Dai, Darong and Shen, Kunrong (2012): A New Stationary Game Equilibrium Induced by Stochastic Group Evolution and Rational Individual Choice.

PDF
MPRA_paper_40586.pdf Download (315kB)  Preview 
Abstract
In the present paper, a new approach to equilibrium selection for very general normal form games has been constructed by introducing stochastic optimal stopping theory into classical evolutionary game theory. That is, the new game equilibrium is induced by both stochastic group evolution and decentralized rational individual choice. Moreover, stability of the game equilibrium is confirmed from both time and space dimensions.
Item Type:  MPRA Paper 

Original Title:  A New Stationary Game Equilibrium Induced by Stochastic Group Evolution and Rational Individual Choice 
English Title:  A New Stationary Game Equilibrium Induced by Stochastic Group Evolution and Rational Individual Choice 
Language:  English 
Keywords:  Stochastic replicator dynamics; Rational choice; Normalform game; Stability 
Subjects:  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:  40586 
Depositing User:  darong dai 
Date Deposited:  09 Aug 2012 09:17 
Last Modified:  24 Feb 2016 04:45 
References:  Alili, L. and A. E. Kyprianou, 2005. Some Remarks on First Passage of Lévy Processes, the American Put and Pasting Principles. Annals of Applied Probability 15, 20622080. Aliprantis, C. D., G. Camera and D. Puzzello, 2007. A Random Matching Theory. Games and Economic Behavior 59, 116. Aumann, R. J., 1987. Correlated Equilibrium as an Expression of Bayesian Rationality. Econometrica 55, 118 Avram, F., A. E. Kyprianou, M. R. Pistorius, 2004. Exit Problems for Spectrally Negative Lévy Processes and Applications to (Canadized) Russian Options. Annals of Applied Probability 14, 215238. Bernheim, B. D., 1984. Rationalizable Strategic Behavior. Econometrica 52, 10071028 Benaim, M and J. W. Weibull, 2003. Deterministic Approximation of Stochastic Evolution in Games. Econometrica 71, 873903. 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., L. Samuelson and P. Young, 2003. Equilibrium Selection in Bargaining Models. Games and Economic Behavior 45, 296328. Bogomolnaia, A. and H. Moulin, 2004. Random Matching under Dichotomous Preferences. Econometrica 72, 257279. Bomze, I. M., 1991. Cross Entropy Minimization in Uninvadable States of Complex Populations. Journal of Mathematical Biology 30, 7387. Cabrales, A., 2000. Stochastic Replicator Dynamics. International Economic Review 41, 451481. Choi, K. J., H. K. Koo and D. Y. Kwak, 2004. Optimal Stopping of Active Portfolio Management. Annals of Economics and Finance 5, 93126. Corradi, V. and R. Sarin, 2000. Continuous Approximations of Stochastic Evolutionary Game Dynamics. Journal of Economic Theory 94, 163191. Dai, D., 2012. Stochastic Versions of Turnpike Theorems in the Sense of Uniform Topology. Annals of Economics and Finance 13, 389431. Duffie, D and Y. N. Sun, 2007. Existence of Independent Random Matching. Annals of Applied Probability 17, 386419. Ellison, G., 1994. Cooperation in the Prisoner’s Dilemma with Anonymous Random Matching. Review of Economic Studies 61, 567588. Foster, D. P. and H. P. Young, 1990. Stochastic Evolutionary Game Dynamics. Theoretical Population Biology 38, 219232. Foster, D. P. and H. P. Young, 2003. Learning, Hypothesis Testing, and Nash Equilibrium. Games and Economic Behavior 45, 7396. Friedman, D., 1991. Evolutionary Games in Economics. Econometrica 59, 637666. Fudenberg, D. and C. Harris, 1992. Evolutionary Dynamics with Aggregate Shocks. Journal of Economic Theory 57, 420441. Fudenberg, D., L. A. Imhof, M. A. Nowak and C. Taylor, 2004. Stochastic Evolution as a Generalized Moran Process. Unpublished manuscript. Garay, B. M. and J. Hofbauer, 2003. Robust Permanence for Ecological Differential Equations, Minimax, and Discretizations. SIAM Journal on Mathematical Analysis 34, 10071039. Guo, X. and L. Shepp, 2001. Some Optimal Stopping Problems with Nontrivial Boundaries for Pricing Exotic Options. Journal of Applied Probability 38, 647658. Harsanyi, J. C., 1966. A General Theory of Rational Behavior in Game Situations. Econometrica 34, 613634. 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. Hobson, D. G., 1998. Volatility Misspecification, Option Pricing and Superreplication via Coupling. Annals of Applied Probability 8, 193205. Hofbauer, J. and L. A. Imhof, 2009. Time Averages, Recurrence and Transience in the Stochastic Replicator Dynamics. Annals of Applied Probability 19, 13471368. Hofbauer, J and K. Sigmund, 2003. Evolutionary Game Dynamics. Bulletin of the American Mathematical Society 40, 479519. Kandori, M., G. Mailath and R. Rob, 1993. Learning, Mutation, and Longrun Equilibria in Games. Econometrica 61, 2956. Karatzas, I. and S. E. Shreve, 1991. Brownian Motion and Stochastic Calculus. Volume 113 of Graduate Texts in Mathematics. New York: SpringerVerlag, second edition. Kohlberg, E. and J. F. Mertens, 1986. On the Strategic Stability of Equilibria. Econometrica 54, 10031037. 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. Matsui, A. and K. Matsuyama, 1995. An Approach to Equilibrium Selection. Journal of Economic Theory 65, 415434. Myneni, R., 1992. The Pricing of the American Option. Annals of Applied Probability 2, 123. Nash, J. F., Jr., 1950. The Bargaining Problem. Econometrica 18, 155162. Nash, J. F., Jr., 1951. NonCooperative Games. Annals of Mathematics 54, 286295. 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. and M. A. Nowak, 2006. The Replicator Equation on Graphs. Journal of Theoretical Biology 243, 8697. 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. Ohtsuki, H. and M. A. Nowak, 2008. Evolutionary Stability on Graphs. Journal of Theoretical Biology 251, 698707. Pacheco, J. M., A. Traulsen and M. A. Nowak, 2006. CoEvolution of Strategy and Structure in Complex Networks with Dynamical Linking. Physical Review Letters 97, 258103. Riedel, F., 2009. Optimal Stopping with Multiple Priors. Econometrica 77, 857908. Ritzberger, K and J. W. Weibull, 1995. Evolutionary Selection in NormalForm Games. Econometrica 63, 13711399. Samuelson, L. and J. Zhang, 1992. Evolutionary Stability in Asymmetric Games. Journal of Economic Theory 57, 363391. Shepp, L. and A. N. Shiryaev, 1993. The Russian Option: Reduced Regret. Annals of Applied Probability 3, 631640. Young, P. H., 1993. The Evolution of Conventions. Econometrica 61, 5784. Zhou, R. L., 1999. Individual and Aggregate Real Balances in a RandomMatching Model. International Economic Review 40, 10091038. 
URI:  https://mpra.ub.unimuenchen.de/id/eprint/40586 