Abstract
Implementation theory tackles the following problem given a social choice correspondence (SCC), find a decentralized mechanism such that for every constellation of the individuals’ preferences, the set of outcomes in equilibrium is exactly the set of socially optimal alternatives (as specified by the correspondence). In this paper we are concerned with implementation by mediated equilibrium; under such an equilibrium, the players’ strategies can be coordinated in a way that discourages deviation. Our main result is a complete characterization of SCCs that are implementable by mediated strong equilibrium. This characterization, in addition to being strikingly concise, implies that some important SCCs that are not implementable by strong equilibrium are in fact implementable by mediated strong equilibrium.
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References
Aumann RJ (1959) Acceptable points in general cooperative n-person games. In: Tucker A, Luce R(eds) Contributions to the Theory of Games, vol 4, pp 287–324. Princeton University Press
Danilov VI (1992) Implementation via Nash equilibria. Econometrica 60(1): 43–56
Dutta B, Sen A (1991) Implementation under strong equilibrium: a complete characterization. J Math Econ 20: 49–67
Fristrup P, Keiding H (2001) Strongly implementable social choice correspondences and the supernucleus. Soc Choice Welf 18: 213–226
Hurwicz L (1960) Optimality and informational efficiency in resource allocation processes. In: Arrow KJ, Karlin S, Suppes P (eds) Mathematical methods in the social sciences. Stanford University Press, Stanford, pp 27–46
Hurwicz L (1972) On informationally decentralized systems. In: Radner R, McGuire CB (eds) Decision and organization. North Holland, Amsterdam, pp 297–336
Maskin E (1979) Implementation and strong Nash equilibrium. In: Laffont JJ (eds) Aggregation and revelation of preferences. North Holland, Amsterdam, pp 433–439
Maskin E (1999) Nash equilibrium and welfare optimality. Rev Econ Stud 66:23–38. This paper was first circulated in 1977
Mizutani M, Hiraide Y, Nishino H (1993) Computational complexity to verify the unstability of effectivity function. Int J Game Theory 22(3): 225–239
Monderer D, Tennenholtz M (2009) Strong mediated equilibrium. Artif Intell 173(1): 180–195
Moulin H, Peleg B (1982) Cores of effectivity functions and implementation theory. J Math Econ 10: 115–145
Nash JF (1950) Equilibrium points in N-person games. Proc Natl Acad Sci USA 36: 48–49
Pattanaik PK (1976a) Counter-threats and strategic manipulation under voting schemes. Rev Econ Stud 43(1): 11–18
Pattanaik PK (1976b) Threats, counter-threats, and strategic voting. Econometrica 44(1): 91–103
Peleg B (1984) Game theoretical analysis of voting in committees. Cambridge University Press, Cambridge
Peleg B (1998) Effectivity functions, game forms, games, and rights. Soc Choice Welf 15: 67–80
Peleg B, Procaccia AD (2007) Mediators enable truthful voting. Discussion paper 451, Center for the Study of Rationality. The Hebrew University of Jerusalem
Peleg B, Winter E (2002) Constitutional implementation. Rev Econ Des 7: 187–204
Rozenfeld O, Tennenholtz M (2007) Routing mediators. In: Proceedings of the 20th international joint conference on artificial intelligence (IJCAI), pp 1488–1493
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Peleg, B., Procaccia, A.D. Implementation by mediated equilibrium. Int J Game Theory 39, 191–207 (2010). https://doi.org/10.1007/s00182-009-0175-4
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DOI: https://doi.org/10.1007/s00182-009-0175-4