Dai, Darong (2012): On the Existence of Pareto Optimal Endogenous Matching. Published in: Economic Research Guardian , Vol. 2, No. 2

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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.
Item Type:  MPRA Paper 

Original Title:  On the Existence of Pareto Optimal Endogenous Matching 
Language:  English 
Keywords:  Stochastic differential cooperative game on time; Endogenous matching; Fair matching; Pareto optimality; 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:  43125 
Depositing User:  darong dai 
Date Deposited:  06 Dec 2012 13:50 
Last Modified:  28 Apr 2016 16:09 
References:  Aliprantis C D, Camera G, Puzzello D (2007). A Random Matching Theory. Games and Economic Behavior 59, 116. Anderson A, Smith L (2010). Dynamic Matching and Evolving Reputations. Review of Economic Studies 77, 329. Andreoni J, Samuelson L (2006). Building Rational Cooperation. Journal of Economic Theory 127, 117 154. Atakan A E (2006). Assortative Matching with Explicit Search Costs. Econometrica 74, 667680. Aumann R (1976). Agreeing to Disagree. The Annals of Statistics 4, 12361239. Bala V, Goyal S (2000). A Noncooperative Model of Network Formation. Econometrica 68, 1181 1229. Beggs A (2002). Stochastic Evolution with Slow Learning. Economic Theory 19, 379405. Benaïm M, Weibull J W (2003). Deterministic Approximation of Stochastic Evolution in Games. Econometrica 71, 873903. Benaïm M, Hofbauer J, Sandholm W H (2008). Robust Permanence and Impermanence for the Stochastic Replicator Dynamic. Journal of Biological Dynamics 2, 180195. Binmore K, Samuelson L, Vaughan R (1995). Musical Chairs: Modeling Noisy Evolution. Games and Economic Behavior 11, 135. Bisin A, Horst U, Özgür O (2006). Rational Expectations Equilibria of Economies with Local Interactions. Journal of Economic Theory 127, 74 116. Bowles S, Gintis H (1998). The Moral Economy of Communities: Structured Populations and the Evolution of ProSocial Norms. Evolution and Human Behavior 19, 325. Börgers T, Sarin R (1997). Learning Through Reinforcement and Replicator Dynamics. Journal of Economic Theory 77, 114. Cabrales A (2000). Stochastic Replicator Dynamics. International Economic Review 41, 451481. Duffie D, Sun Y (2007). Existence of Independent Random Matching. Annals of Applied Probability 17, 386419. Eeckhout J, Kircher P (2010). Sorting and Decentralized Price Competition. Econometrica 78, 539574. 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. Fudenberg D, Levine D K (1993). Steady State Learning and Nash Equilibrium. Econometrica 61, 547573. Fudenberg D, Harris C (1992). Evolutionary Dynamics with Aggregate Shocks. Journal of Economic Theory 57, 420441. Gale J, Binmore K, Samuelson L (1995). Learning to be Imperfect: The Ultimatum Game. Games and Economic Behavior 8, 5690. Galeotti A, Goyal S, Kamphorst J (2006). Network Formation with Heterogeneous Players. Games and Economic Behavior 54, 353372. Gilboa I, Matsui A (1992). A Model of Random Matching. Journal of Mathematical Economics 21, 185 197. Haag M, Lagunoff R (2006). Social Norms, Local Interaction, and Neighborhood Planning. International Economic Review 47, 265296. Hofbauer J, Sigmund K (2003). Evolutionary Game Dynamics. Bulletin of the American Mathematical Society 40, 479519. Hofbauer J, Imhof L (2009). Time Averages, Recurrence and Transience in the Stochastic Replicator Dynamics. Annals of Applied Probability 19, 13471368. Hoppe H C, Moldovanu B, Sela A (2009). The Theory of Assortative Matching Based on Costly Signals. Review of Economic Studies 76, 253281. Imhof L A (2005). The LongRun Behavior of the Stochastic Replicator Dynamics. Annals of Applied Probability 15, 10191045. Imhof L A, Nowak M A (2006). Evolutionary Game Dynamics in a WrightFisher Process. Journal of Mathematical Biology 52, 667681. Kandori M, Mailath G, Rob R (1993). Learning, Mutation, and Longrun Equilibria in Games. Econometrica 61, 2956. Maynard Smith J (1982). Evolution and the Theory of Games. New York: Cambridge University Press. Nowak M A, Sasaki A, Taylor C, Fudenberg D (2004). Emergence of Cooperation and Evolutionary Stability in Finite Populations. Nature 428, 646650. Ohtsuki H, Pacheco J M, Nowak M A (2007). Evolutionary Graph Theory: Breaking the Symmetry between Interaction and Replacement. Journal of Theoretical Biology 246, 681694. OkunoFujiwara M, Postlewaite A (1995). Social Norms and Random Matching Games. Games and Economic Behavior 9, 79–109. Pacheco J M, Traulsen A, Ohtsuki H, Nowak M A (2008). Repeated Games and Direct Reciprocity under Active Linking. Journal of Theoretical Biology 250, 723–731. Pacheco J M, Traulsen A, Nowak M A (2006). CoEvolution of Strategy and Structure in Complex Networks with Dynamical Linking. Physical Review Letters 97, 258103. Podczeck K, Puzzello D (2012). Independent Random Matching. Economic Theory 50, 129. Pollicott M, Weiss H (2001). The Dynamics of SchellingType Segregation Models and a Nonlinear Graph Laplacian Variational Problem. Advances in Applied Mathematics 27, 1740. Øksendal B, Sulem A (2005). Applied Stochastic Control of Jump Diffusions. Berlin: SpringerVerlag. Riedel F (2009). Optimal Stopping with Multiple Priors. Econometrica 77, 857908. Schelling T (1969). Models of Segregation. American Economic Review 59, 488493. Schelling T (1971). Dynamic Models of Segregation. Journal of Mathematical Sociology 1, 143186. Shimer R, Smith L (2000). Assortative Matching and Search. Econometrica 68, 343369. Skyrms B, Pemantle R (2000). A Dynamic Model of Social Network Formation. Proceedings of the National Academy of Sciences of the United States of America 97, 93409346. Takahashi S (2010). Community Enforcement when Players Observe Partners’ Past Play. Journal of Economic Theory 145, 4262. Weibull J (1995). Evolutionary Game Theory. Cambridge, MA: The MIT Press. Young P (1993). The Evolution of Conventions. Econometrica 61, 5784. Zhang J (2004). A Dynamic Model of Residential Segregation. Journal of Mathematical Sociology 28, 147 170. 
URI:  https://mpra.ub.unimuenchen.de/id/eprint/43125 