Dai, Darong (2012): On the existence and stability of Pareto optimal endogenous matching with fairness.

PDF
MPRA_paper_40457.pdf Download (483kB)  Preview 
Abstract
In the current paper, we study the asymmetric normalform 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 optimalstopping 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 wellknown Girsanov Theorem.
Item Type:  MPRA Paper 

Original Title:  On the existence and stability of Pareto optimal endogenous matching with fairness 
English Title:  On the Existence and Stability of Pareto Optimal Endogenous Matching with Fairness 
Language:  English 
Keywords:  Stochastic differential cooperative game on time; Pareto optimal endogenous matching; Stable matching; Fairness; Induced game equilibrium; Stochastic replicator dynamics; Adaptive learning 
Subjects:  C  Mathematical and Quantitative Methods > C7  Game Theory and Bargaining Theory > C78  Bargaining Theory ; Matching Theory C  Mathematical and Quantitative Methods > C7  Game Theory and Bargaining Theory > C70  General C  Mathematical and Quantitative Methods > C6  Mathematical Methods ; Programming Models ; Mathematical and Simulation Modeling > C62  Existence and Stability Conditions of Equilibrium 
Item ID:  40457 
Depositing User:  darong dai 
Date Deposited:  04 Aug 2012 02:37 
Last Modified:  15 Jan 2016 11:46 
References:  Anderlini, L., 1999. Communication, Computability, and Common Interest Games. Games and Economic Behavior 27, 137. Andreoni, J. and L. Samuelson, 2006. Building Rational Cooperation. Journal of Economic Theory 127, 117154. Aumann, R., 1976. Agreeing to Disagree. The Annals of Statistics 4, 12361239. Aumann, R. J., and S. Sorin, 1989. Cooperation and Bounded Recall. Games and Economic Behavior 1, 539. Axelrod, R., 1984. The Evolution of Cooperation. Basic Books, New York. Benaim, M. and M. W. Hirsch, 1999. Mixed Equilibria and Dynamical Systems Arising from Fictitious Play in Perturbed Games. Games and Economic Behavior 29, 3672. Benaim, M., J. Hofbauer and W. H. Sandholm, 2008. Robust Permanence and Impermanence for the Stochastic Replicator Dynamic. Journal of Biological Dynamics 2, 180195. Binmore, K., L. Samuelson and R. Vaughan, 1995. Musical Chairs: Modeling Noisy Evolution. Games and Economic Behavior 11, 135. Binmore, K. and L. Samuelson, 1997. Muddling Through: Noisy Equilibrium Selection. Journal of Economic Theory 74, 235265. Binmore, K. and L. Samuelson, 1999. Evolutionary Drift and Equilibrium Selection. Review of Economic Studies 66, 363393. Borgers, T. and R. Sarin, 1997. Learning Through Reinforcement and Replicator Dynamics. Journal of Economic Theory 77, 114. Cabrales, A., 2000. Stochastic Replicator Dynamics. International Economic Review 41, 451481. Canning, D., 1992. Average Behavior in Learning Models. Journal of Economic Theory 57, 442472. Carlsson, H. and E. Van Damme, 1993. Global Games and Equilibrium Selection. Econometrica 61, 9891018. Dai, D., 2012. Stochastic Versions of Turnpike Theorems in the Sense of Uniform Topology. Annals of Economics and Finance 13, 389431. Ellison, G., 1993. Learning, Local Interaction, and Coordination. Econometrica 61, 1047 1071. Ellison, G., 1994. Cooperation in the Prisoner's Dilemma with Anonymous Random Matching. Review of Economic Studies 61, 567588. Ellison, G., 2000. Basins of Attraction, LongRun Stochastic Stability, and the Speed of Stepby Step Evolution. Review of Economic Studies 67, 1745. Ellison, G. and D. Fudenberg, 2000. Learning Purified Mixed Equilibria. Journal of Economic Theory 90, 84115. Foster, D. P. and H. P. Young, 1990. Stochastic Evolutionary Game Dynamics. Theoretical Population Biology 38, 219232. Fudenberg, D. and D. Kreps, 1993. Learning Mixed Equilibria. Games and Economic Behavior 5, 320367. Fudenberg, D. and D. K. Levine, 1993. Steady State Learning and Nash Equilibrium. Econometrica 61, 547573. Fudenberg, D. and E. Maskin, 1986. The Folk Theorem in Repeated Games with Discounting or with Incomplete Information. Econometrica 50, 533554. Fudenberg, D. and E. Maskin, 1990. Evolution and Cooperation in Noisy Repeated Games. American Economic Review 80, 274279. Fudenberg, D. and C. Harris, 1992. Evolutionary Dynamics with Aggregate Shocks. Journal of Economic Theory 57, 420441. Gale, J., K. Binmore and L. Samuelson, 1995. Learning to be Imperfect: The Ultimatum Game. Games and Economic Behavior 8, 5690. Harsanyi, J., 1973. Games with Randomly Disturbed Payoffs: A New Rationale for Mixed Strategy Equilibrium Points. International Journal of Game Theory 2, 123. Harsanyi, J. and R. Selten, 1988. A General Theory of Equilibrium Selection in Games. Cambridge, MA: The MIT Press. Higham, D. J., X. R. Mao and A. M. Stuart, 2003. Strong Convergence of EulerType Methods for Nonlinear Stochastic Differential Equations. SIAM Journal on Numerical Analysis 40, 10411063. Hofbauer, J. and L. A. Imhof, 2009. Time Averages, Recurrence and Transience in the Stochastic Replicator Dynamics. Annals of Applied Probability 19, 13471368. Imhof, L. A., 2005. The LongRun Behavior of the Stochastic Replicator Dynamics. Annals of Applied Probability 15, 10191045. Imhof, L. A and M. A. Nowak, 2006. Evolutionary Game Dynamics in a WrightFisher Process. Journal of Mathematical Biology 52, 667681. Jordan, J., 1993. Three Problems in Learning MixedStrategy Nash Equilibria. Games and Economic Behavior 5, 368386. Kandori, M., 1992. Social Norms and Community Enforcement. Review of Economic Studies 59, 6380. Kandori, M., G. Mailath and R. Rob, 1993. Learning, Mutation, and Longrun Equilibria in Games. Econometrica 61, 2956. Kirchkamp, O. and R. Nagel, 2007. Naive Learning and Cooperation in Network Experiments. Games and Economic Behavior 58, 269292. Kohlberg, E. and J. F. Mertens, 1986. On the Strategic Stability of Equilibria. Econometrica 54, 10031037. Kreps, D. M., P. R. Milgrom, J. Roberts and R. J. Wilson, 1982. Rational Cooperation in the Finitely Repeated Prisoners’ Dilemma. Journal of Economic Theory 27, 245252. Matsui, A., 1991. CheapTalk and Cooperation in a Society. Journal of Economic Theory 54, 245258. Matsui, A. and K. Matsuyama, 1995. An Approach Equilibrium Selection. Journal of Economic Theory 65, 415434. Maynard Smith, J., 1982. Evolution and the Theory of Games. New York: Cambridge University Press. Nash, J. F., Jr., 1950. The Bargaining Problem. Econometrica 18, 155162. Nowak, M. A., A. Sasaki, C. Taylor and D. Fudenberg, 2004. Emergence of Cooperation and Evolutionary Stability in Finite Populations. Nature 428, 646650. Ohtsuki, H., J. M. Pacheco and M. A. Nowak, 2007. Evolutionary Graph Theory: Breaking the Symmetry between Interaction and Replacement. Journal of Theoretical Biology 246, 681694. OkunoFujiwara, M. and A. Postlewaite, 1995. Social Norms and Random Matching Games. Games and Economic Behavior 9, 79–109. Riedel, F., 2009. Optimal Stopping with Multiple Priors. Econometrica 77, 857908. Samuelson, L. and J. Zhang, 1992. Evolutionary Stability in Asymmetric Games. Journal of Economic Theory 57, 363391. Schreiber, S. J., M. Benaim and K. A. S. Atchadé, 2011. Persistence in Fluctuating Environments. Journal of Mathematical Biology 62, 655683. Selten, R. and R. Stoecker, 1986. End Behavior in Sequences of Finite Prisoner’s Dilemma Supergames: A Learning Theory Approach. Journal of Economic Behavior and Organization 7, 4770. Shapley, L. S., 1953. A Value for nPerson Games, in “Contributions to the Theory of Games II (Ann. Math. Studies, 28)” (H.W. Kuhn and A.W. Tucker Eds.), 307317, Princeton University Press, Princeton. van Damme, E., 1987. Stability and Perfection of Nash Equilibria. Berlin: Springer Verlag. Weibull, J., 1995. Evolutionary Game Theory. Cambridge, MA: The MIT Press. Young, H. P. and D. Foster, 1991. Cooperation in the Short and in the Long Run. Games and Economic Behavior 3, 145156. Young, P., 1993. The Evolution of Conventions. Econometrica 61, 5784. 
URI:  https://mpra.ub.unimuenchen.de/id/eprint/40457 