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Fair Divisions as Attracting Nash Equilibria of Simple Games

  • Marco Galbiati

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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  1. Antonio Cabrales, 1996. "Adaptive dynamics and the implementation problem with complete information," Economics Working Papers 179, Department of Economics and Business, Universitat Pompeu Fabra.
  2. Kim, Y.G. & Sobel, J., 1993. "An Evolutionary Approach to Pre-Play Communication," Working Papers 93-02, University of Iowa, Department of Economics.
  3. 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.
  4. 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.
  5. Antonio Cabrales & Giovanni Ponti, 2000. "Implementation, Elimination Of Weakly Dominated Strategies And Evolutionary Dynamics," Working Papers. Serie AD 2000-18, Instituto Valenciano de Investigaciones Económicas, S.A. (Ivie).
  6. Marco Galbiati, 2006. "Fair Divisions as Attracting Nash Equilibria of Simple Games," Economics Working Papers ECO2006/24, European University Institute.
  7. Maskin, Eric & Sjostrom, Tomas, 2002. "Implementation theory," Handbook of Social Choice and Welfare, in: K. J. Arrow & A. K. Sen & K. Suzumura (ed.), Handbook of Social Choice and Welfare, edition 1, volume 1, chapter 5, pages 237-288 Elsevier.
  8. Postlewaite, Andrew & Wettstein, David, 1989. "Feasible and Continuous Implementation," Review of Economic Studies, Wiley Blackwell, vol. 56(4), pages 603-11, October.
  9. repec:fth:calaec:6-98 is not listed on IDEAS
  10. Brams,Steven J. & Taylor,Alan D., 1996. "Fair Division," Cambridge Books, Cambridge University Press, number 9780521556446.
  11. 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.
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