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Ranking Friends

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  • Yossi Feinberg
  • Willemien Kets

Abstract

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

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Keywords: Cooperation; repeated games; ranking profiles; networks JEL Classification Numbers: D85; C73; L14; Z13; C72;

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  1. David Miller & Nageeb Ali, 2008. "Cooperation and Collective Enforcement in Networked Societies," 2008 Meeting Papers 970, Society for Economic Dynamics.
  2. Michi Kandori, 2010. "Social Norms and Community Enforcement," Levine's Working Paper Archive 630, David K. Levine.
  3. Lippert, Steffen & Spagnolo, Giancarlo, 2005. "Networks of Relations and Social Capital," CEPR Discussion Papers 5078, C.E.P.R. Discussion Papers.
  4. 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.
  5. Giancarlo Spagnolo & Steffen Lippert, 2004. "Networks of Relations," Econometric Society 2004 North American Winter Meetings 496, Econometric Society.
  6. 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.
  7. 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.
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