Limitation of Efficiency: Strategy-Proofness and Single-Peaked Preferences with Many Commodities

In this paper, we study a resource allocation problem of economies with many commodities and single-peaked preferences. It is known that the uniform rule is the unique allocation mechanism satisfying strategy-proofness, Pareto efficiency and anonymity, if the number of good is only one and preferences are single peaked. (Sprumont [7].) However, if the number of goods is greater than one, the situation drastically changes and a tradeoff between efficiency and strategy-proofness arises. The generalized uniform rule in multiple-commodity settings is still strategy-proof, but not Pareto efficient in general. In this paper, we show that in a class of all strategy-proof mechanisms the generalized uniform rule is a "second best" strategy-proof mechanism in that there is no other strategy-proof mechanism which gives a "better" outcome than the generalized uniform rule in terms of Pareto domination.

Strategy-proof Sharing

We consider the problem of sharing a divisible good, where agents prefer more to less. First, we prove that a sharing rule satisfies strategy proofness if and only if it has the quasi-constancy property: no one changes her own share by changing her announcements. Next, by constructing a system of linear equations in a manner that is consistent with quasi-constancy, we provide a way to find every strategy-proof sharing rule. Finally, we identify a necessary and sufficient condition for the existence of non-constant, strategy-proof sharing rules, by examining the relationship between the constancy of strategy-proof sharing rules and the dimension of the solution space of the linear system.Strategy-proofness, Bossiness, Non-constancy, Quasi-constancy.

Almost-dominant Strategy Implementation

Though some economic environments provide allocation rules that are implementable in dominant strategies (strategy-proof), a significant number of environments yield impossibility results. On the other hand, while there are quite general possibility results regarding implementation in Nash or Bayesian equilibrium, these equilibrium concepts make strong assumptions about the knowledge that players possess, or about the way they deal with uncertainty. As a compromise between these two notions, we propose a solution concept built on one premise: Players who do not have much to gain by manipulating an allocation rule will not bother to manipulate it. We search for efficient allocation rules for 2-agent exchange economies that never provide players with large gains from cheating. Though we show that such rules are very inequitable, we also show that some such rules are significantly more flexible than those that satisfy the stronger condition of strategy-proofness.Strategy-proof, almost dominant strategy

Strategy-Proofness and Efficiency Are Incompatible in Production Economies

In a production economy where a single private good is produced via a non-linear concave technology, no direct mechanism satisfies strategy-proofness and efficiency if the preference domain contains the class of linear preferences.

Game theory

game theory

Social Choice and Just Institutions: New Perspectives

It has become accepted that social choice is impossible in absence of interpersonal comparisons of well-being. This view is challenged here. Arrow obtained an impossibility theorem only by making unreasonable demands on social choice functions. With reasonable requirements, one can get very attractive possibilities and derive social preferences on the basis of non-comparable individual preferences. This new approach makes it possible to design optimal second-best institutions inspired by principles of fairness, while traditionally the analysis of optimal second-best institutions was thought to require interpersonal comparisons of well-being. In particular, this new approach turns out to be especially suitable for the application of recent philosophical theories of justice formulated in terms of fairness, such as equality of resources.social welfare, social choice, fairness, egalitarian-equivalence

Natural implementation with partially honest agents in economic environments

In this paper, we introduce the weak and the strong notions of partially honest agents (Dutta and Sen, 2012), and then study implementation by natural price-quantity mechanisms (Saijo et al., 1996, 1999) in pure exchange economies with three or more agents in which pure-consequentialistically rational agents and partially honest agents coexist. Firstly, assuming that there exists at least one partially honest agent in either the weak notion or the strong notion, the class of efficient social choice correspondences which are Nash-implementable by such mechanisms is characterized. Secondly, the (unconstrained) Walrasian correspondence is shown to be implementable by such a mechanism when there is at least one partially honest agent of the strong type, which may provide a behavioral foundation for decentralized implementation of the Walrasian equilibrium. Finally, in this set-up, the effects of honesty on the implementation of more equitable Pareto optimal allocations can be viewed as negligible.