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On the Existence and Stability of Pareto Optimal Endogenous Matching with Fairness

  • Dai, Darong
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    In the current paper, we study the asymmetric normal-form game between two heterogeneous groups of populations by employing the stochastic replicator dynamics driven by Lévy process. A new game equilibrium, i.e., the game equilibrium of a stochastic differential cooperative game on time, is derived by introducing optimal-stopping technique into evolutionary game theory, which combines with the Pareto optimal standard leads us to the existence of Pareto optimal endogenous matching. Moreover, stability of the Pareto optimal endogenous matching is confirmed by essentially using the well-known Girsanov Theorem.

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    Paper provided by University Library of Munich, Germany in its series MPRA Paper with number 40560.

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    Date of creation: 08 Aug 2012
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    Handle: RePEc:pra:mprapa:40560
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    1. Canning, David, 1992. "Average behavior in learning models," Journal of Economic Theory, Elsevier, vol. 57(2), pages 442-472, August.
    2. Selten, Reinhard & Stoecker, Rolf, 1986. "End behavior in sequences of finite Prisoner's Dilemma supergames A learning theory approach," Journal of Economic Behavior & Organization, Elsevier, vol. 7(1), pages 47-70, March.
    3. Aumann, Robert J. & Sorin, Sylvain, 1989. "Cooperation and bounded recall," Games and Economic Behavior, Elsevier, vol. 1(1), pages 5-39, March.
    4. Jordan J. S., 1993. "Three Problems in Learning Mixed-Strategy Nash Equilibria," Games and Economic Behavior, Elsevier, vol. 5(3), pages 368-386, July.
    5. Binmore, Ken & Samuelson, Larry, 1999. "Evolutionary Drift and Equilibrium Selection," Review of Economic Studies, Wiley Blackwell, vol. 66(2), pages 363-93, April.
    6. Carlsson, H. & van Damme, E.E.C., 1993. "Global games and equilibrium selection," Other publications TiSEM 49a54f00-dcec-4fc1-9488-4, Tilburg University, School of Economics and Management.
    7. Ellison, Glenn, 2000. "Basins of Attraction, Long-Run Stochastic Stability, and the Speed of Step-by-Step Evolution," Review of Economic Studies, Wiley Blackwell, vol. 67(1), pages 17-45, January.
    8. David Kreps & Paul Milgrom & John Roberts & Bob Wilson, 2010. "Rational Cooperation in the Finitely Repeated Prisoners' Dilemma," Levine's Working Paper Archive 239, David K. Levine.
    9. Andreoni,J. & Samuelson,L., 2003. "Building rational cooperation," Working papers 4, Wisconsin Madison - Social Systems.
    10. Matsui Akihiko & Matsuyama Kiminori, 1995. "An Approach to Equilibrium Selection," Journal of Economic Theory, Elsevier, vol. 65(2), pages 415-434, April.
    11. Fudenberg Drew & Kreps David M., 1993. "Learning Mixed Equilibria," Games and Economic Behavior, Elsevier, vol. 5(3), pages 320-367, July.
    12. D. Foster & P. Young, 2010. "Stochastic Evolutionary Game Dynamics," Levine's Working Paper Archive 493, David K. Levine.
    13. Tilman B�rgers & Rajiv Sarin, . "Learning Through Reinforcement and Replicator Dynamics," ELSE working papers 051, ESRC Centre on Economics Learning and Social Evolution.
    14. Binmore, Ken & Samuelson, Larry, 1997. "Muddling Through: Noisy Equilibrium Selection," Journal of Economic Theory, Elsevier, vol. 74(2), pages 235-265, June.
    15. D. Fudenberg & C. Harris, 2010. "Evolutionary Dynamics with Aggregate Shocks," Levine's Working Paper Archive 496, David K. Levine.
    16. Glen Ellison, 2010. "Learning, Local Interaction, and Coordination," Levine's Working Paper Archive 391, David K. Levine.
    17. KOHLBERG, Elon & MERTENS, Jean-François, . "On the strategic stability of equilibria," CORE Discussion Papers RP -716, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    18. Nash, John, 1950. "The Bargaining Problem," Econometrica, Econometric Society, vol. 18(2), pages 155-162, April.
    19. Darong Dai, 2012. "Stochastic Versions of Turnpike Theorems in the Sense of Uniform Topology," Annals of Economics and Finance, Society for AEF, vol. 13(2), pages 381-423, November.
    20. Young, H Peyton, 1993. "The Evolution of Conventions," Econometrica, Econometric Society, vol. 61(1), pages 57-84, January.
    21. Nowak, Martin & Sasaki, Akira & Fudenberg, Drew & Taylor, Christine, 2004. "Emergence of Cooperation and Evolutionary Stability in Finite Populations," Scholarly Articles 3196331, Harvard University Department of Economics.
    22. Frank Riedel, 2009. "Optimal Stopping With Multiple Priors," Econometrica, Econometric Society, vol. 77(3), pages 857-908, 05.
    23. Benaim, Michel & Hirsch, Morris W., 1999. "Mixed Equilibria and Dynamical Systems Arising from Fictitious Play in Perturbed Games," Games and Economic Behavior, Elsevier, vol. 29(1-2), pages 36-72, October.
    24. Kirchkamp, Oliver & Nagel, Rosemarie, 2007. "Naive learning and cooperation in network experiments," Games and Economic Behavior, Elsevier, vol. 58(2), pages 269-292, February.
    25. Ken Binmore & Larry Samuelson, 2010. "Evolutionary Drift and Equilibrium Selection," Levine's Working Paper Archive 390, David K. Levine.
    26. Ellison, Glenn & Fudenberg, Drew, 2000. "Learning Purified Mixed Equilibria," Journal of Economic Theory, Elsevier, vol. 90(1), pages 84-115, January.
    27. Binmore Kenneth G. & Samuelson Larry & Vaughan Richard, 1995. "Musical Chairs: Modeling Noisy Evolution," Games and Economic Behavior, Elsevier, vol. 11(1), pages 1-35, October.
    28. 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.
    29. D. Fudenberg & E. Maskin, 2010. "Evolution and Cooperation in Noisy Repeated Games," Levine's Working Paper Archive 546, David K. Levine.
    30. John C. Harsanyi & Reinhard Selten, 1988. "A General Theory of Equilibrium Selection in Games," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262582384, June.
    31. Peyton Young & Dean Foster, 2010. "Cooperation in the Short and in the Long Run," Levine's Working Paper Archive 494, David K. Levine.
    32. Samuelson, Larry & Zhang, Jianbo, 1992. "Evolutionary stability in asymmetric games," Journal of Economic Theory, Elsevier, vol. 57(2), pages 363-391, August.
    33. A. Cabrales, 2010. "Stochastic Replicator Dynamics," Levine's Working Paper Archive 489, David K. Levine.
    34. A. Matsui, 2010. "Cheap-Talk and Cooperation in a Society," Levine's Working Paper Archive 536, David K. Levine.
    35. Robert J Aumann, 1999. "Agreeing to Disagree," Levine's Working Paper Archive 512, David K. Levine.
    36. Michi Kandori, 2010. "Social Norms and Community Enforcement," Levine's Working Paper Archive 630, David K. Levine.
    37. Gale, John & Binmore, Kenneth G. & Samuelson, Larry, 1995. "Learning to be imperfect: The ultimatum game," Games and Economic Behavior, Elsevier, vol. 8(1), pages 56-90.
    38. P. Young, 1999. "The Evolution of Conventions," Levine's Working Paper Archive 485, David K. Levine.
    39. Matsui, Akihiko, 1991. "Cheap-talk and cooperation in a society," Journal of Economic Theory, Elsevier, vol. 54(2), pages 245-258, August.
    40. L. Samuelson & J. Zhang, 2010. "Evolutionary Stability in Asymmetric Games," Levine's Working Paper Archive 453, David K. Levine.
    41. Fudenberg, Drew & Maskin, Eric, 1986. "The Folk Theorem in Repeated Games with Discounting or with Incomplete Information," Econometrica, Econometric Society, vol. 54(3), pages 533-54, May.
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