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Fair Divisions as Attracting Nash Equilibria of Simple Games

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  • Marco Galbiati

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

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  1. 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.
  2. Maskin, Eric & Sjostrom, Tomas, 2001. "Implementation Theory," Working Papers 5-01-1, Pennsylvania State University, Department of Economics.
  3. 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.
  4. Antonio Cabrales, . "Adaptive Dynamics and the Implementation Problem with Complete Information," ELSE working papers 009, ESRC Centre on Economics Learning and Social Evolution.
  5. Galbiati, Marco, 2008. "Fair divisions as attracting Nash equilibria of simple games," Economics Letters, Elsevier, vol. 100(1), pages 72-75, July.
  6. 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.
  7. 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.
  8. Postlewaite, Andrew & Wettstein, David, 1989. "Feasible and Continuous Implementation," Review of Economic Studies, Wiley Blackwell, vol. 56(4), pages 603-11, October.
  9. Brams,Steven J. & Taylor,Alan D., 1996. "Fair Division," Cambridge Books, Cambridge University Press, number 9780521556446, April.
  10. Kim, Yong-Gwan & Sobel, Joel, 1995. "An Evolutionary Approach to Pre-play Communication," Econometrica, Econometric Society, vol. 63(5), pages 1181-93, September.
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Cited by:
  1. Marco Galbiati, 2006. "Fair Divisions as Attracting Nash Equilibria of Simple Games," Economics Working Papers ECO2006/24, European University Institute.

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