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Ranking Friends

  • Feinberg, Yossi

    (Stanford University)

  • Kets, Willemien

    (Northwestern University)

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 Stanford University, Graduate School of Business in its series Research Papers with number 2127.

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Date of creation: Dec 2012
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Handle: RePEc:ecl:stabus:2127
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  1. Lippert, Steffen & Spagnolo, Giancarlo, 2011. "Networks of relations and Word-of-Mouth Communication," Games and Economic Behavior, Elsevier, vol. 72(1), pages 202-217, May.
  2. Ellison, Glenn, 1994. "Cooperation in the Prisoner's Dilemma with Anonymous Random Matching," Review of Economic Studies, Wiley Blackwell, vol. 61(3), pages 567-88, July.
  3. Takahashi, Satoru, 2010. "Community enforcement when players observe partners' past play," Journal of Economic Theory, Elsevier, vol. 145(1), pages 42-62, January.
  4. Matthew Haag & Roger Lagunoff, 2000. "social Norms, Local Interaction and Neighborhood Planning," Levine's Working Paper Archive 2049, David K. Levine.
  5. 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.
  6. Kandori, Michihiro, 1992. "Social Norms and Community Enforcement," Review of Economic Studies, Wiley Blackwell, vol. 59(1), pages 63-80, January.
  7. Giancarlo Spagnolo & Steffen Lippert, 2004. "Networks of Relations," Econometric Society 2004 North American Winter Meetings 496, Econometric Society.
  8. Pramila Krishnan & Emanuela Sciubba, 2006. "Links and Architecture in Village Networks," Birkbeck Working Papers in Economics and Finance 0614, Birkbeck, Department of Economics, Mathematics & Statistics.
  9. 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.
  10. Alexander Wolitzky, 2013. "Cooperation with Network Monitoring," Review of Economic Studies, Oxford University Press, vol. 80(1), pages 395-427.
  11. 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.
  12. 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.
  13. 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.
  14. David A. Miller & S. Nageeb Ali, 2009. "Enforcing Cooperation in Networked Societies," 2009 Meeting Papers 115, Society for Economic Dynamics.
  15. 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.
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