Nash implementing non-monotonic social choice rules by awards

Summary. By a slight generalization of the definition of implementation (called implementation by awards), Maskin monotonicity is no more needed for Nash implementation. In fact, a weaker condition, to which we refer as almost monotonicity is both necessary and sufficient for social choice correspondences to be Nash implementable by awards. Hence our framework paves the way to the Nash implementation of social choice rules which otherwise fail to be Nash implementable. In particular, the Pareto social choice rule, the majority rule and the strong core are almost monotonic (hence Nash implementable by awards) while they are not Maskin monotonic (hence fail to be Nash implementable in the standard framework).Received: 12 April 2004, Revised: 18 March 2005, JEL Classification Numbers: D 79.I thank François Maniquet, Efe Ok and Ipek Ozkal-Sanver for their valuable contributions. The paper is part of a project on Electoral System Design supported by Bilgi University Research Fund.     

Money or friends: Social identity and deception in networks

Strategic communication occurs in virtually all committee decision environments. Theory suggests that small differences in monetary incentives between committee members can leave deception a strategically optimal decision (Crawford and Sobel, 1982; Galeotti et al., 2013). At the same time, in natural environments social incentives can also play an important role in determining the way people share or withhold truthful information. Unfortunately, little is known about how monetary and social incentives interact to determine truth-telling. We investigate this issue by first building a novel model and then testing its equilibrium predictions using laboratory data. In the absence of social identity, the model׳s predictions are supported: there is more truthful communication between those who share monetary incentives than those who do not. We find that the effect of identity is asymmetric: sharing the same identity does not promote truth-telling but holding different identities reduces truthfulness. Overall, as compared to environments lacking social identity, committees with both monetary and social incentives exhibit truthful communication substantially less frequently.     

Individually rational, budget-balanced mechanisms and allocation of surplus

We investigate the issue of implementation via individually rational ex-post budget-balanced Bayesian mechanisms. We show that all decision rules generating a nonnegative expected social surplus are implementable via such mechanisms if and only if the probability distribution of the agents’ type profiles satisfies two conditions: the well-known condition of Crémer and McLean [1988. Full extraction of the surplus in Bayesian and dominant strategy auctions, Econometrica 56, 1247–1257] and the Identifiability condition introduced in this paper. We also show that these conditions are necessary for ex-post efficiency to be attainable with budget balance and individual rationality, and that the expected social surplus in these mechanisms can be distributed in any desirable way. Lastly, we demonstrate that, like Crémer–McLean condition, the Identifiability condition is generic if there are at least three agents.     

An efficiency characterization of plurality social choice on simple preference domains

Summary. We consider a model of social choice dealing with the problem of choosing a subset from a set of objects (e.g. candidate selection, membership, and qualification problems). Agents have trichotomous preferences for which objects are partitioned into three indifference classes, goods, bads, and nulls, or dichotomous preferences for which each object is either a good or a bad. We characterize plurality-like social choice rules on the basis of the three main axioms, known as Pareto efficiency, anonymity, and independence.Received: 29 August 2003, Revised: 3 June 2004, JEL Classification Numbers: D70, D71, D72.Biung-Ghi Ju: I am grateful to William Thomson and Jianbo Zhang for their helpful comments and discussions. I also thank Brandon Dupont, the participants in seminars at Iowa State University, University of Kansas, and the Midwest Theory Meeting at University of Notre Dame. I thank an anonymous referee for detailed comments and suggestions that were very helpful in simplifying the proof of Theorem 1 and in revising the paper.     

Rationalizable implementation

We consider the implementation of social choice functions under complete information in rationalizable strategies. A strict version of the monotonicity condition introduced by Maskin is necessary under the solution concept of rationalizability. Assuming the social choice function is responsive, i.e. in distinct states it selects distinct outcomes, we show that strict Maskin monotonicity is also sufficient under a mild “no worst alternative” condition. In particular, no economic condition is required. We discuss how our results extend when the social choice function is not responsive.     

Subgame perfect implementation: A necessary and almost sufficient condition

We present a necessary and almost sufficient condition for subgame perfect implementation of social choice correspondences. In societies with at least three individuals, any social choice correspondence which satisfies no veto power and our necessary Condition α is subgame perfect implementable. Thus Condition α is analogous to monotonicity which, by Maskin's celebrated characterization, is necessary and, in a similar way, almost sufficient for Nash implementation.     

Not quite the best response: truth-telling,strategy-proof matching,and the manipulation of others

Following the advice of economists, school choice programs around the world have lately been adopting strategy-proof mechanisms. However, experimental evidence presents a high variation of truth-telling rates for strategy-proof mechanisms. We crash test the connection between the strategy-proofness of the mechanism and truth-telling. We employ a within-subjects design by making subjects take two simultaneous decisions: one with no strategic uncertainty and one with some uncertainty and partial information about the strategies of other players. We find that providing information about the out-of-equilibrium strategies played by others has a negative and significant effect on truth-telling rates. That is, most participants in our within-subjects design try and fail to best-respond to changes in the environment. We also find that more sophisticated subjects are more likely to play the dominant strategy (truth-telling) across all the treatments. These results have potentially important implications for the design of markets based on strategy-proof matching mechanisms.     

Binary games with many players

Summary. We examine a problem with n players each facing the same binary choice. One choice is superior to the other. The simple assumption of competition - that an individual’s payoff falls with a rise in the number of players making the same choice, guarantees the existence of a unique symmetric equilibrium (involving mixed strategies). As n increases, there are two opposing effects. First, events in the middle of the distribution - where a player finds itself having made the same choice as many others - become more likely, but the payoffs in these events fall. In opposition, events in the tails of the distribution - where a player finds itself having made the same choice as few others - become less likely, but the payoffs in these events remain high. We provide a sufficient condition (strong competition) under which an increase in the number of players leads to a reduction in the equilibrium probability that the superior choice is made.Received: 24 July 2003, Revised: 24 January 2005, JEL Classification Numbers: C72, D02, D49, L19.Flavio M. Menezes: Correspondence toThis paper has benefitted from comments by an anonymous referee and seminar participants at the ANU, Boston University, Harvard University Law, Economics and Organization Seminar, University of Wisconsin and at the Econometrics Society Australasian Meetings, Auckland New Zealand. We also thank Lucian Bebchuk, Eddie Dekel, Oliver Hart, Luis Kaplov, Paulo Monteiro and John Quiggin for very useful comments. All errors are our own. Menezes acknowledges the financial support from ARC (grant no. 00000055) and the hospitality of EPGE/FGV and RSPAS/ANU.     

Purification of incentive compatible allocations

In implementation theory it is common to consider social choice functions that map to lotteries over outcomes. For example, virtual implementation has been used widely with social choice functions that involve randomization. This paper investigates (in incomplete information environments) the possibility of purification of such social choice functions, where purification means that the “replacement” social choice function maps to outcomes rather than distributions over outcomes, is incentive compatible and generates the same distribution over payoffs and outcomes as the original social choice function. Received: July 31, 2000; revised version: December 2, 2002 RID="*" ID="*" Thanks are due to Ole Nielsen, Terence Tao and Lin Zhou for helpful conversations. Thanks are also due to an anonymous referee for detailed comments.     

Undominated Nash Implementation with Collusion and Renegotiation

This article looks at implementation in economic environments when agents have perfect information about the state of the world, but cannot commit not to renegotiate bad outcomes or to collude against each other. If renegotiation satisfies a weak condition of disagreement point monotonicity, then any Pareto-efficient social choice function can be implemented if there are at least three agents who play undominated Nash equilibria. The mechanism does not use modulo or integer games, has no bad mixed strategy equilibria, and is “bounded.”Journal of Economic LiteratureClassification Number: D71.     

Nash implementation with a private good

Summary. I construct a general model of social planning problems, including mixed production economies and regulatory problems with negative externalities as special cases, and I give simple mechanisms for Nash implementation under three increasingly general sets of assumptions. I first construct a continuous mechanism to implement the (constrained) Lindahl allocations of an economy, and I then extend this to arbitrary social choice rules based on prices. I end with a mechani sm to implement any monotonic social choice rule, assuming only the existence of a private (not necessarily transferable) good. In that general case, each agent simply reports an upper contour set, an outcome, and I need two agents to make binary numerical announcements. I do not require the usual no-veto-power condition. Received: February 19, 1998; revised version: January 30, 2002     

Endogenous Selection of Institutions and Their Exogenous Effects

Institutions shape social outcomes, yet institutions themselves are products of political choices. When institutional choices are determined by the same political and social processes that they shape, institutions are endogenously selected. Here I address the question of whether this endogenous institutional selection necessarily implies endogenous institutional effects. If it does, the use of institutional parameters as independent variables explaining policy outcomes and properties of the resulting political regimes, widespread in the literature on comparative political institutions, is hard to justify. I argue, however, that strategic choice of the rules of the game implies designers' ability to obtain their preferred institutional effects only under conditions of complete information. Under incomplete information, ex-post institutional effects do not need to be endogenous, since at the time of designing the rules the designers were not in position to control the selection of these effects. The reason why the choice of the rules does not imply the choice of their effects lies in the intervening and interactive (rather than additive) role played by the environmental parameters, including players' own characteristics, that are not revealed at the time of the institutional choice. Additionally to the model which illustrates the logic of the argument and the workings of intervening structural effects, I find supporting evidence in the processes of design of election laws in post-communist Europe, where stages of design and implementation followed each other in a very quick succession yet were characterized by substantial changes in manifested institutional preferences of the key political players.     

Would I lie to you? On social preferences and lying aversion

This paper reinterprets the evidence on lying or deception presented in Gneezy (Am. Econ. Rev. 95(1):384–394, 2005). We show that Gneezy’s data are consistent with the simple hypothesis that people are one of two kinds: either a person will never lie, or a person will lie whenever she prefers the outcome obtained by lying over the outcome obtained by telling the truth. This implies that so long as lying induces a preferred outcome over truth-telling, a person’s decision of whether to lie may be completely insensitive to other changes in the induced outcomes, such as exactly how much she monetarily gains relative to how much she hurts an anonymous partner. We run new but broadly similar experiments to those of Gneezy in order to test this hypothesis. While we also confirm that there is an aversion to lying in our subject population, our data cannot reject the simple hypothesis described above either.

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Coalitional Bayesian Nash implementation in differential information economies

Summary. A mechanism coalitionally implements a social choice set if any outcome of the social choice set can be achieved as a coalitional Bayesian Nash equilibrium of a mechanism and vice versa. We say that a social choice set is coalitionally implementable if there is a mechanism which coalitionally implements it. Our main theorem proves that a social choice set is coalitionally implementable if and only if it is interim individually rational, interim efficient, coalitional B ayesian incentive compatible, and satisfies a coalitional Bayesian monotonicity condition as well as a closure condition. As an application of our main result, we show that the private core and the private Shapley value of an economy with differential information are coalitionally implementable. Received: January 12, 1998; revised version: March 30, 2000     

Implementation with partial provability

We extend implementation theory by allowing the social choice function to depend on more than just the preferences of the agents and allowing agents to support their statements with hard evidence. We show that a simple condition on evidence is necessary for the implementation of a social choice function f when the preferences of the agents are state independent and sufficient for implementation for any preferences (including state dependent) with at least three agents if the social planner can perform small monetary transfers beyond those called for by f. If transfers can be large, f can be implemented in a game with perfect information when there are at least two players under a boundedness assumption. For both results, transfers only occur out of equilibrium. The use of evidence enables implementation which is robust in the sense that the planner needs little information about agents? preferences or beliefs and agents need little information about each others? preferences. Our results are robust to evidence forgery at any strictly positive cost.     

Coordination with communication under oath

We focus on the design of an institutional device aimed to foster coordination through communication. We explore whether the social psychology theory of commitment, implemented via a truth-telling oath, can reduce coordination failure. Using a classic coordination game, we ask all players to sign voluntarily a truth-telling oath before playing the game with cheap talk communication. Three results emerge with commitment under oath: (1) coordination increased by nearly 50%; (2) senders’ messages were significantly more truthful and actions more efficient, and (3) receivers’ trust of messages increased.     

Fully sincere voting

In a general social choice framework where the requirement of strategy-proofness may not be sensible, we call a social choice rule fully sincere if it never gives any individual an incentive to vote for a less-preferred alternative over a more-preferred one and provides an incentive to vote for an alternative if and only if it is preferred to the default option that would result from abstaining. If the social choice rule can depend only on the number of votes that each alternative receives, those rules satisfying full sincerity are convex combinations of the rule that chooses each alternative with probability equal to the proportion of the vote it receives and an arbitrary rule that ignores voters' preferences. We note a sense in which the natural probabilistic analog of approval voting is the fully sincere rule that allows voters maximal flexibility in expressing their preferences and gives these preferences maximal weight.     

Ex post implementation

We analyze the problem of fully implementing a social choice set in ex post equilibrium. We identify an ex post monotonicity condition that is necessary and—in economic environments—sufficient for full implementation in ex post equilibrium. We also identify an ex post monotonicity no veto condition that is sufficient. Ex post monotonicity is satisfied in all single crossing environments with strict ex post incentive constraints.We show by means of two classic examples that ex post monotonicity does not imply nor is it implied by Maskin monotonicity. The single unit auction with interdependent valuations is shown to satisfy ex post monotonicity but not Maskin monotonicity. We further describe a Pareto correspondence that fails ex post monotonicity but satisfies Maskin monotonicity.     

Lexicographic choice under variable capacity constraints

In several matching markets, to achieve diversity, agents' priorities are allowed to vary across an institution's available seats, and the institution is let to choose agents in a lexicographic fashion based on a predetermined ordering of the seats, called a (capacity-constrained) lexicographic choice rule. We provide a characterization of lexicographic choice rules and a characterization of deferred acceptance mechanisms that operate based on a lexicographic choice structure under variable capacity constraints. We discuss some implications for the Boston school choice system and show that our analysis can be helpful in applications to select among plausible choice rules.     

Counting combinatorial choice rules

I count the number of combinatorial choice rules that satisfy certain properties: Kelso–Crawford substitutability, and independence of irrelevant alternatives. The results are important for two-sided matching theory, where agents are modeled by combinatorial choice rules with these properties. The rules are a small, and asymptotically vanishing, fraction of all choice rules. But they are still exponentially more than the preference relations over individual agents—which has positive implications for the Gale–Shapley algorithm of matching theory.