability functions considered in Hammond (1994), as well as other
non-Archimedean probabilities, are incorporated into decision trees.
As before, the consequentialist axioms imply the existence of a
preference ordering satisfying independence. In the case of rational
probability functions, those axioms, together with continuity and a
new refinement assumption, imply the maximization of a somewhat novel
lexicographic expected utility preference relation. This is equivalent
to maximization of expected utility in the ordering of the relevant
non-Archimedean field.

**PDF file of
preprint**

**Non-Archimedean Subjective Probabilities
in Decision Theory and Games** Stanford University Department of
Economics Working Paper No. 97-038; abbreviated version published
in *Mathematical Social Sciences* **38** (1999),
139–156.

**Abstract:**

To allow conditioning on counterfactual events, zero probabilities can
be replaced by infinitesimal probabilities that range over a
non-Archimedean ordered field. This paper considers a suitable
minimal field that is a complete metric space. Axioms similar to
those in Anscombe and Aumann (1963) and in Blume, Brandenburger and
Dekel (1991) are used to characterize preferences which: (i) reveal
unique non-Archimedean subjective probabilities within the field; and
(ii) can be represented by the non-Archimedean subjective expected
value of any real-valued von Neumann–Morgenstern utility
function in a unique cardinal equivalence class, using the natural
ordering of the field.

**PDF file of
working paper**

**Expected Utility in Non-Cooperative
Game Theory** in S. Barberà, P.J. Hammond, and
C. Seidl (eds.) *Handbook of Utility Theory, Vol. 2:
Extensions* (Boston: Kluwer Academic Publishers, 2004) ch. 18,
pp. 982–1063.

**Abstract:**

This sequel to previous chapters on objective and subjective expected
utility reviews conditions for players in a non-cooperative game to be
Bayesian rational — i.e., to choose a strategy maximizing the
expectation of each von Neumann–Morgenstern utility function in
a unique cardinal equivalence class. In classical Nash equilibrium
theory, players’ mixed strategies involve objective
probabilities. In the more recent rationalizability approach
pioneered by Bernheim and Pearce, players’ possibly inconsistent
beliefs about other players’ choices are described by unique
subjective probabilities. So are their beliefs about other
players’ beliefs, etc. Trembles, together with various notions
of perfection and properness, are seen as motivated by the need to
exclude zero probabilities from players’ decision trees. The
work summarized here, however, leaves several foundational issues
unsatisfactorily resolved.

**PDF file
of preprint**

**Utility Invariance in Non-Cooperative Games**
in U. Schmidt and S. Traub (eds.)
*Advances in Public Economics: Utility, Choice, and Welfare:
A Festschrift for Christian Seidl* (Springer Verlag, 2005),
pp. 31–50.

**Abstract:**

Game theory traditionally specifies players’ numerical payoff functions.
Following the concept of utility invariance in modern social choice theory,
this paper explores what is implied
by specifying equivalence classes of utility function profiles instead.
Within a single game,
utility transformations that depend on other players’ strategies
preserve players’ preferences over their own strategies,
and so most standard non-cooperative solution concepts.
Quantal responses and evolutionary dynamics
are also considered briefly.
Classical concepts of ordinal and cardinal non-comparable utility
emerge when the solution is required to be invariant
for an entire class of “consequentialist game forms” simultaneously.

**PDF file of preprint**

**Beyond Normal Form Invariance:
First Mover Advantage in Two-Stage Games with or without Predictable Cheap Talk,**
in Prasanta Pattanaik, Koichi Tadenuma, Yongsheng Xu, and Naoki Yoshihara (eds.)
*Rational Choice and Social Welfare: Theory and Applications
(Essays in Honor of Kotaro Suzumura)* (Berlin: Springer, 2008), pp. 215–233.

**Abstract:**

Von Neumann (1928) not only introduced a fairly general version of the
extensive form game concept. He also hypothesized that only the normal
form was relevant to rational play. Yet even in Battle of the Sexes,
this hypothesis seems contradicted by players' actual behaviour in
experiments. Here a refined Nash equilibrium is proposed for games
where one player moves first, and the only other player moves second
without knowing the first move. The refinement relies on a tacit
understanding of the only credible and straightforward perfect
Bayesian equilibrium in a corresponding game allowing a predictable
direct form of cheap talk.

**PDF file of preprint**

**Isolation, Assurance and Rules: Can Rational Folly Supplant Foolish Rationality?**
in Kaushik Basu and Ravi Kanbur (eds.) *Arguments for a Better World:
Essays in Honor of Amartya Sen: Volume I, Ethics, Welfare, and Measurement*
(Oxford: Oxford University Press, 2009), ch. 28, pp. 523–534.

**Abstract:**

Consider an “isolation paradox” game with many identical players.
By definition, conforming to a rule which maximizes average utility
is individually a strictly dominated strategy.
Suppose, however, that some players think “quasi-magically”
in accordance with evidential (but not causal) decision theory.
That is, they act as if others’ disposition to conform, or not,
is affected by their own behavior,
even though they do not actually believe there is a causal link.
Standard game theory excludes this. Yet such “rational folly”
can sustain “rule utilitarian” cooperative behavior.
Comparisons are made with Newcomb’s problem,
and with related attempts to resolve prisoner’s dilemma.

**PDF file of preprint**

**Consequentialist Demographic Norms
and Parenting Rights** *Social Choice and Welfare* **5**
(1988), 127–145; also in W. Gaertner and
P.K. Pattanaik (eds.) *Distributive Justice and Inequality*
(Berlin: Springer-Verlag, 1988), pp. 39–57.

**Abstract:**

This paper extends the author’s recent work on dynamically
consistent consequentialist social norms for an unrestricted domain of
decision trees with risk to trees in which the population is a
variable consequence — i.e., endogenous. Given a form of
ethical liberalism and ethical irrelevance of distant ancestors,
classical utilitarianism is implied (provided also that a weak
continuity condition is met). The “repugnant conclusion”
that having many poor people may be desirable can be avoided by
denying that individuals’ interests extend to the circumstances
of their birth. But it is better avoided by recognizing that
potential parents have legitimate interests concerning the sizes of
their families.

**Consequentialist Decision Theory and
Utilitarian Ethics** in F. Farina, F. Hahn, and
S. Vannucci (eds.) *Ethics, Rationality, and Economic
Behaviour* (Oxford: Clarendon Press, 1996), pp. 92–118.

**Abstract:**

Suppose that a social behaviour norm specifies ethical decisions at
all decision nodes of every finite decision tree whose terminal nodes
have consequences in a given domain. Suppose too that behaviour is
both consistent in subtrees and continuous as probabilities vary.
Suppose that the social consequence domain consists of profiles of
individual consequences defined broadly enough so that only
individuals’ random consequences should matter, and not the
structure of any decision tree. Finally, suppose that each individual
has a “welfare behaviour norm” coinciding with the social
norm for decision trees where only that individual’s random
consequences are affected by any decision. Then, after suitable
normalizations, the social norm must maximize the expected value of a
sum of individual welfare functions over the feasible set of random
consequences. Moreover, individuals who never exist can be accorded a
zero welfare level provided that any decision is acceptable on their
behalf. These arguments lead to a social objective whose structural
form is that of classical utilitarianism, even though individual
welfare should probably be interpreted very differently from classical
utility.

**PDF file of preprint**

**Social Welfare Functionals on Restricted
Domains and in Economic Environments** (with Georges Bordes and
Michel Le Breton) “Social Welfare Functionals on Restricted
Domains and in Economic Environments,” *Journal of Public
Economic Theory* **7** (2005), 1–25.

Arrow’s “impossibility” and similar classical theorems are usually proved for an unrestricted domain of preference profiles. Recent work extends Arrow’s theorem to various restricted but “saturating” domains of privately oriented, continuous, (strictly) convex, and (strictly) monotone “economic preferences” for private and/or public goods. For strongly saturating domains of more general utility profiles, this paper provides similar extensions of Wilson’s theorem and of the strong and weak “welfarism” results due to d’Aspremont and Gevers and to Roberts. Hence, for social welfare functionals with or without interpersonal comparisons of utility, most previous classification results in social choice theory apply equally to strongly saturating economic domains.

**Roberts’ Weak Welfarism
Theorem: A Minor Correction** Stanford University Department of
Economics Working Paper No. 99-021.

**Abstract:**

Roberts’ “weak neutrality” or “weak
welfarism” theorem concerns Sen social welfare functionals which
are defined on an unrestricted domain of utility function profiles and
satisfy independence of irrelevant alternatives, the Pareto condition,
and a form of weak continuity. Roberts claimed that the induced
welfare ordering on social states has a one-way representation by a
continuous, monotonic real-valued function defined on the Euclidean
space of interpersonal utility vectors. A counter-example shows that
weak continuity is insufficient; a minor strengthening to pairwise
continuity is proposed instead and its sufficiency demonstrated.

**PDF file**

**Equity, Arrow’s Conditions, and
Rawls’ Difference Principle** *Econometrica* **44**
(1976), 793–804; reprinted in K.J. Arrow and G. Debreu
(eds.), *Landmark Papers in General Equilibrium Theory, Social
Choice and Welfare* (Edward Elgar, 2002), ch. 35,
pp. 679–690; and (without appendix) in F.H. Hahn and
M. Hollis (eds.), *Philosophy and Economic Theory* (Oxford
University Press, 1979), ch. X, pp. 155–163.

**Abstract:**

An Arrow social welfare function was designed not to incorporate any
interpersonal comparisons. But some notions of equity rest on
interpersonal comparisons. It is shown that a generalized social
welfare function, incorporating interpersonal comparisons, can satisfy
modifications of the Arrow conditions, and also a strong version of an
equity axiom due to Sen. One such generalized social welfare function
is the lexicographic form of Rawls’ difference principle or
maximin rule. This kind of generalized social welfare function is the
only kind satisfying the modified Arrow conditions, the equity axiom,
and a condition which underlies Suppes’ grading principle.

**JSTOR link for paper**

**Why Ethical Measures of Inequality
Need Interpersonal Comparisons** *Theory and Decision* **7**
(1976), 263–274.

**Abstract:**

An ethical measure of income inequality corresponds to a social
ordering of income distributions. Without interpersonal comparisons,
the only possible social orderings are dictatorial, so there can be no
ethical inequality measure. Interpersonal comparisons allow a very
much richer set of possible social orderings, and the construction of
ethical measures of inequality.

**Equity in Two-Person Situations: Some
Consequences** *Econometrica* **47** (1979),
1127–1135.

**Abstract:**

Suppose that social choice is based on interpersonal comparisons of
welfare levels. Suppose too that, whenever all but two persons are
indifferent between two options, a choice is made between these
options which is equitable, in some sense. Then provided that
individual welfare functions are unrestricted, and social choice is
independent of irrelevant alternatives, it follows that social choice
is always equitable, in the same sense. This applies when equity means
satisfying Suppes’ indifference rule, or Suppes’ original
justice criterion, or the lexicographic extension of Rawls’
difference principle.

**JSTOR link for paper**

**Independence of Irrelevant
Interpersonal Comparisons** *Social Choice and Welfare*
**8** (1991), 1–19.

**Abstract:**

Arrow’s independence of irrelevant alternatives (IIA) condition
makes social choice depend only on personal rather than interpersonal
comparisons of relevant social states, and so leads to dictatorship.
Instead, a new “independence of irrelevant interpersonal
comparisons” (IIIC) condition allows anonymous Paretian social
welfare functionals such as maximin and Sen’s
“leximin,” even with an unrestricted preference domain. But
when probability mixtures of social states are considered, even IIIC
may not allow escape from Arrow’s impossibility theorem for
individuals’ (ex-ante) expected utilities. Modifying IIIC to
permit dependence on interpersonal comparisons of relevant probability
mixtures allows Vickrey–Harsanyi utilitarianism.

**PDF file of preprint**

**Interpersonal Comparisons of Utility:
Why and how they are and should be made** in J. Elster and
J.E. Roemer (eds.), *Interpersonal Comparisons of
Well-Being* (Cambridge: Cambridge University Press, 1991),
ch. 7, pp. 200–254; reprinted in A.P. Hamlin
(ed.) *Ethics and Economics, Vol. I* (Edward Elgar, 1996),
ch. 22, pp. 410–464.

**Abstract:**

A satisfactory complete normative criterion for individualistic
ethical decision-making under uncertainty such as Harsanyi’s
(*Journal of Political Economy* 1955) requires a single
fundamental utility function for all individuals which is fully
interpersonally comparable. The paper discusses reasons why
interpersonal comparisons of utility (ICUs) have been eschewed in the
past and argues that most existing approaches, both empirical and
ethical, to ICUs are flawed. Either they confound facts with values,
or they are based on unrealistic hypothetical decisions in an
“original position”. Instead ICUs need to be recognized for
what they really are — preferences for different kinds of
people.

**PDF file of preprint**

**Harsanyi’s Utilitarian Theorem: A
Simpler Proof and Some Ethical Connotations** in R. Selten
(ed.) *Rational Interaction: Essays in Honor of John Harsanyi*
(Berlin: Springer-Verlag, 1992), pp. 305–319.

**Abstract:**

Harsanyi’s utilitarian theorem states that the social welfare
function is the weighted sum of individuals’ utility functions
if: (i) society maximizes expected social welfare; (ii) individuals
maximize expected utility; (iii) society is indifferent between two
probability distributions over social states whenever all individuals
are. After giving a simpler proof, an alternative axiomatic
foundation for Vickrey–Harsanyi utilitarianism is provided. By
making using an extended version of Harsanyi’s concept of a
player’s “type” in the theory of games with incomplete
information, the problem of forming social objectives when there is
incomplete information can also be resolved, at least in principle.

**PDF file of preprint**

**Interpersonally Comparable Utility** (with
Marc Fleurbaey) in S. Barberà, P.J. Hammond, and
C. Seidl (eds.) *Handbook of Utility Theory, Vol. 2:
Extensions* (Boston: Kluwer Academic Publishers, 2004) ch. 21,
pp. 1181–1285.

**Abstract:**

This chapter supplements the earlier reviews in Hammond (1991a) and
Suzumura (1996) by concentrating on four issues. The first is that in
welfare economics interpersonal comparisons are only needed to go
beyond Pareto efficiency or Pareto improvements. The second concerns
the need for interpersonal comparisons in social choice theory, to
escape Arrow’s impossibility theorem. The third issue is how to
revise Arrow’s independence of irrelevant alternatives condition
so that interpersonal comparisons can be accommodated. Finally, and
most important, the chapter presents a form of utilitarianism in which
interpersonal comparisons can be interpreted as ethical preferences
for different personal characteristics.

**PDF file of preprint**

**Social Choice of Individual and
Group Rights** in W.A. Barnett, H. Moulin, M. Salles,
and N. Schofield (eds.), *Social Choice, Welfare, and
Ethics* (Cambridge: Cambridge University Press, 1995), ch. 3,
pp. 55–77.

**Abstract:**

Individual rights can generally be respected if and, except in rare
special cases, only if they apply to independent components of a
Cartesian product space of social states, and also each individual is
indifferent to how others exercise their rights. This is true whether
or not the Pareto criterion is satisfied. Group rights can also be
respected if they apply to the independent components for the
different individual members of the group. This holds not only for
social choice rules, but also for outcomes that arise when individuals
and groups use equilibrium strategies in some game form. So only
exceptionally is it possible to respect all rights. The paper
concludes by considering different ways of including rights in the
social states which are the object of individual preference and of
social choice.

**PDF file of
preprint**

**Game Forms versus Social Choice
Rules as Models of Rights** in K.J. Arrow, A.K. Sen, and
K. Suzumura (eds.) *Social Choice Re-examined, Vol. II*
(IEA Conference Volume No. 117) (London: Macmillan, 1997)
ch. 11, pp. 82–95.

**Abstract:**

The paper begins by defining multi-valued game forms which generalize
social choice rules. It also defines the effectiveness relations that
represent the rights induced by such game forms. When one-way instead
of two-way rights are allowed, it also demonstrates yet further
difficulties in finding a social choice rule to respect all rights.
Finally, to deal with the problem that game forms typically contain
arbitrary features of no consequence to a society or to its individual
members, it is also suggested that one should define both social
choice and individual values over sets consisting of
“consequentially equivalent” classes of strategic game
forms.

**PDF file of preprint**

**Rights, Free Exchange, and Widespread
Externalities** in J.-F. Laslier, M. Fleurbaey,
N. Gravel and A. Trannoy (eds.) *Freedom in Economics: New
Perspectives in Normative Analysis* (London and New York:
Routledge, 1998), ch. 11, pp. 139–157.

**Abstract:**

Sen’s libertarian paradox is ascribed to the inevitable conflict
between the Pareto criterion and individuals’ rights to create
negative externalities. Finite coalitions can effect exchanges of
rights through Coaseian bargains in order to resolve inefficiencies
due to local externalities. With a continuum of agents, however,
finite coalitions are powerless to affect widespread externalities,
except those that are regulated by policies such as inefficiently
allocated quotas. Then finite coalitions may gain by exchanging such
quotas, but Pareto improvements may require originally unused quotas
to be confiscated. Thus, the voluntary exchange of rights may
exacerbate widespread externalities.

**PDF file of preprint**

**Equal Rights to Trade and Mediate**
*Social Choice and Welfare* (Special issue on “The axiomatic
theory of resource allocation — In honour of Louis Gevers”
edited by C. d’Aspremont and F. Maniquet) **21**
(2003), 181–193.

**Abstract:**

For economies with a fixed finite set of traders, few results
characterize Walrasian equilibria by their social choice properties.
Pareto efficient allocations typically require lump-sum transfers.
Other characterizations based on the core or strategyproofness apply
only when, as in continuum economies, agents cannot influence prices
strategically. Or the results concern social choice with a variable
number of agents. This paper considers allocations granting agents
equal rights to choose net trade vectors within a convex cone and, in
order to exclude autarky, an additional right to mediate mutually
beneficial transactions. Under standard assumptions, these properties
characterize Walrasian equilibria without transfers.

**PDF file of preprint** ; **Springer link**

**Dual Interpersonal Comparisons of
Utility and the Welfare Economics of Income Distribution**
*Journal of Public Economics* **7** (1977), 51–71.

**Abstract:**

Interpersonal comparisons can be of utility levels and/or of utility
differences. Comparisons of levels can be used to define equity in
distributing income. Comparisons of differences can be used to
construct an additive Bergson social welfare function over income
distributions. When both utility levels and utility differences are
compared, one can require the constructed additive Bergson social
welfare function to indicate a preference for more equitable income
distributions. This restricts the form of both the individual utility
functions and the optimal distribution of income. The form of these
restrictions depends on whether the levels and differences of the
*same* utility functions are being compared.

**ScienceDirect
link**.

**Progress in the Theory of Social Choice
and Distributive Justice** in S. Zandvakili (ed.) *Research in
Economic Inequality, Vol. 7: Inequality and Taxation*
pp. 87–106; revised version of English original whose
Italian translation was published in L. Sacconi (ed.) *La
decisione: Razionalità collettiva e strategie nell’
amministrazione e nelle organizzazioni* (Milano: Franco Angeli,
1986), ch. 3, pp. 89–106.

**Abstract:**

By definition, “consequentialist” behaviour in finite
decision trees is explicable by its consequences. Both
cost–benefit tests and “consequentialist” choices of
economic policy necessarily require distributional judgements. These
should emerge from a social welfare objective incorporating
interpersonal comparisons. To accommodate them, Arrow’s IIA
condition should be weakened to independence of ethically irrelevant
alternatives. When consequences are risky, dynamically consistent
consequentialist behaviour on an unrestricted domain of finite
decision trees entails maximizing expected social welfare. Combined
with an “ethical liberalism” condition, this leads to
“fundamental” utilitarianism, which requires a further
weakening of IIA to independence of ethically irrelevant mixed
alternatives.

**PDF file of
preprint**

**Irreducibility, Resource Relatedness, and
Survival in Equilibrium with Individual Non-Convexities** in
R. Becker, M. Boldrin, R. Jones, and W. Thomson
(eds.) *General Equilibrium, Growth, and Trade II: The Legacy of
Lionel W. McKenzie* (San Diego: Academic Press, 1993),
ch. 4, pp. 73–115.

**Abstract:**

Standard results in general equilibrium theory, such as existence and
the second efficiency and core equivalence theorems, are most easily
proved for compensated equilibria. A new condition establishes that,
even with individual non-convexities, in compensated equilibrium any
agent with a cheaper feasible net trade is also in uncompensated
equilibrium. Some generalizations of McKenzie’s irreducibility
assumption are then presented. They imply that (almost) no agent is at
a cheapest point, so the easier and more general results for
compensated equilibria become true for uncompensated equilibria.
Survival of all consumers in uncompensated equilibrium also depends on
satisfying an additional assumption that is similar to irreducibility.

**PDF file of preprint**

**Walrasian Equilibrium without Survival:
Equilibrium, Efficiency, and Remedial Policy** (with Jeffrey
L. Coles) in K. Basu, P.K. Pattanaik, and
K. Suzumura (eds.) *Choice, Welfare and Development: A
Festschrift in Honour of Amartya K. Sen* (Oxford: Oxford University
Press, 1995), ch. 3, pp. 32–64.

**Abstract:**

Standard general equilibrium theory excludes starvation by assuming
that everybody can survive without trade. Because trade cannot harm
consumers, they can therefore also survive with trade. Here this
assumption is abandoned, and equilibria in which not everybody
survives are investigated. A simple example is discussed, along with
possible policies which might reduce starvation. Thereafter, for
economies with a continuum of agents, the usual results are
established — existence of equilibrium, the two fundamental
efficiency theorems of welfare economics, and core equivalence. Their
validity depends on some special but not very stringent assumptions
needed to deal with natural non-convexities in each consumer’s
feasible set.

**PDF file of preprint**

**Efficiency with Non-Convexities:
Extending the ‘Scandinavian Consensus’ Approaches**
(with Antonio Villar) *Scandinavian Journal of Economics* **100**
(1998), 11–32; also in T.M. Andersen and K.O. Moene
(eds.) *Public Policy and Economic Theory* (Oxford: Blackwell,
1998), pp. 11–32.

**Abstract:**

There are two distinct “Scandinavian consensus” approaches
to public good supply, both based on agents’ willingness to pay.
A Wicksell–Foley public competitive equilibrium arises from a
negative consensus in which no change of public environment, together
with associated taxes and subsidies which finance it, will be
unanimously approved. Alternatively, in a Lindahl or valuation
equilibrium, charges for the public environment induce a positive
consensus. To allow general non-convexities to be regarded as aspects
of the public environment, we extend recent generalizations of these
equilibrium notions and prove counterparts to both the usual
fundamental efficiency theorems of welfare economics.

**PDF file of preprint**

**Valuation Equilibrium Revisited** (with
Antonio Villar) in A. Alkan, C.D. Aliprantis, and
N.C. Yannelis (eds.) *Current Trends in Economics: Theory and
Applications: Proceedings of the Third International Meeting of the
Society for the Advancement of Economic Theory* (Berlin: Springer,
1999), pp. 201–214.

**Abstract:**

This paper extends the notion of valuation equilibrium which applies
to market economies involving the choice of a public environment.
Unlike some other recent work, it is assumed here that consumers and
firms evaluate alternative environments taking market prices as given
(hence this notion is closer to that of competitive equilibria). It
is shown that valuation equilibria with balanced tax schemes yield
efficient allocations and that efficient allocations can be
decentralized as valuation equilibria, with tax schemes that may be
unbalanced.

**Competitive Market Mechanisms as Social
Choice Procedures** in K.J. Arrow, A.K. Sen and K. Suzumura (eds.)
*Handbook of Social Choice and Welfare, Vol. II*
(Amsterdam: North-Holland, 2011), ch. 15, pp. 47–151.

**Abstract:**

A competitive market mechanism is a prominent example of a non-binary
social choice rule, typically defined for a special class of economic
environments in which each social state is an economic allocation of
private goods, and individuals' preferences concern only their own
personal consumption. This chapter begins by discussing which Pareto
efficient allocations can be characterized as competitive equilibria
with lump-sum transfers. It also discusses existence and
characterization of such equilibria without lump-sum transfers. The
second half of the chapter focuses on continuum economies, for which
such characterization results are much more natural given that agents
have negligible influence over equilibrium prices.

** PDF file of preprint**

**Limits to the Potential Gains from
Economic Integration and Other Supply Side Policies**
(with Jaume Sempere) *Economic Journal*
**105** (1995), 1180–1204.

**Abstract:**

Classical welfare economics demonstrates potential Pareto improvements
from “supply side” policy changes that increase the
efficiency of aggregate production. Special cases reviewed here
concern market integration through customs unions and the gains from
international trade. These classical results require incentive
incompatible lump-sum transfers. Generally, other policies must
compensate deserving losers. Following Dixit and Norman, we consider a
freeze of consumer post-tax prices, wages and dividends, with tax
rates and producer prices left to clear markets. Actual Pareto
improvements are then generated by uniform poll subsidies. With
appropriately distributed external tariff revenue, neither
international transfers nor free disposal are required.

**JSTOR link for paper**

**Gains from Trade versus Gains from
Migration: What Makes Them So Different?** (with Jaume Sempere)
*Journal of Public Economic Theory* **8** (2006), 145–170.

**Abstract:**

Would unrestricted “economic” migration enhance the
potential gains from free trade? With free migration, consumers’
feasible sets become non-convex. Under standard assumptions, however,
Walrasian equilibrium exists for a continuum of individuals with
dispersed ability to afford each of a finite set of possible migration
plans. Then familiar conditions ensuring potential Pareto gains from
trade also ensure that free migration generates similar supplementary
gains, relative to an arbitrary status quo. As with the gains from
customs unions, however, wealth may have to be redistributed across
international borders.

**PDF file of preprint**

**Migration with Local Public Goods and
the Gains from Changing Places** (with Jaume Sempere)
*Economic Theory* **41** (2009), 359–377.

**Abstract:**

For an economy without public goods, in Hammond and Sempere (2006) we
show that, under fairly standard assumptions, freeing migration would
enhance the potential Pareto gains from free trade. This paper
presents a generalization allowing local public goods subject to
congestion. Our new result relies on policies which, unlike in the
standard literature on fiscal externalities, fix both local public
goods and congestion levels at their status quo values. Such policies
allow constrained efficient and potentially Pareto improving
population exchanges regulated only through appropriate residence
charges, which can be regarded as Pigouvian congestion taxes.

**PDF file of preprint** ;
**Springer link**

**Continuum Economies with Finite Coalitions:
Core, Equilibrium and Widespread Externalities** (with Mamoru Kaneko
and Myrna Holtz Wooders) *Journal of Economic Theory* **49**
(1989), 113–134.

**Abstract:**

We develop a new model of a continuum economy with coalitions
consisting of only finite numbers of agents. The core, called the
*f*-core, is the set of allocations that are stable against
improvement by finite coalitions and feasible by trade within finite
coalitions. Even with widespread externalities — preferences
depend on own consumptions and also on the entire allocation up to the
null set — we obtain the result that the *f*-core coincides
with the Walrasian allocations. Without widespread externalities, the
*f*-core, the Aumann core, and the Walrasian allocations all
coincide; however, with widespread externalities there is no obvious
natural definition of the Aumann core.

**ScienceDirect
link**

**Four Characterizations of Constrained
Pareto Efficiency in Continuum Economies with Widespread
Externalities** *Japanese Economic Review* **46** (1995),
103–124.

**Abstract:**

In continuum economies, widespread externalities are those over which
each individual has negligible control. Nash–Walrasian
equilibria with lump-sum transfers are defined, and their existence
proved. They are then characterized by the property of
“*f*-constrained Pareto efficiency” for finite
coalitions. More general “private good” Nash–Walrasian
equilibria are characterized as private good constrained Pareto
efficient. Introducing complete Pigou taxes or subsidies leads to
equilibria that are characterized by constrained efficiency and
*f*-constrained efficiency for given levels of the widespread
externalities. But full efficiency requires resolving the public good
problem of determining those aggregate externalities or, equivalently,
of setting appropriate Pigou prices.

**PDF
file of preprint**

**History as a Widespread Externality in
Some Arrow–Debreu Market Games** in G. Chichilnisky
(ed.), *Markets, Information and Uncertainty: Essays in Economic
Theory in Honor of Kenneth J. Arrow* (Cambridge: Cambridge
University Press, 1999) ch. 16, pp. 328–361.

**Abstract:**

Two Arrow–Debreu market games are formulated whose
straightforward Nash equilibria are Walrasian. Both have an auctioneer
setting prices to maximize net sales value. In the second an
additional redistributive agency maximizes welfare through optimal
lump-sum transfers. In intertemporal economies, however, subgame
imperfections can arise because agents understand how current
decisions such as those determining investment influence either future
prices (with finitely many agents), or future redistribution (even in
continuum economies). The latter observation undermines the second
efficiency theorem of welfare economics. Indeed, when the state of the
economy affects future policy, it functions like a “widespread
externality.”

**PDF file of
preprint**

**On f-Core Equivalence in a
Continuum Economy with General Widespread Externalities**

**Abstract:**

This paper partially extends the *f*-core equivalence theorem of
Hammond, Kaneko and Wooders (1989) for continuum economies with
widespread externalities — i.e., those over which each
individual has negligible control. Externalities need not result
directly from trading activities. Neither free disposal of divisible
goods nor monotone preferences are assumed. Instead, a slightly
strengthened form of local non-satiation suffices. However, in general
it is proved only that any *f*-core allocation is a compensated
Nash–Walrasian equilibrium. Finally, the proof uses an
elementary argument which does not rely on Lyapunov’s theorem or
convexity of the integral of a correspondence w.r.t. a non-atomic
measure.

**PDF file of preprint**

**History: Sunk Cost, or Widespread Externality?**
*Rivista Internazionale di Scienze Sociali* (2007), n. 2, 161–185.

**Abstract:**

In an intertemporal Arrow–Debreu economy with a continuum of
agents, suppose that the auctioneer sets prices while the government
institutes optimal lump-sum transfers period by period. An earlier
paper showed how subgame imperfections arise because agents understand
how their current decisions such as those determining investment will
inuence future lump-sum transfers. This observation undermines the
second effciency theorem of welfare economics and makes "history" a
widespread externality. A two-period model is used to investigate the
constrained efficiency properties of different kinds of equilibrium.
Possibilities for remedial policy are also discussed.

**PDF file of preprint**

**The Power of Small Coalitions in Large Economies**
Stanford University, Institute of Mathematical Studies in the Social Sciences,
Economics Technical Report No. 501;
in M.O.L. Bacharach, M.A.H. Dempster and J.L. Enos (eds.)
*Mathematical Models in Economics (1990)*, chapter 3;
volume available online (2010) at this
**link** .

**Abstract:**

As long as coalitions eventually become large, the Debreu–Scarf
limit theorem for the core holds even if coalitions are restricted in
size so that their proportion of agents shrinks to zero as the economy
becomes infinitely large. Corresponding results hold for non-replica
economies. In a limiting continuum economy, the core equivalence
theorem holds even if there must be a “measure-consistent”
partition of a coalition into self-sufficient subcoalitions each with
a finite number of agents. These results help relate standard results
to those presented in collaboration with Kaneko and Wooders concerning
finite coalitions in continuum economies.

**PDF file of preprint** ;
**PDF file of online article**

**Overlapping Expectations and
Hart’s Conditions for Equilibrium in a Securities Model**
*Journal of Economic Theory* **31** (1983), 170–175;
reprinted in J.-M. Grandmont (ed.), *Temporary Equilibrium:
Selected Readings* (New York: Academic Press, 1988),
pp. 156–161.

**Abstract:**

Hart (*J. Econ. Theory* **9** (1974), 293–311) gave
conditions for equilibrium to exist in a securities model where each
agent undertakes asset transactions to maximize expected utility of
wealth. These conditions rule out agents wanting to undertake
unbounded balanced transactions to reach a Pareto superior allocation
given their expectations. With mild extra assumptions to make agents
unwilling to risk incurring unbounded losses on their portfolios,
Hart’s conditions become equivalent to an assumption of
“overlapping expectations,” which is comparable to a much
weaker form of Green’s “common expectations”
(*Econometrica* **41** (1973), 1103–1124).

**ScienceDirect
link**

**The Implementation of Social
Choice Rules: Some General Results on Incentive Compatibility**
(with Partha S. Dasgupta and Eric S. Maskin) *Review of
Economic Studies* (Symposium on Incentive Compatibility), **46**
(1979), 185–216.

**Abstract:**

A social choice rule *f* is a correspondence which associates
with each possible configuration φ of individuals’
characteristics and each feasible set of alternatives *A* a
choice set *f*(φ, *A*) ⊂ *A*, interpreted as
the welfare optima of *A*. *f* is said to be implemented by
a game form *g* if the equilibrium outcome set of *g* (with
respect to the selected solution concept) is nonempty and contained in
*f*(φ, *A*) ⊂ *A* for all φ and *A*.
The general question of the implementability of social choice rules
for four well-known solution concepts: dominant strategy equilibrium,
Bayesian equilibrium, maximin equilibrium, and Nash equilibrium is
studied in detail in this paper.

**JSTOR link for paper**

**Straightforward Individual
Incentive Compatibility in Large Economies** *Review of Economic
Studies* (Symposium on Incentive Compatibility), **46** (1979),
263–282.

**Abstract:**

It is intuitively obvious and generally known that the competitive
resource allocation mechanism is, in a private economy with a
nonatomic measure space of agents, individually incentive compatible.
This paper characterizes the entire class of individually incentive
compatible mechanisms in such economies as those which can be
decentralized by allowing each agent to choose his own allocation from
a constraint set that is independent of his own characteristics.
Conditions are given for the competitive mechanism, without lump-sum
transfers, to be the only Pareto satisfactory incentive compatible
mechanism. A particular kind of “fair” Lindahl equilibrium
has parallel properties in a corresponding economy with public goods.

**JSTOR link for paper**

**Fully Progressive Taxation** (with
Partha S. Dasgupta) *Journal of Public Economics* **13**
(1980), 141–154.

**Abstract:**

In the Mirrlees model of optimal income taxation, each worker’s
true ability can be inferred from his income and the hours he works.
Yet, a fully optimal ability tax is incentive incompatible. We show
that, if both consumption and leisure are normal goods in each
worker’s common utility function, the optimal incentive
compatible allocation is the maximin optimum, with each worker
enjoying the same utility level. This allocation can be implemented
by a tax on ability as revealed by the most skilled kind of labor the
worker offers, or by a tax on his average productivity.

**ScienceDirect link**

**Markets as Constraints:
Multilateral Incentive Compatibility in Continuum Economies**
*Review of Economic Studies* **54** (1987), 399–412;
extended abstract in P. Kleinschmidt and F.J. Radermacher
(eds.), *Proceedings of the SOR Conference, Passau, 1987*
pp. 57–8.

**Abstract:**

A symmetric allocation in a continuum is “multilaterally
incentive compatible” if no finite coalition of privately
informed agents can manipulate it by combining deception with hidden
trades of exchangeable goods. Sufficient conditions for multilateral
incentive compatibility are that all agents face the same linear
prices for exchangeable goods, and that indistinguishable agents face
identical budget sets. The same conditions are necessary under
assumptions which extend those under which the second efficiency
theorem of welfare economics holds in a continuum economy. Markets for
exchangeable goods emerge as binding constraints on the set of Pareto
efficient allocations with private information.

**JSTOR link for paper**

**Incentives and Allocation
Mechanisms** in R. van der Ploeg (ed.), *Advanced Lectures in
Quantitative Economics* (New York: Academic Press, 1990),
ch. 6, pp. 213–248.

**Abstract:**

When individuals are privately informed of their own abilities and
tastes, many first-best Pareto efficient allocations become
infeasible. True feasibility requires an allocation to emerge from a
game form with incomplete information. In English auctions when
bidders know their willingness to pay, they have dominant strategies
and the equilibrium outcome depends only on their willingness to pay.
But in Dutch auctions bidders’ beliefs about each other are also
important. A generalized version of the “revelation
principle” is demonstrated. Random dominant strategy mechanisms
for simple finite economies are characterized by means of simple
linear inequalities.

**On the Impossibility of Perfect
Capital Markets** in P. Dasgupta, D. Gale, O. Hart,
and E. Maskin (eds.), *Economic Analysis of Markets and Games:
Essays in Honor of Frank Hahn* (Cambridge, Mass.: M.I.T. Press,
1992), pp. 527–560.

**Abstract:**

Perfect capital markets require linear budget constraints, without
credit rationing creating any tight borrowing constraints before the
end of agents’ economic lifetimes. Yet lifetime linear budget
constraints are totally unenforceable. This paper considers what
allocations can be enforced through monitoring in a simple two period
economy when agents have private information regarding their
endowments. Then default may not become apparent soon enough for any
economic penalty to be an effective deterrent. Instead, borrowing
constraints must be imposed to control fraud (moral hazard). Adverse
selection often implies that some borrowing constraints must bind,
creating inevitable capital market imperfections.

**PDF file of preprint**

**A Revelation Principle for (Boundedly)
Bayesian Rationalizable Strategies** in R.P. Gilles and
P.H.M. Ruys (eds.), *Imperfections and Behavior in Economic
Organizations* (Boston: Kluwer Academic Publishers, 1994)
ch. 3, pp. 39–70.

**Abstract:**

The revelation principle is reconsidered in the light of recent work
questioning its general applicability, as well as other work on the
Bayesian foundations of game theory. Implementation in rationalizable
strategies is considered. A generalized version of the revelation
principle is proposed recognizing that, unless agents all have
dominant strategies, the outcome of any allocation mechanism depends
not only upon agents’ “intrinsic” types, but also upon
their beliefs about other agents and their strategic behaviour. This
generalization applies even if agents are “boundedly
rational” in the sense of being Bayesian rational only with
respect to bounded models of the game form.

**PDF file of preprint**

**Asymptotically Walrasian
Strategy-Proof Exchange** (with José Córdoba)
*Mathematical Social Sciences* **36** (1998), 185–212.

**Abstract:**

In smooth exchange economies with a continuum of agents, any Walrasian
mechanism is Pareto efficient, individually rational, anonymous, and
strategy-proof. Barberà and Jackson’s recent results imply
that no such efficient mechanism is the limit of resource-balanced,
individually rational, anonymous and non-bossy strategy-proof
allocation mechanisms for an expanding sequence of finite economies.
For a broad class of smooth random exchange economies, relaxing
anonymity and non-bossiness admits mechanisms which, as the economy
becomes infinitely large, are asymptotically Walrasian for all except
one “balancing” agent, while being manipulable with
generically vanishing probability. Also considered are some
extensions to non-Walrasian mechanisms.

**PDF file of preprint**

**Multilaterally Strategy-Proof Mechanisms
in Random Aumann–Hildenbrand Macroeconomies** in
M. Wooders (ed.) *Topics in Game Theory and Mathematical
Economics: Essays in Honor of Robert J. Aumann* (Providence,
RI: American Mathematical Society), pp. 171–187.

By definition, multilaterally strategy-proof mechanisms are immune to manipulation not only by individuals misrepresenting their preferences, but also by finite coalitions exchanging tradeable goods on the side. Continuum economies are defined in which both agents’ identifiers and their privately known characteristics are joint i.i.d. random variables. For such economies, conditions are given for multilateral strategy-proofness to imply decentralization by a budget constraint with linear prices for tradeable goods and lump-sum transfers independent of individual characteristics. Also, adapting Aumann’s [1964a] key proof avoids using Lyapunov’s theorem or its corollary, Richter’s theorem on integrating a correspondence w.r.t. a non-atomic measure.

**Perfected Option Markets in Economies
with Adverse Selection** European University Institute, Working
Paper 89/426; presented at the Econometric Society European Meeting,
Munich, 1989.

**Abstract:**

In economies with adverse selection, Arrow–Debreu contingent
commodity contracts must satisfy incentive constraints. Following
Prescott and Townsend (in *Econometrica* 1984), an
Arrow–Debreu economy is considered with a continuum of agents
whose feasible sets are artificially restricted by imposing these
incentive constraints. Equilibria in such an economy must be
incentive-constrained Pareto efficient. It is shown that deterministic
equilibria of this kind are achievable through “perfected”
option markets with non-linear pricing in a way which makes the
incentive constraints self-enforcing. Rothschild, Stiglitz and others
have shown, however, that these equilibria must be vulnerable to free
entry by profit seeking firms.

PDF file

**Approximate Measures of Social
Welfare and the Size of Tax Reform** in D. Bös,
M. Rose, and C. Seidl (eds.), *Beiträge zur neueren
Steuertheorie* (Berlin: Springer-Verlag, 1984),
pp. 95–115.

**Abstract:**

This paper deals with second order approximations to changes of
welfare measured by social welfare functions. In the framework of
piecemeal policy the impacts of tax reforms to social welfare are
considered. Three different kinds of social welfare functions are
employed: an arbitrary Bergsonian, a social welfare function based on
money metric utility for individuals, and a money metric of social
welfare. Furthermore Pareto improving reforms are discussed. If
possible, the optimal direction and the optimal size of a tax reform
are determined.

**Project Evaluation by Potential Tax
Reform** *Journal of Public Economics* **30** (1986),
1–36.

**Abstract:**

Shadow prices are derived for small open economies with several
production sectors experiencing constant returns to scale. Small
projects affect the balance of trade, domestic prices (of non-traded
goods and factors), and sector scales. Only domestic prices affect
welfare, and only if there is not “domestic price
equalization”. Generally, a project’s net benefits depend
upon the potential tax (and tariff) reform made possible (or
necessary) through the balance of trade effect. Border prices are
right for traded goods, but domestic good shadow pricing requires
knowing the direction of at least one reversible available tax reform,
and presuming optimality with respect to available reforms.

**ScienceDirect
link**

**Money Metric Measures of Individual
and Social Welfare Allowing for Environmental Externalities** in
W. Eichhorn (ed.) *Models and Measurement of Welfare and
Inequality* (Berlin: Springer-Verlag, 1994),
pp. 694–724.

Even with environmental externalities, money metric measures of individual welfare can often be constructed by methods similar to those of Vartia (1983), provided that individual’s willingness to pay functions are known. Satisfactory money metric measures of social welfare are harder, however. Following Feldstein (1974) and Rosen (1976), a “uniform” money metric measure is proposed, based on the uniform poll subsidy (or tax) to all individuals which produces the same gain (or loss) in social welfare. Finally, problems with the definition of such measures when faced with “environmental catastrophe” are discussed.

**Reassessing the Diamond–Mirrlees
Efficiency Theorem** in P.J. Hammond and G.D. Myles (eds.)
*Incentives, Organization, and Public Economics: Papers in Honour of
Sir James Mirrlees* (Oxford University Press, 2000), ch. 12,
pp. 193–216.

Diamond and Mirrlees (1971) provide sufficient conditions for a second-best Pareto efficient allocation with linear commodity taxation to require efficient production when a finite set of consumers have continuous single-valued demand functions. This paper considers a continuum economy allowing indivisible goods, other individual non-convexities, and some forms of non-linear pricing for consumers. Provided consumers have appropriately monotone preferences and dispersed characteristics, robust sufficient conditions ensure that a strictly Pareto superior incentive compatible allocation with efficient production results when a suitable expansion of each consumer’s budget constraint accompanies any reform which enhances production efficiency. Appropriate cost–benefit tests can identify small efficiency enhancing projects.

**Ex-ante and Ex-post Welfare Optimality
under Uncertainty** *Economica* **48** (1981),
235–250.

**Abstract:**

Suppose that either (i) individuals’ subjective probabilities
differ from society’s probability assessments, or (ii) social
attitudes to individual risk differ from individuals’ own
attitudes to risk. Then the social welfare function will not respect
individuals’ own preferences for trade in contingent
commodities, and Arrow–Debreu markets will not be able to bring
about a full ex-post welfare optimum. This paper examines the extent
to which markets can bring about such an ex-post welfare optimum.
Contingent lump-sum transfers each period are required. Then it
suffices to have spot markets each period, provided that
consumers’ von Neumann–Morgenstern utility functions are
“separable backwards” in time.

**JSTOR link for paper**

**Theoretical Progress in Public
Economics: A Provocative Assessment** *Oxford Economic Papers*
**42** (1990), 6–33; also in P.J.N. Sinclair and
M.D.E. Slater (eds.) *Taxation, Private Information and
Capital* (Oxford: Clarendon Press, 1991).

**Abstract:**

The following twelve issues are each briefly discussed: the blindness
of the invisible hand to injustice; a misleading efficiency theorem;
truthful revelation of feasibility constraints; delusions of first
best; deadweight losses as sunk costs; markets as failures; the nth
best as enemy of the good; intermonetary comparisons of gains and
losses; few worthwhile changes are small; surplus economics; surplus
econometrics; and unbalanced policies. Unbalanced policy changes
should be evaluated by estimating the probabilities of different joint
frequency distributions of welfare relevant attributes and welfare net
gains for all individuals in the population, together with the budget
deficits or surpluses.

**The Moral Status of Profits and
Other Rewards: A Perspective from Modern Welfare Economics** in
R. Cowan and M.J. Rizzo (eds.) *Profits and Morality*
(Chicago: University of Chicago Press, 1995), ch. 4,
pp. 88–123.

**Abstract:**

Standard neoclassical welfare economics justifies competitive profit
maximization by firms. But when lump-sum transfers are used to achieve
distributive justice, a firm’s owners and managers are entitled
only to “normal” profits paid for services rendered. Yet
with private information about effort or technology, not even
efficient production is always desirable, let alone profit
maximization. Furthermore, some profits should then be distributed
specifically to the firm’s managers as incentive payments. In
intertemporal economies these conclusions are reinforced, and profits
harder even to define. Finally, it is argued that valuing freedom for
its own sake may make profits more acceptable than otherwise.

**PDF file of preprint**

**Spurious Deadweight Gains ** (with
Giovanni Facchini and Hiroyuki Nakata) *Economics Letters*
**72** (2001), 33–37.

**Abstract:**

Marshallian consumer surplus (MCS) is generally an inaccurate measure
of welfare change because it neglects income effects. Suppose these
effects overturn the usual demand response to a price change. Then,
the deadweight loss from a distortionary tax or subsidy has the wrong
sign, that is, there is a spurious deadweight gain.

**PDF file of preprint**

** Monte Carlo Simulation of
Macroeconomic Risk with a Continuum of Agents: The Symmetric Case**
(with Yeneng Sun) *Economic Theory* **21** (2003),
743–766; also in C.D. Aliprantis *et al.* (eds.) *Assets,
Beliefs, and Equilibria in Economic Dynamics: Essays in Honor of
Mordecai Kurz* (Berlin: Springer-Verlag, 2003),
pp. 709–732.

**Abstract:**

Suppose a large economy with individual risk is modeled by a continuum
of pairwise exchangeable random variables (i.i.d., in particular).
Then the relevant stochastic process is jointly measurable only in
degenerate cases. Yet in Monte Carlo simulation, the average of a
large finite draw of the random variables converges almost surely.
Several necessary and sufficient conditions for such “Monte Carlo
convergence” are given. Also, conditioned on the associated Monte
Carlo σ-algebra, which represents macroeconomic risk, individual
agents’ random shocks are independent. Furthermore, a converse
to one version of the classical law of large numbers is proved.

**PDF file of preprint** ; **Springer link**

**Joint Measurability and the One-way
Fubini Property for a Continuum of Independent Random Variables**
(with Yeneng Sun) *Proceedings of the American Mathematical
Society* **134** (2006), 737–747.

**Abstract:**

As is well known, a continuous parameter process with mutually
independent random variables is not jointly measurable in the usual
sense. This paper proposes using a natural “one-way Fubini”
property that guarantees a unique meaningful solution to this joint
measurability problem when the random variables are independent even
in a very weak sense. In particular, if F is the smallest extension of
the usual product sigma-algebra such that the process is measurable,
then there is a unique probability measure ν on F such that the
integral of any ν-integrable function is equal to a double integral
evaluated in one particular order. Moreover, in general this measure
cannot be further extended to satisfy a two-way Fubini property.
However, the extended framework with the one-way Fubini property not
only shares many desirable features previously demonstrated under the
stronger two-way Fubini property, but also leads to a new
characterization of the most basic probabilistic concept —
stochastic independence in terms of regular conditional distributions.

**PDF file**; **AMS link**

** The Essential Equivalence of Pairwise
and Mutual Conditional Independence ** (with Yeneng Sun)
*Probability Theory and Related Fields* **135** (2006),
415–427.

**Abstract:**

For a large collection of random variables, pairwise conditional
independence and mutual conditional independence are shown to be
essentially equivalent. Unlike in the finite setting, a large
collection of random variables remains essentially conditionally
independent under further conditioning. The essential equivalence of
pairwise and multiple versions of exchangeability also follows as a
corollary. Our proof is based on an iterative extension of Bledsoe and
Morse’s completion of a product measure on a pair of measure
spaces.

**PDF file**

** Monte Carlo Simulation of Macroeconomic
Risk with a Continuum of Agents: The General Case** (with Yeneng
Sun) *Economic Theory* DOI 10.1007/s00199-007-0279-7 (published
online, 7 September 2007).

**Abstract:**

In large random economies with heterogeneous agents, a standard
stochastic framework presumes a random macro state, combined with
idiosyncratic micro shocks. This can be formally represented by a
random process consisting of a continuum of random variables that are
conditionally independent given the macro state. However, this process
satisfies a standard joint measurability condition only if there is
essentially no idiosyncratic risk at all. Based on iteratively
complete product measure spaces, we characterize the validity of the
standard stochastic framework via Monte Carlo simulation as well as
event-wise measurable conditional probabilities. These general
characterizations also allow us to strengthen some earlier results
related to exchangeability and independence.

**PDF file of Warwick Economics Research Paper**;
**Preprint version** ;
**Springer link**

** Characterization of Risk: A Sharp Law of Large Numbers **
(with Yeneng Sun). Warwick Economic Research Paper, no. 806 (2007).

**Abstract:**

An extensive literature in economics uses a continuum of random
variables to model individual random shocks imposed on a large
population. Let *H* denote the Hilbert space of square-integrable random
variables. A key concern is to characterize the family of all *H*-valued
functions that satisfy the law of large numbers when a large sample of
agents is drawn at random. We use the iterative extension of an
infinite product measure introduced in Hammond and Sun (2006) to
formulate a ÒsharpÓ law of large numbers. We prove that an *H*-valued
function satisfies this law if and only if it is both
Pettis-integrable and norm integrably bounded.

**PDF file**

** Affine Models of the Joint Dynamics of Exchange Rates and Interest Rates**
(with Bing Anderson and Cyrus A. Ramezani)
*Journal of Financial and Quantitative Analysis* **45** (2010), 1341–1365.

**Abstract:**

This paper extends the affine class of term structure models
to describe the joint dynamics of exchange rates and interest rates.
In particular, the issue of how to reconcile the low volatility of interest rates
with the high volatility of exchange rates is addressed.
The incomplete market approach of introducing exchange rate volatility
that is orthogonal to both interest rates and the pricing kernels
is shown to be infeasible in the affine setting.
Models in which excess exchange rate volatility is orthogonal to interest rates
but not orthogonal to the pricing kernels are proposed,
and validated via Kalman filter estimation
of maximal 5-factor models for 6 country pairs.

**Cambridge Journals link**

**Individual Welfare and Subjective Well-Being:
Comments on ‘Subjective Well-Being, Income, Economic Development and Growth’
by Daniel W. Sacks, Betsey Stevenson, and Justin Wolfers,”
**
(with Federica Liberini and Eugenio Proto);
in Claudia Sepúlveda, Ann Harrison, and Justin Yifu Lin (eds.)
*ABCDE 2011: Development Challenges in a Postcrisis World *
(Washington, DC: World Bank, 2013) pp. 339–353.

**Abstract**:

Sacks, Stevenson and Wolfers (2010) question earlier results like Easterlin's
showing that long-run economic growth often fails
to improve individuals’ average reports of their own subjective well-being (SWB).
We use *World Values Survey* data to establish
that the proportion of individuals reporting happiness level *h*,
and whose income falls below any fixed threshold,
always diminishes as *h* increases.
The implied positive association between income and reported happiness
suggests that it is possible in principle
to construct multi-dimensional summary statistics based on reported SWB
that could be used to evaluate economic policy.

**PDF file of preprint**

**Do Happier Britons Have More Income? First-Order Stochastic Dominance Relations
**
(with Federica Liberini and Eugenio Proto);
CAGE Online Working Paper 165,
Research Centre on Competitive Advantage in the Global Economy, University of Warwick, 2013.

**Abstract**:

For British Household Panel Survey data,
given any self-reported life satisfaction level except the highest,
the conditional income distribution first-order stochastically dominates
the corresponding conditional distribution given any lower level.
The conditional distribution for completely satisfied subjects, however,
is stochastically dominated by several other conditional distributions.
This “top anomaly” excludes any standard ordered discrete choice econometric model
where satisfaction depends on income.
The observed stochastic dominance relations, including the top anomaly,
are consistent with an estimated multinomial logit model
that includes background demographic and educational variables,
along with the difference between individual log income and its conditional expectation.

**PDF file**

**A Three-Stage Experimental Test of Revealed Preference**
(with Stefan Traub); CAGE Online Working Paper 71,
Research Centre on Competitive Advantage in the Global Economy, University of Warwick, 2012.

**Abstract**:

A powerful test of Varian's (1982) generalised axiom of revealed preference (GARP)
with two goods requires the consumer's budget line to pass through
two demand vectors revealed as chosen given other budget sets.
In an experiment using this idea, each of 41 student subjects
faced a series of 16 successive grouped portfolio selection problems.
Each group of selection problems had up to three stages,
where later budget sets depended on that subject's choices
at earlier stages in the same group.
Only 49% of subjects' choices were observed to satisfy GARP exactly,
even by our relatively generous nonparametric test.

**PDF file of preprint**

**Laboratory Games and Quantum Behaviour:
The Normal Form with a Separable State Space**
Warwick Economics Research Paper, no. 969 (2011);
presented at Quantum Physics Meets TARK, University of Groningen.

**Abstract**:
To describe quantum behaviour, Kolmogorov’s definition of probability
is extended to accommodate subjective beliefs
in a particular “laboratory game”
that a Bayesian rational decision maker plays
with Nature, Chance and an Experimenter.
The Experimenter chooses an orthonormal subset
of a complex Hilbert space of quantum states;
Nature chooses a state in this set
along with an observation in a measurable space of experimental outcomes
that influences Chance’s choice of random consequence.
Imposing quantum equivalence allows the trace of the product
of a density and a likelihood operator to represent
the usual Bayesian expectation of a likelihood function
w.r.t. a subjective prior.

**PDF file of preprint**

Based on file translated from T