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

Preview |
PDF
MPRA_paper_43125.pdf Download (319kB) | Preview |

## Abstract

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.

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: | 01 Oct 2019 18:10 |

References: | Aliprantis C D, Camera G, Puzzello D (2007). A Random Matching Theory. Games and Economic Behavior 59, 1-16. Anderson A, Smith L (2010). Dynamic Matching and Evolving Reputations. Review of Economic Studies 77, 3-29. 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, 667-680. Aumann R (1976). Agreeing to Disagree. The Annals of Statistics 4, 1236-1239. 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, 379-405. Benaïm M, Weibull J W (2003). Deterministic Approximation of Stochastic Evolution in Games. Econometrica 71, 873-903. Benaïm M, Hofbauer J, Sandholm W H (2008). Robust Permanence and Impermanence for the Stochastic Replicator Dynamic. Journal of Biological Dynamics 2, 180-195. Binmore K, Samuelson L, Vaughan R (1995). Musical Chairs: Modeling Noisy Evolution. Games and Economic Behavior 11, 1-35. 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 Pro-Social Norms. Evolution and Human Behavior 19, 3-25. Börgers T, Sarin R (1997). Learning Through Reinforcement and Replicator Dynamics. Journal of Economic Theory 77, 1-14. Cabrales A (2000). Stochastic Replicator Dynamics. International Economic Review 41, 451-481. Duffie D, Sun Y (2007). Existence of Independent Random Matching. Annals of Applied Probability 17, 386-419. Eeckhout J, Kircher P (2010). Sorting and Decentralized Price Competition. Econometrica 78, 539-574. 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, 567-588. Fudenberg D, Levine D K (1993). Steady State Learning and Nash Equilibrium. Econometrica 61, 547-573. Fudenberg D, Harris C (1992). Evolutionary Dynamics with Aggregate Shocks. Journal of Economic Theory 57, 420-441. Gale J, Binmore K, Samuelson L (1995). Learning to be Imperfect: The Ultimatum Game. Games and Economic Behavior 8, 56-90. Galeotti A, Goyal S, Kamphorst J (2006). Network Formation with Heterogeneous Players. Games and Economic Behavior 54, 353-372. 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, 265-296. Hofbauer J, Sigmund K (2003). Evolutionary Game Dynamics. Bulletin of the American Mathematical Society 40, 479-519. Hofbauer J, Imhof L (2009). Time Averages, Recurrence and Transience in the Stochastic Replicator Dynamics. Annals of Applied Probability 19, 1347-1368. Hoppe H C, Moldovanu B, Sela A (2009). The Theory of Assortative Matching Based on Costly Signals. Review of Economic Studies 76, 253-281. Imhof L A (2005). The Long-Run Behavior of the Stochastic Replicator Dynamics. Annals of Applied Probability 15, 1019-1045. Imhof L A, Nowak M A (2006). Evolutionary Game Dynamics in a Wright-Fisher Process. Journal of Mathematical Biology 52, 667-681. Kandori M, Mailath G, Rob R (1993). Learning, Mutation, and Long-run Equilibria in Games. Econometrica 61, 29-56. 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, 646-650. Ohtsuki H, Pacheco J M, Nowak M A (2007). Evolutionary Graph Theory: Breaking the Symmetry between Interaction and Replacement. Journal of Theoretical Biology 246, 681-694. Okuno-Fujiwara 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). Co-Evolution 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, 1-29. Pollicott M, Weiss H (2001). The Dynamics of Schelling-Type Segregation Models and a Nonlinear Graph Laplacian Variational Problem. Advances in Applied Mathematics 27, 17-40. Øksendal B, Sulem A (2005). Applied Stochastic Control of Jump Diffusions. Berlin: Springer-Verlag. Riedel F (2009). Optimal Stopping with Multiple Priors. Econometrica 77, 857-908. Schelling T (1969). Models of Segregation. American Economic Review 59, 488-493. Schelling T (1971). Dynamic Models of Segregation. Journal of Mathematical Sociology 1, 143-186. Shimer R, Smith L (2000). Assortative Matching and Search. Econometrica 68, 343-369. 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, 9340-9346. Takahashi S (2010). Community Enforcement when Players Observe Partners’ Past Play. Journal of Economic Theory 145, 42-62. Weibull J (1995). Evolutionary Game Theory. Cambridge, MA: The MIT Press. Young P (1993). The Evolution of Conventions. Econometrica 61, 57-84. Zhang J (2004). A Dynamic Model of Residential Segregation. Journal of Mathematical Sociology 28, 147 -170. |

URI: | https://mpra.ub.uni-muenchen.de/id/eprint/43125 |