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Fair Divisions as Attracting Nash Equilibria of Simple Games

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Author Info
Marco Galbiati

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Abstract

We consider the problem of allocating a finite number of divisible homogeneous goods to N = 2 individuals, in a way which is both envy-free and Pareto optimal. Building on Thomson (2005 Games and Economic Behavior), a new simple mechanism is presented here with the following properties: a) the mechanism fully implements the desired divisions, i.e. for each preference profile the set of equilibrium outcomes coincides with the set of fair divisions; b) the set of equilibria is a global attractor for the best-reply dynamics. Thus, players myopically adapting their strategies settle down in an fair division. The result holds even if mixed strategies are used.

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Paper provided by European University Institute in its series Economics Working Papers with number ECO2006/24.

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Date of creation: 2006
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Handle: RePEc:eui:euiwps:eco2006/24

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Related research
Keywords: Fair divisions; envy-free; implementation; best reply dynamics;

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Find related papers by JEL classification:
C78 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Bargaining Theory; Matching Theory
C73 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Stochastic and Dynamic Games; Evolutionary Games

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  1. Postlewaite, Andrew & Wettstein, David, 1989. "Feasible and Continuous Implementation," Review of Economic Studies, Blackwell Publishing, vol. 56(4), pages 603-11, October. [Downloadable!] (restricted)
  2. Sjostrom Tomas, 1994. "Implementation in Undominated Nash Equilibria without Integer Games," Games and Economic Behavior, Elsevier, vol. 6(3), pages 502-511, May. [Downloadable!] (restricted)
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  3. Varian, Hal R., 1974. "Equity, envy, and efficiency," Journal of Economic Theory, Elsevier, vol. 9(1), pages 63-91, September. [Downloadable!] (restricted)
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  4. Antonio Cabrales & Giovanni Ponti, 2000. "Implementation, Elimination of Weakly Dominated Strategies and Evolutionary Dynamics," Review of Economic Dynamics, Elsevier for the Society for Economic Dynamics, vol. 3(2), pages 247-282, April. [Downloadable!] (restricted)
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  5. Bhaskar Dutta & Arunava Sen & Rajiv Vohra, 1994. "Nash implementation through elementary mechanisms in economic environments," Review of Economic Design, Springer, vol. 1(1), pages 173-203, December. [Downloadable!] (restricted)
  6. Saijo, Tatsuyoshi & Tatamitani, Yoshikatsu & Yamato, Takehiko, 1999. "Characterizing Natural Implementability: The Fair and Walrasian Correspondences," Games and Economic Behavior, Elsevier, vol. 28(2), pages 271-293, August. [Downloadable!] (restricted)
  7. Eric Maskin & Tomas Sjostrom, 2001. "Implementation Theory," Economics Working Papers 0006, Institute for Advanced Study, School of Social Science. [Downloadable!]
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  8. Cabrales, Antonio, 1999. "Adaptive Dynamics and the Implementation Problem with Complete Information," Journal of Economic Theory, Elsevier, vol. 86(2), pages 159-184, June. [Downloadable!] (restricted)
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  9. Kim, Yong-Gwan & Sobel, Joel, 1995. "An Evolutionary Approach to Pre-play Communication," Econometrica, Econometric Society, vol. 63(5), pages 1181-93, September. [Downloadable!] (restricted)
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  10. Saijo, Tatsuyoshi & Tatamitani, Yoshikatsu & Yamato, Takehiko, 1996. "Toward Natural Implementation," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 37(4), pages 949-80, November.
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