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Ranking Friends

  • Yossi Feinberg
  • Willemien Kets

We investigate the scope for cooperation within a community engaged in repeated reciprocal interactions. Players seek the help of others and approach them sequentially according to some fixed order, that is, a ranking profile. We study the ranking profiles that are most effective in sustaining cooperation in equilibrium, that is, profiles that support full cooperation in equilibrium under the largest set of parameters. These are the profiles that spread the costs of helping others equally among the members of the community. We show that, generically, these socially optimal ranking profiles correspond to Latin squares: profiles in which each player appears in a given position exactly once in other players' list. In addition, we study equilibria with bilateral enforcement in which only the victims punish non-cooperating deviators. We show that the Latin squares in which every two players rank each other at the same position can sustain cooperation for the widest range of parameters in this case.

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Paper provided by Northwestern University, Center for Mathematical Studies in Economics and Management Science in its series Discussion Papers with number 1557.

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Date of creation: 12 Jan 2012
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Handle: RePEc:nwu:cmsems:1557
Contact details of provider: Postal: Center for Mathematical Studies in Economics and Management Science, Northwestern University, 580 Jacobs Center, 2001 Sheridan Road, Evanston, IL 60208-2014
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Web page: http://www.kellogg.northwestern.edu/research/math/
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  1. David A. Miller & S. Nageeb Ali, 2009. "Enforcing Cooperation in Networked Societies," 2009 Meeting Papers 115, Society for Economic Dynamics.
  2. Krishnan, Pramila & Sciubba, Emanuela, 2008. "Links and Architecture in Village Networks," CEPR Discussion Papers 6787, C.E.P.R. Discussion Papers.
  3. Aliprantis, C.D. & Camera, G. & Puzzello, D., 2007. "Bilateral matching with Latin squares," Journal of Mathematical Economics, Elsevier, vol. 43(2), pages 99-114, February.
  4. Takahashi, Satoru, 2010. "Community enforcement when players observe partners' past play," Journal of Economic Theory, Elsevier, vol. 145(1), pages 42-62, January.
  5. Glen Ellison, 2010. "Cooperation in the Prisoner's Dilemma with Anonymous Random Matching," Levine's Working Paper Archive 631, David K. Levine.
  6. Alexander Wolitzky, 2013. "Cooperation with Network Monitoring," Review of Economic Studies, Oxford University Press, vol. 80(1), pages 395-427.
  7. Matthew Haag & Roger Lagunoff, 2000. "social Norms, Local Interaction and Neighborhood Planning," Levine's Working Paper Archive 2049, David K. Levine.
  8. B. Douglas Bernheim & Michael D. Whinston, 1990. "Multimarket Contact and Collusive Behavior," RAND Journal of Economics, The RAND Corporation, vol. 21(1), pages 1-26, Spring.
  9. Kandori, Michihiro, 1992. "Social Norms and Community Enforcement," Review of Economic Studies, Wiley Blackwell, vol. 59(1), pages 63-80, January.
  10. Spagnolo, Giancarlo & Lippert, Steffen, 2004. "Networks of Relations," SSE/EFI Working Paper Series in Economics and Finance 570, Stockholm School of Economics, revised 03 May 2005.
  11. Matthew O. Jackson & Tomas Rodriguez-Barraquer & Xu Tan, 2012. "Social Capital and Social Quilts: Network Patterns of Favor Exchange," American Economic Review, American Economic Association, vol. 102(5), pages 1857-97, August.
  12. Francesco Nava & Michele Piccione, 2012. "Efficiency in repeated games with local interaction and uncertain local monitoring," LSE Research Online Documents on Economics 54250, London School of Economics and Political Science, LSE Library.
  13. Mihm, Maximilian & Toth, Russell & Lang, Corey, 2009. "What Goes Around Comes Around: A Theory of Indirect Reciprocity in Networks," Working Papers 09-07, Cornell University, Center for Analytic Economics.
  14. Giovanni Maggi, 1999. "The Role of Multilateral Institutions in International Trade Cooperation," American Economic Review, American Economic Association, vol. 89(1), pages 190-214, March.
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