Subgame perfect implementation: A necessary and almost sufficient condition

Abreu, Dilip; Sen, Arunava

doi:10.1016/0022-0531(90)90003-3

Cited by 134 publications

(111 citation statements)

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“…2 The set of individuals is denoted by x f1Y 2Y F F F Y ng. Let i be a ®nite set of possible states of endowment vectors, let i be a ®nite set of possible types for agent i, and let i i Â i .…”

Section: The Framework Of Analysismentioning

confidence: 99%

“…For complete information environments, characterization results were given by Maskin [14], Hurwicz, Maskin, Postlewaite [12], Repullo [28], Sajio [29], Moore and Repullo [19], Dutta and Sen [5], Danilov [4], and others for Nash implementation; Moore and Repullo [18], Abreu and Sen [2] and others for implementation using re®ne-ments of Nash equilibrium; Matsushima [15] and Abreu and Sen [3] for virtual Nash implementation. For incomplete information environments, characterization results were given by Postlewaite and Schmeidler [25], Palfrey, and Srivastava [20,21], Mookherjee and Reichelstein [17], Jackson [13], Hong [9] among many others for Bayesian implementation; by Palfrey and Srivastava [23] and Mookherjee and Reichelstein [17] for implementation in using re®nements of Bayesian equilibrium; Abreu and Matsushima [1], Matsushima [16], Duggan [7], and Tian [35] for virtual Bayesian implementation.…”

Section: Introductionmentioning

confidence: 99%

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Bayesian implementation in exchange economies with state dependent preferences and feasible sets

Tian¹

1999

Social Choice and Welfare

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Abstract. This paper considers Bayesian and Nash implementation in exchange economic environments with state dependent preferences and feasible sets. We fully characterize Bayesian implementability for both di use and non-di use information structures. We show that, in exchange economic environments with three or more individuals, a social choice set is Bayesian implementable if and only if closure, non-con®scatority, Bayesian monotonicity, and Bayesian incentive compatibility are satis®ed. As such, it improves upon and contains as special cases previously known results about Nash and Bayesian implementation in exchange economic environments. We show that the individual rationality and continuity conditions, imposed in Hurwicz et al. [12], can be weakened to the non-con®scatority and can be dropped, respectively, for Nash implementation. Thus we also give a full characterization for Nash implementation when endowments and preferences are both unknown to the designer.

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Section: The Framework Of Analysismentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Bayesian implementation in exchange economies with state dependent preferences and feasible sets

Tian¹

1999

Social Choice and Welfare

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“…Monotonicity (Maskin (1999)), a necessary condition for Nash implementation, is violated for allocations at the boundary of the feasible set. However, we know since the seminal work of Moore-Repullo (1988) and Abreu-Sen (1990) that monotonicity is no longer necessary for subgame perfect implementation. We …rst show that the Walrasian correspondence de…ned over this class of exchange economies is not implementable in subgame perfect equilibrium.…”

Section: Introductionmentioning

confidence: 99%

“…For instance, for a class of exchange economies in which preferences are continuous, convex and strongly monotone, it is now well-known that the Walrasian correspondence is not monotonic, (see, e.g., Hurwicz-Maskin-Postlewaite (1995)). The violation of monotonicity occurs for Walrasian allocations that are at the boundary of the feasible set 1 . Hurwicz (1979) and Schmeidler (1980) have constructed mechanisms that implement the Walrasian correspondence but in which o¤ equilibrium allocations may award negative quantities to some agents.…”

Section: Introductionmentioning

confidence: 99%

Subgame Perfect Implementation and the Walrasian Correspondence

Bochet

2003

SSRN Journal

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Consider a class of exchange economies in which preferences are continuous, convex and strongly monotonic. It is well known that the Walrasian correspondence, de…ned over such a class of economies, is not implementable in Nash Equilibrium. Monotonicity (Maskin (1999)), a necessary condition for Nash implementation, is violated for allocations at the boundary of the feasible set. However, we know since the seminal work of Moore-Repullo (1988) and Abreu-Sen (1990) that monotonicity is no longer necessary for subgame perfect implementation. We …rst show that the Walrasian correspondence de…ned over this class of exchange economies is not implementable in subgame perfect equilibrium. Indeed, the assumption of di¤erentiability cannot be relaxed unless one imposes parametric restrictions on the environment, like assumption EE.3 in Moore-Repullo (1988).Next, assuming di¤erentiability, we construct a sequential mechanism that fully implements the Walrasian correspondence in subgame perfect and strong subgame perfect equilibrium.. We take care of the boundary problem that was prominent in the Nash implementation literature. Moreover, our mechanism is based on price-allocation announcements and …ts the very description of Walrasian Equilibrium.Keywords: Walrasian equilibrium, double implementation, subgame perfect equilibrium, strong subgame perfect equilibrium. This paper is partially based on chapter 2 of my Phd thesis completed at Brown University. I thank Francois Maniquet, Roberto Serrano and Rajiv Vohra for helpful discussions and comments on this topic. I also thank William Thomson for some very helpful comments on a previous draft of this paper. contact: olivier.bochet@fundp.ac.be y University of Namur and CORE.

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“…Within the context of implementation theory there have been significant developments in the characterization of social choice rules that can be implemented in dominant strategies [20,32]; in Nash equilibria [83-85, 112, 143]; or in refined Nash equilibria such as subgame perfect equilibria [2,87], undominated Nash equilibria [1,46,48,96], trembling hand perfect Nash equilibria [123]; or in Bayesian Nash equilibria [45,95,97,106]. Excellent survey articles on implementation theory are [47,85,94].…”

Section: Definition 5 a Social Choice Correspondence π : E → A Is Samentioning

confidence: 99%

Decentralized Resource Allocation Mechanisms in Networks: Realization and Implementation

Stoenescu

Teneketzis

Systems and Control: Foundations &Amp; Applications

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Summary.We discuss how decentralized network resource allocation problems fit within the context of mechanism design (realization theory and implementation theory), and how mechanism design can provide useful insight into the nature of decentralized network resource allocation problems. The discussion is guided by the unicast problem with routing and Quality of Service (QoS) requirements, and the multi-rate multicast service provisioning problem in networks. For these problems we present decentralized resource allocation mechanisms that achieve the solution of the corresponding centralized resource allocation problem and are informationally efficient. We show how the aforementioned mechanisms can be embedded into the general framework of realization theory, and indicate how realization theory can be used to establish the mechanisms' informational efficiency in certain instances. We also present a conjecture related to implementation in Nash equilibria of the optimal centralized solution of the unicast service provisioning problem. Introduction: Motivation and ChallengesToday's fast paced world requires a vast amount of information exchange in order to operate efficiently. With the various technological advances the number of types of services being offered (e.g. telephone connections, live audio broadcasting, live video broadcasting, library database access, e-mail, world wide web), is constantly increasing. Each type of service imposes different Quality of Service (QoS) requirements (e.g. delay, percentage of data packet loss, jitter) on the delivery methods. To address these needs extensive communication networks were developed in the past century. Many of these networks (such as telephone networks) were initially designed for the delivery of certain types of information and were later adapted to accommodate new information exchange needs.Most of today's networks, called integrated services networks, support the delivery of a variety of services to their users. One of the main challenges in integrated services networks is the design of resource allocation strategies which guarantee the

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Subgame perfect implementation: A necessary and almost sufficient condition

Cited by 134 publications

References 8 publications

Bayesian implementation in exchange economies with state dependent preferences and feasible sets

Bayesian implementation in exchange economies with state dependent preferences and feasible sets

Subgame Perfect Implementation and the Walrasian Correspondence

Decentralized Resource Allocation Mechanisms in Networks: Realization and Implementation

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