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On the Optimality of the Equality Matching Form of Sociality

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  • Carmona, Guilherme

Abstract

We consider a two-player game in which one player can take a costly action (i.e., to provide a favor) that is bene¯cial to the other. The game is in¯nitely repeated and each player is equally likely to be the one who can provide the favor in each period. In this context, equality matching is de¯ned as a strategy in which each player counts the number of times she has given in excess of received and she gives if and only if this number has not reached an upper bound. We show that the equality matching strategy is simple, self-enforcing, symmetric, and irreducible. Furthermore, we show that the utility for each player is at least as high under equality matching as under any other simple, self-enforcing, symmetric, and irreducible strategy of the same complexity. Thus, we rationalize equality matching as being an e±cient way to achieve those properties. This result is applied to risk sharing in village economies and used to rationalize the observed correlations between individual consump- tion and individual income and between present and past transfers across individuals.

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Bibliographic Info

Paper provided by Universidade Nova de Lisboa, Faculdade de Economia in its series FEUNL Working Paper Series with number wp489.

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Length: 37 pages
Date of creation: 2006
Date of revision:
Handle: RePEc:unl:unlfep:wp489

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  1. Kalai, Ehud & Stanford, William, 1988. "Finite Rationality and Interpersonal Complexity in Repeated Games," Econometrica, Econometric Society, vol. 56(2), pages 397-410, March.
  2. Mertens, Jean-Francois, 2002. "Stochastic games," Handbook of Game Theory with Economic Applications, in: R.J. Aumann & S. Hart (ed.), Handbook of Game Theory with Economic Applications, edition 1, volume 3, chapter 47, pages 1809-1832 Elsevier.
  3. Narayana Kocherlakota, 2010. "Implications of Efficient Risk Sharing Without Commitment," Levine's Working Paper Archive 2053, David K. Levine.
  4. Townsend, R.M., 1991. "Risk and Insurance in Village India," University of Chicago - Economics Research Center 91-3, Chicago - Economics Research Center.
  5. Ethan Ligon & Jonathan P. Thomas & Tim Worrall, 2002. "Informal Insurance Arrangements with Limited Commitment: Theory and Evidence from Village Economies," Review of Economic Studies, Oxford University Press, vol. 69(1), pages 209-244.
  6. Ehud Kalai, 1987. "Bounded Rationality and Strategic Complexity in Repeated Games," Discussion Papers 783, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
  7. Ernst Fehr & Joseph Henrich & Robert Boyd, 2003. "In Search of Homo Economicus: Behavioral Experiments in 15 Small- Scale Societies," Microeconomics 0305009, EconWPA.
  8. Okuno-Fujiwara Masahiro & Postlewaite Andrew, 1995. "Social Norms and Random Matching Games," Games and Economic Behavior, Elsevier, vol. 9(1), pages 79-109, April.
  9. La Ferrara, Eliana, 2003. "Kin Groups and Reciprocity: A Model of Credit Transactions in Ghana," CEPR Discussion Papers 3705, C.E.P.R. Discussion Papers.
  10. Kandori, Michihiro, 1992. "Social Norms and Community Enforcement," Review of Economic Studies, Wiley Blackwell, vol. 59(1), pages 63-80, January.
  11. 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.
  12. Koeppl Thorsten V., 2006. "Differentiability of the Efficient Frontier when Commitment to Risk Sharing is Limited," The B.E. Journal of Macroeconomics, De Gruyter, vol. 6(1), pages 1-6, April.
  13. Ariel Rubinstein, 1997. "Finite automata play the repeated prisioners dilemma," Levine's Working Paper Archive 1639, David K. Levine.
  14. Abreu, Dilip, 1988. "On the Theory of Infinitely Repeated Games with Discounting," Econometrica, Econometric Society, vol. 56(2), pages 383-96, March.
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