Virtual Nash implementation with admissible support

A social choice correspondence (SCC) is virtually implementable if it is ?$?$-close (in the probability simplex) to some (exactly) implementable correspondence [Abreu, D., Sen, A., 1991. Virtual Implementation in Nash Equilibrium. Econometrica 59, 997–1021] proved that, without restriction on the set of alternatives receiving strictly positive probability at equilibrium, every SCC is virtually implementable in Nash Equilibrium. We study virtual implementation when the supports of equilibrium lotteries are restricted. We provide a necessary and sufficient condition, imposing joint restrictions on SCCs and admissible supports. Next, we discuss how to construct supports, and we underline an important difficulty. Finally, we study virtual implementation when the support is restricted to the efficient or individually rational alternatives.     

Feasible implementation of taxation methods

This paper studies implementation of taxation methods in one-commodity environments in which the incomes of the agents are unknown to the planner. Feasibility out of equilibrium imposes that the mechanism depend on the environment. We present two mechanisms. The first one, which requires complete information, implements every taxation method in Nash, strong and coalition-proof equilibrium. The second, where informational requirements are relaxed, implements a large class of consistent and monotone methods in subgame perfect equilibrium. Neither mechanism employs the off-equilibrium devices used by the general theory. Under fully private information no method is implementable. Received: 12 March 1997 / Accepted: 21 July 1998     

When does universal peace prevail? Secession and group formation in conflict

This paper analyzes secession and group formation in the general model of contests due to Esteban and Ray (1999). This model encompasses as special cases rent seeking contests and policy conflicts, where agents lobby over the choice of a policy in a one-dimensional policy space. We show that in both models the grand coalition is the efficient coalition structure and agents are always better off in the grand coalition than in a contest among singletons. Individual agents (in the rent seeking contest) and extremists (in the policy conflict) only have an incentive to secede when they anticipate that their secession will not be followed by additional secessions. Incentives to secede are lower when agents cooperate inside groups. The grand coalition emerges as the unique subgame perfect equilibrium outcome of a sequential game of coalition formation in rent seeking contests. Received: March 2004, Accepted: October 2004, JEL Classification: D72, D74 We thank Joan Maria Esteban, Kai Konrad, Debraj Ray, Stergios Skaperdas and two anonymous referees for helpful comments on the paper. We also benefitted from comments by seminar participants in Barcelona, Istanbul, Paris and WZB Berlin.     

Full Nash implementation of neutral social functions

This paper characterizes neutral social functions that are fully implementable. A neutral social function must be monotonic and simple to be fully implementable under either the Nash equilibrium concept or the strong Nash equilibrium concept. If a neutral social function is monotonic and simple, then the social function is fully implementable by a set of Nash equilibria. For finite alternative sets a neutral social function will be fully implementable by a set of strong Nash equilibria if and only if it is monotonic, simple and dictatorial.     

Implementation and orderings of public information

We explore the relationship between public information and implementable outcomes in an environment characterized by random endowments and private information. We show that if public signals carry no information about private types, then an exact relationship holds: a more informative public signal structure, in the sense of Blackwell, induces a smaller set of ex-ante implementable social choice functions. This holds for a large set of implementation standards, including Nash implementation, and Bayesian incentive compatibility. The result extends the notion, dating to Hirshleifer (1971), that public information can have negative value to an endowment economy under uncertainty.Received: 23 September 2003, Accepted: 30 July 2004, JEL Classification: D80Colin M. Campbell: I thank two referees and seminar participants at the 2002 meetings of the Society for Economic Design, at the 2003 Winter Meetings of the Econometric Society, and at Yale University for helpful input.     

COALITION FORMATION AND BARGAINING PROTOCOLS: A REVIEW OF THE LITERATURE

This paper offers a review of the vast literature regarding bargaining and coalition formation. This topic has been generally described as the attempt to provide strategic foundations to cooperative solution concepts. It can therefore be seen as the linking ring between the non‐cooperative and the cooperative game‐theoretic approach to coalition formation. Its central role in economic theory and its relatively long history that goes back to the Nash program have fostered a large academic production, including surveys. Nonetheless, this paper will focus on an aspect that is often neglected in the dedicated surveys: the specificities of the bargaining protocols leading to different outcomes. Although generally downgraded to the rank of details, the differences in bargaining protocols, even when minor, can cause significant changes in fundamental aspects such as the possibility to reach full cooperation, the distribution of final pay‐offs and the time taken to reach an agreement. Focused on externalities‐free games, therefore on bargaining protocols sustaining solution concepts for cooperative games in characteristic function form, the paper aims at providing a brief but exhaustive review of the topic that could result in a very useful tool for any researcher approaching the subject of coalitional bargaining.     

Nash and dominant strategy implementation in economic environments

When environments are ‘rich’, single-valued social choice functions which are implementable in Nash strategies are implementable in dominant strategies. Moreover the Gibbard–Satterthwaite impossibility theorem of implementation in dominant strategies has been extended to differential economic environments. Therefore it is important to study implementation for non-rich environments. We characterize for quasi-linear utility functions mechanisms which are implementable in dominant strategies (providing a generalization of the Groves–Clarke mechanisms) and in Nash strategies. This second type of mechanisms differ from the first only by the types of transfers they allow. Properties of these mechanisms such as balancedness, individual rationality and robustness with respect to coalitions are then studied.     

Implementation of Pareto efficient allocations

This paper considers Nash implementation and double implementation of Pareto efficient allocations for production economies. We allow production sets and preferences are unknown to the planner. We present a well-behaved mechanism that fully implements Pareto efficient allocations in Nash equilibrium. The mechanism then is modified to fully doubly implement Pareto efficient allocations in Nash and strong Nash equilibria. The mechanisms constructed in the paper have many nice properties such as feasibility and continuity. In addition, they use finite-dimensional message spaces. Furthermore, the mechanism works not only for three or more agents, but also for two-agent economies.     

Nash implementing social choice rules with restricted ranges

We consider Nash implementation of social choice rules with restricted ranges, i.e., where some of the available alternatives are chosen at no preference profile. We show that the appropriate adaptation of Maskin monotonicity to this context depends on the range of the mechanisms: the wider is this range, the weaker is the monotonicity condition to be used. As a result, mechanisms employing outcome functions which allow for out-of-range alternatives at off-equilibrium messages can Nash implement social choice rules which fail to be Nash implementable by mechanisms whose ranges are restricted to the range of the social choice rule to be implemented. The Walrasian social choice correspondence is a particular instance of this. Moreover, social choice rules which are not Maskin monotonic can be “monotonized” by the addition of artificial out-of-range alternatives—a point we illustrate through Solomon’s Dilemma.     

Endogenous coalition formation in contests

This paper analyzes coalition formation in a model of contests with linear costs. Agents first form groups and then compete by investing resources. Coalitions fight for a prize that is assumed to be subject to rivalry, so its value is non-increasing in the size of the group that obtains it. This formulation encompasses as particular cases some models proposed in the rent-seeking literature. We show that the formation of groups generates positive spillovers and analyze two classes of games of coalition formation. A contest among individual agents is the only stable outcome when individual defections leave the rest of the group intact. More concentrated coalition structures, including the grand coalition, are stable when groups collapse after a defection, provided that rivalry is not too strong. Results in a sequential game of coalition formation suggest that there exists a non-monotonic relationship between the level of underlying rivalry and the level of social conflict.

“If men were supplied with every thing in the same abundance, justice and injustice would be equally unknown among mankind.” David Hume (1740), A Treatise of Human Nature

I thank Luis Corchón, Joan Esteban, Michelle Garfinkel and József Sákovics for their comments and suggestions on the paper.     

基于不对称Nash协商模型的多Agent造船供应链协商机制研究

供应链成员企业之间的协商是供应链管理的一个重要方面,供应链上节点企业通过协商才能进行有效的合作。本文在分析船舶制造企业与供应商协商机制的基础上,将多Agent技术运用到合作企业的协商过程中,利用Nash不对称协商模型,为造船供应链企业的利益分配提供有效参考。     

Implementation of solutions to the problem of fair division when preferences are single-peaked

We consider the problem of fairly allocating an infinitely divisible commodity among a group of agents with single-peaked preferences. We address the issue of (Nash)-implementability of solutions to this problem. As the lack of monotonicity of preferences often causes solutions to violate no veto power, the classic Maskin-type theorems cannot be invoked. Instead, we show that more powerful theorems due to Danilov-Yamato and Sjöström can help settle implementation questions for most of the central fairness concepts, generally in the positive.     

Endogenous household interaction

Most econometric models of intrahousehold behavior assume that household decision making is efficient, i.e., utility realizations lie on the Pareto frontier. In this paper, we investigate this claim by adding a number of participation constraints to the household allocation problem. Short-run constraints ensure that each spouse obtains a utility level at least equal to what they would realize under (inefficient) Nash equilibrium. Long-run constraints ensure that each spouse obtains a utility level at least equal to what they would realize by cheating on the efficient allocation and receiving Nash equilibrium payoffs in all successive periods. Given household characteristics and the (common) discount factor of the spouses, not all households may be able to attain payoffs on the Pareto frontier. We estimate these models using a Method of Simulated Moments estimator and data from one wave of the Panel Study of Income Dynamics. We find that both short- and long-run constraints are binding for sizable proportions of households in the sample. We conclude that it is important to carefully model the constraint sets household members face when modeling household allocation decisions, and to allow for the possibility that efficient outcomes may not be implementable for some households.     

On Maskin monotonicity of solution based social choice rules

Howard (J Econ Theory 56:142–159, 1992) argues that the Nash bargaining solution is not Nash implementable, as it does not satisfy Maskin monotonicity. His arguments can be extended to other bargaining solutions as well. However, by defining a social choice correspondence that is based on the solution rather than on its realizations, one can overcome this shortcoming. We even show that such correspondences satisfy a stronger version of monotonicity that is even sufficient for Nash implementability.     

Switching from complete to incomplete information

We construct an elementary mechanism [Dutta, B., Sen, A., Vohra, R., 1995. Nash implementation through elementary mechanisms in economic environments. Review of Economic Design 1, 173–203] that Nash implements the constrained Walrasian correspondence. We extend it to incomplete and non-exclusive information economies by enlarging the message space of agents. In addition, measurability restrictions on allocations with respect to prices proper to constrained rational expectations equilibria are imposed in the outcome function. We show that by imposing such restrictions, the mechanism Bayesian implements the constrained rational expectations equilibrium correspondence. This result shows game-theoretic connections between these two market equilibrium concepts. However, these connections are obtained at the price of strong restrictions on the behavior of agents.     

Repeated implementation and complexity considerations

A game form is commitment-free if single actions of players do not have physical consequences, i.e., affect the continuation game. Such game can be thought to represent inifinite interaction with complete patience. A choice rule can be Nash implemented via a commitment-free mechanism if and only if it coincides with the feasible set of a normal form game. However, when players are complexity averse (in the lexicographic sense), then any Nash implementable choice rule becomes available. I am very grateful to Matt Jackson and a referee for their comments. I also thank Klaus Kultti and Hannu Salonen for useful conversations.     

The Rise of Individual Performance Pay

Existing empirical evidence suggests that individual performance pay is more prevalent in human‐capital‐intensive industries. We introduce a model that can contribute to explain this. In a repeated game model of relational contracting, we analyze the conditions for implementing peer‐dependent incentive regimes when agents possess indispensable human capital. We show that the larger the share of values that the agents can hold up, the lower is the implementable degree of peer‐dependent incentives. In a setting with complementary tasks, we show that although team‐based incentives are optimal if agents are dispensable, it may be costly, and, in fact, suboptimal, to provide team incentives when the agents become indispensable.     

Coalitional stability in the location problem with single-dipped preferences: An application of the minimax theorem

This study considers a situation in which agents choose the location of a public facility from a street according to a given mechanism. Agents have single-dipped preferences over a set of feasible locations. We analyze coalitional behavior for any given mechanism for this situation. We identify a necessary and sufficient condition for a mechanism to possess a strong Nash equilibrium by applying the minimax theorem of von Neumann and Morgenstern (1944). We introduce a class of core solutions and show that these solutions are characterized by strong Nash implementability. As a byproduct of these results, we propose a simple mechanism that implements any core solution in strong Nash equilibria.     

Implementation of optimal contracts under adverse selection

This paper studies a 2-agent, 2-type principal-multiagent model of adverse selection under the assumption that the agents each have complete information. We construct a mechanism implementing the first-best contracts in Nash equilibrium that: satisfies a condition related to individual rationality, is renegotiation-proof, has a small-sized message space, achieves unique implementation and satisfies undomination of Nash equilibrium strategies. Moreover, we prove that other requirements which relate to individual rationality (different from the one satisfied by our mechanism) are not compatible with implementation of the first-best contracts. Received: 27 July 1998 / Accepted: 26 May 2000     

Dynamic patterns in similarity-based cooperation: an agent-based investigation

Understanding what motivates and fosters collective actions has major implications in the governance and management of organizations, in the regulation and design of public policies, and has long attracted the interests of scholars and practitioners in business and economics. This paper deals with how groups of agents emerge in a dynamic contest characterized by lack of formal structure and uncertainty regarding the possible individual outcomes, focusing on the features of the cooperators and on the dynamics emerging among them. Through the development of a stylized agent-based model we start by showing how similarity in values can be a successful driver for cooperation but are also able to highlight the limits of such process, by looking at how and how much agents cooperate with similar others. A second-version of the model, where memory of past interactions has a role, introduces further dynamics and is able to create successful and relatively stable groups.