×

Co-evolutionary dynamics and Bayesian interaction games. (English) Zbl 1282.91050

Summary: Recently there has been a growing interest in evolutionary models of play with endogenous interaction structure. We call such processes co-evolutionary dynamics of networks and play. We study a co-evolutionary process of networks and play in settings where players have diverse preferences. In the class of potential games we provide a closed-form solution for the unique invariant distribution of this process. Based on this result we derive various asymptotic statistics generated by the co-evolutionary process. We give a complete characterization of the random graph model, and stochastically stable states in the small noise limit. Thereby we can select among action profiles and networks which appear jointly with non-vanishing frequency in the limit of small noise in the population. We further study stochastic stability in the limit of large player populations.

MSC:

91A22 Evolutionary games
91A07 Games with infinitely many players
05C80 Random graphs (graph-theoretic aspects)
PDFBibTeX XMLCite
Full Text: DOI Link

References:

[1] Anderson S, de Palma A, Thisse J (1992) Discrete choice theory of product differentiation. The MIT Press, Cambridge · Zbl 0857.90018
[2] Blume L (1993) Statistical mechanics of strategic interaction. Games Econ Behav 5: 387–424 · Zbl 0797.90123 · doi:10.1006/game.1993.1023
[3] Blume L (1997) Population games. In: Arthur W, Durlauf S, Lane D (eds) The economy as an evolving complex system II, SFI studies in the science of complexity, vol XXVII. Addison-Wesley, Menlo-Park, pp 425–462
[4] Bollobás B, Janson S, Riordan O (2007) The phase transition in inhomogeneous random graphs. Random Struct Algorithm 31(1): 3–122 · Zbl 1123.05083 · doi:10.1002/rsa.20168
[5] den Hollander F (2000) Large deviations. Fields institute monographs. American Mathematical Society, Providence
[6] Durrett R (2007) Random graph dynamics, Cambridge series in statistical and probabilistic mathematics. Cambridge University Press, Cambridge
[7] Ely J, Sandholm WH (2005) Evolution in Bayesian games I: theory. Games Econ Behav 53: 83–109 · Zbl 1127.91004 · doi:10.1016/j.geb.2004.09.003
[8] Ethier SN, Kurtz TG (1986) Markov processes: characterization and convergence. Wiley, New York
[9] Fudenberg D, Levine DK (1998) The theory of learning in games. The MIT Press, Cambridge · Zbl 0939.91004
[10] Golub B, Jackson MO (2010) How homophily affects diffusion and learning in networks. Mimeo. http://arxivorg/abs/08114013 . Accessed 26 September 2010
[11] Goyal S, Vega-Redondo F (2005) Network formation and social coordination. Games Econ Behav 50: 178–207 · Zbl 1109.91323 · doi:10.1016/j.geb.2004.01.005
[12] Hofbauer J, Sandholm WH (2007) Evolution in games with randomly disturbed payoffs. J Econ Theory 132: 47–69 · Zbl 1142.91343 · doi:10.1016/j.jet.2005.05.011
[13] Hofbauer J, Sigmund K (1988) The theory of evolution and dynamical systems. Cambridge University Press, Cambridge · Zbl 0678.92010
[14] Horst U, Scheinkman JA (2006) Equilibria in systems of social interactions. J Econ Theory 130(1): 44–77 · Zbl 1141.91343 · doi:10.1016/j.jet.2005.02.012
[15] Jackson MO, Watts A (2002) On the formation of interaction networks in social coordination games. Games Econ Behav 41: 265–291 · Zbl 1037.91017 · doi:10.1016/S0899-8256(02)00504-3
[16] Kandori M, Mailath G, Rob R (1993) Learning, mutation, and long run equilibria in games. Econometrica 61: 29–56 · Zbl 0776.90095 · doi:10.2307/2951777
[17] Monderer D, Shapley L (1996) Potential games. Games Econ Behav 14: 124–143 · Zbl 0862.90137 · doi:10.1006/game.1996.0044
[18] Park J, Newman M (2004) The statistical mechanics of networks. Phys Rev E 70: 066117 · doi:10.1103/PhysRevE.70.066117
[19] Sandholm WH (2007) Pigouvian pricing and stochastic evolutionary implementation. J Econ Theory 132: 367–382 · Zbl 1142.91344 · doi:10.1016/j.jet.2005.09.005
[20] Sandholm WH (2010a) Orders of limits for stationary distributions, stochastic dominance, and stochastic stability. Theor Econ 5: 1–26 · Zbl 1194.91045 · doi:10.3982/TE554
[21] Sandholm WH (2010b) Population games and evolutionary dynamics. The MIT Press, Cambridge · Zbl 1208.91003
[22] Söderberg B (2002) General formalism for inhomogeneous random graphs. Phys Rev E 66: 066121–066126 · doi:10.1103/PhysRevE.66.066121
[23] Staudigl M (2010a) Co-evolutionary dynamics and bayesian interaction games. EUI Working papers. European University Institute, Florence
[24] Staudigl M (2010b) Co-evolutionary dynamics of networks and play PhD Thesis. Department of Economics, University of Vienna, Vienna
[25] Staudigl M (2010c) On a general class of stochastic co-evolutionary dynamics. Working Paper No: 1001. Department of Economics, University of Vienna, Vienna
[26] Staudigl M (2011) Potential games in volatile environments. Games Econ Behav 72(1): 271–287 · Zbl 1236.91118 · doi:10.1016/j.geb.2010.08.004
[27] Vega-Redondo F (2007) Complex social networks, econometric society monograph series. Cambridge University Press, Cambridge · Zbl 1145.91004
[28] Young H (1993) The evolution of conventions. Econometrica 61(1): 57–84 · Zbl 0773.90101 · doi:10.2307/2951778
[29] Young HP (2003) The diffusion of innovations in social networks. In: Blume LE, Durlauf SN (eds) The economy as an evolving complex system III. Oxford University Press, New York
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.