TY - JOUR
T1 - Fault tolerant implementation
AU - Eliaz, Kfir
N1 - Funding Information:
We show that a profile, not covered by the previous two cases (either a unanimous agreement on a price-allocation pair such that at least one player cannot afford his bundle, or at least three players disagree), cannot be a k-FTNE of the game. Suppose that 3a* E Ek(G, p) which is not covered by cases 1 or 2. The outcomes of the action profiles in which k players deviate from a* are determined according to rule G3 of the mechanism. We construct an action profile a E B(a*, k) having the following properties: a set M of k players coordinate on an allocation x in which some player j ¢ M receives a bundle xj that is different from the bundle that he announced in a~ and which he strictly prefers to Wj (for example, by adding goods free of charge to his initial bundle). In addition, i is different from any allocation announced by players outside of M and satisfies LiEMUU} (Xi) = LiEMUU} (Wi). The set M and player j are chosen suchthatintheoutcomeg(a),playerjdoesnottrade.6However,givena.:i-ifjdeviatesfromajtotheannouncement of the players in M, he obtains the bundle xi: By construction, this deviation is profitable, a contradiction. II Acknowledgements. I would like to thank my adviser, Ariel Rubinstein, for his help, encouragement and support throughout this project. I thank the editor of this journal and two thoughtful referees for helping me substantially improve this paper. I would also like to thank Markus Brunnenneier, Tilman Borgers.Yoram Hamo, Leonardo Felli, Jacob Glazer, Phillipe Jehiel, Matthew Jackson, Michael Ornstein, Michele Piccione, Ilya Segal and Ran Spiegler for their many helpful comments. I thank seminar participants at the University of Bristol, Cambridge, University of Michigan, NYU, LSE, Princeton, UCL, Summer in Tel-Aviv and Games 2000 for their valuable feedback. I appreciate the hospitality extended to me by STICERD at the London School of Economics where part of this research was undertaken. This research was partially supported by the Israel Science Foundation founded by the Israel Academy of Sciences and Humanities. Financial Support from the European Commission's Marie Currie Fellowship (TMR grant) is gratefully acknowledged.
PY - 2002/7
Y1 - 2002/7
N2 - In this paper we investigate the implementation problem arising when some of the players are "faulty" in the sense that they fail to act optimally. The planner and the non-faulty players only know that there can be at most k faulty players in the population. However, they know neither the identity of the faulty players, their exact number nor how faulty players behave. We define a solution concept which requires a player to optimally respond to the non-faulty players regardless of the identity and actions of the faulty players. We introduce a notion of fault tolerant implementation, which unlike standard notions of full implementation, also requires robustness to deviations from the equilibrium. The main result of this paper establishes that under symmetric information any choice rule that satisfies two properties - k- monotonicity and no veto power - can be implemented by a strategic game form if there are at least three players and the number of faulty players is less than 1/2n - 1. As an application of our result we present examples of simple mechanisms that implement the constrained Walrasian function and a choice rule for the efficient allocation of an indivisible good.
AB - In this paper we investigate the implementation problem arising when some of the players are "faulty" in the sense that they fail to act optimally. The planner and the non-faulty players only know that there can be at most k faulty players in the population. However, they know neither the identity of the faulty players, their exact number nor how faulty players behave. We define a solution concept which requires a player to optimally respond to the non-faulty players regardless of the identity and actions of the faulty players. We introduce a notion of fault tolerant implementation, which unlike standard notions of full implementation, also requires robustness to deviations from the equilibrium. The main result of this paper establishes that under symmetric information any choice rule that satisfies two properties - k- monotonicity and no veto power - can be implemented by a strategic game form if there are at least three players and the number of faulty players is less than 1/2n - 1. As an application of our result we present examples of simple mechanisms that implement the constrained Walrasian function and a choice rule for the efficient allocation of an indivisible good.
UR - http://www.scopus.com/inward/record.url?scp=0036655944&partnerID=8YFLogxK
U2 - 10.1111/1467-937X.t01-1-00023
DO - 10.1111/1467-937X.t01-1-00023
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AN - SCOPUS:0036655944
VL - 69
SP - 589
EP - 610
JO - Review of Economic Studies
JF - Review of Economic Studies
SN - 0034-6527
IS - 3
ER -