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Robust stochastic stability. (English) Zbl 1319.91033
Summary: A strategy profile of a game is called robustly stochastically stable if it is stochastically stable for a given behavioral model independently of the specification of revision opportunities and tie-breaking assumptions in the dynamics. We provide a simple radius-coradius result for robust stochastic stability and examine several applications. For the logit-response dynamics, the selection of potential maximizers is robust for the subclass of supermodular symmetric binary action games. For the mistakes model, the weaker property of strategic complementarity suffices for robustness in this class of games. We also investigate the robustness of the selection of risk-dominant strategies in coordination games under best-reply and the selection of Walrasian strategies in aggregative games under imitation.

MSC:
91A22 Evolutionary games
91A26 Rationality and learning in game theory
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[1] Alós-Ferrer, C, Finite population dynamics and mixed equilibria, Int. Game Theory Rev., 5, 263-290, (2003) · Zbl 1058.91004
[2] Alós-Ferrer, C, Cournot vs. Walras in oligopoly models with memory, Int. J. Ind. Organ., 22, 193-217, (2004)
[3] Alós-Ferrer, C; Ania, AB, The evolutionary stability of perfectly competitive behavior, Econ. Theor., 26, 497-516, (2005) · Zbl 1106.91002
[4] Alós-Ferrer, C; Weidenholzer, S, Contagion and efficiency, J. Econ. Theory, 143, 251-274, (2008) · Zbl 1151.91364
[5] Alós-Ferrer, C, Learning, bounded memory, and inertia, Econ. Lett., 101, 134-136, (2008) · Zbl 1255.91054
[6] Alós-Ferrer, C; Schlag, K; Anand, P (ed.); Pattanaik, P (ed.); Puppe, C (ed.), Imitation and learning, (2009), Oxford
[7] Alós-Ferrer, C; Kirchsteiger, G, General equilibrium and the emergence of (non) market clearing trading institutions, Econ. Theor., 44, 339-360, (2010) · Zbl 1195.91083
[8] Alós-Ferrer, C; Kirchsteiger, G; Walzl, M, On the evolution of market institutions: the platform design paradox, Econ. J., 120, 215-243, (2010)
[9] Alós-Ferrer, C; Netzer, N, The logit-response dynamics, Games Econ. Behav., 68, 413-427, (2010) · Zbl 1207.91017
[10] Alós-Ferrer, C; Shi, F, Imitation with asymmetric memory, Econ. Theor., 49, 193-215, (2012) · Zbl 1276.91031
[11] Beggs, A, Waiting times and equilibrium selection, Econ. Theor., 25, 599-628, (2005) · Zbl 1127.91009
[12] Bergin, J; Lipman, BL, Evolution with state-dependent mutations, Econometrica, 64, 943-956, (1996) · Zbl 0862.90142
[13] Bergin, J; Bernhardt, D, Comparative learning dynamics, Int. Econ. Rev., 45, 431-465, (2004)
[14] Bergin, J; Bernhardt, D, Cooperation through imitation, Games Econ. Behav., 67, 376-388, (2009) · Zbl 1180.91050
[15] Blume, L, The statistical mechanics of strategic interaction, Games Econ. Behav., 5, 387-424, (1993) · Zbl 0797.90123
[16] Blume, L.: Population Games. In: Arthur, B., Durlauf, S., Lane, D. (eds.) The economy as an evolving complex system II, pp. 425-460. Addison-Wesley, Reading, MA (1997) · Zbl 1035.91006
[17] Blume, L, How noise matters, Games Econ. Behav., 44, 251-271, (2003) · Zbl 1056.91011
[18] Candogan, O; Ozdaglar, A; Parrilo, P, Dynamics in near-potential games, Games Econ. Behav., 82, 66-90, (2013) · Zbl 1282.91048
[19] Dokumaci, E., Sandholm, W. H.: Stochastic Evolution with Perturbed Payoffs and Rapid Play. University of Wisconsin-Madison, Mimeo (2008)
[20] Ellison, G, Learning, local interaction, and coordination, Econometrica, 61, 1047-1071, (1993) · Zbl 0802.90143
[21] Ellison, G; Fudenberg, D, Word-of mouth communication and social learning, Q. J. Econ., 110, 95-126, (1995) · Zbl 0827.90039
[22] Ellison, G, Basins of attraction, long-run stochastic stability, and the speed of step-by-step evolution, Rev. Econ. Stud., 67, 17-45, (2000) · Zbl 0956.91027
[23] Friedman, JW; Mezzetti, C, Learning in games by random sampling, J. Econ. Theory, 98, 55-84, (2001) · Zbl 0994.91006
[24] Gerber, A; Bettzüge, MO, Evolutionary choice of markets, Econ. Theor., 30, 453-472, (2007) · Zbl 1109.91378
[25] Hofbauer, J; Sorger, G, A differential game approach to evolutionary equilibrium selection, Int. Game Theory Rev., 4, 17-31, (2002) · Zbl 1017.91009
[26] Josephson, J; Matros, A, Stochastic imitation, Games Econ. Behav., 49, 244-259, (2004) · Zbl 1093.91010
[27] Kandori, M; Mailath, GJ; Rob, R, Learning, mutation, and long run equilibria in games, Econometrica, 61, 29-56, (1993) · Zbl 0776.90095
[28] Kandori, M; Rob, R, Evolution of equilibria in the long run: a general theory and applications, J. Econ. Theory, 65, 383-414, (1995) · Zbl 0837.90139
[29] Kim, Y, Equilibrium selection in n-person coordination games, Games Econ. Behav., 15, 203-227, (1996) · Zbl 0859.90131
[30] Klaus, B; Klijn, F; Walzl, M, Stochastic stability for roommate markets, J. Econ. Theory, 145, 2218-2240, (2010) · Zbl 1203.91202
[31] Leininger, W, Fending off one means fending off all: evolutionary stability in submodular games, Econ. Theor., 29, 713-719, (2006) · Zbl 1120.91005
[32] Marden, JR; Shamma, JS, Revisiting log-linear learning: asynchrony, completeness and payoff-based implementation, Games Econ. Behav., 75, 788-808, (2012) · Zbl 1239.91017
[33] Maruta, T., Okada, A.: Stochastically stable equilibria in coordination games with multiple populations, Mimeo (2009) · Zbl 1237.91013
[34] Maruta, T, Binary games with state dependent stochastic choice, J. Econ. Theory, 103, 351-376, (2002) · Zbl 1137.91324
[35] Monderer, D; Shapley, L, Potential games, Games Econ. Behav., 14, 124-143, (1996) · Zbl 0862.90137
[36] Monte, D., Said, M.: The value of (bounded) memory in a changing world. Econ. Theor. (2014). doi:10.1007/s00199-013-0771-1 · Zbl 1291.91051
[37] Morris, S, Contagion, Rev. Econ. Stud., 67, 57-78, (2000) · Zbl 0960.91016
[38] Myatt, DP; Wallace, C, A multinomial probit model of stochastic evolution, J. Econ. Theory, 113, 286-301, (2003) · Zbl 1158.91307
[39] Myatt, DP; Wallace, C, An evolutionary analysis of the volunteer’s dilemma, Games Econ. Behav., 62, 67-76, (2008) · Zbl 1135.91310
[40] Myatt, DP; Wallace, C, When does one bad apple spoil the barrel? an evolutionary analysis of collective action, Rev. Econ. Stud., 75, 499-527, (2008) · Zbl 1138.91345
[41] Oechssler, J, An evolutionary interpretation of mixed-strategy equilibria, Games Econ. Behav., 21, 203-237, (1997) · Zbl 0891.90187
[42] Okada, D; Tercieux, O, Log-linear dynamics and local potential, J. Econ. Theory, 14, 1140-1164, (2012) · Zbl 1258.91021
[43] Possajennikov, A, Evolutionary foundations of aggregate-taking behavior, Econ. Theor., 21, 921-928, (2003) · Zbl 1112.91005
[44] Rhode, P; Stegeman, M, A comment on “learning, mutation, and long-run equilibria in games”, Econometrica, 64, 443-449, (1996) · Zbl 0873.90132
[45] Ritzberger, K; Weibull, J, Evolutionary selection in normal-form games, Econometrica, 63, 1371-1399, (1995) · Zbl 0841.90127
[46] Robles, J, Evolution, bargaining, and time preferences, Econ. Theor., 35, 19-36, (2008) · Zbl 1133.91020
[47] Robson, AJ; Vega-Redondo, F, Efficient equilibrium selection in evolutionary games with random matching, J. Econ. Theory, 70, 65-92, (1996) · Zbl 0859.90138
[48] Sandholm, WH, Simple and clever decision rules for a model of evolution, Econ. Lett., 61, 165-170, (1998) · Zbl 0914.90280
[49] Sandholm, WH, Orders of limits for stationary distributions, stochastic dominance, and stochastic stability, Theor. Econ., 5, 1-26, (2010) · Zbl 1194.91045
[50] Schaffer, M, Evolutionarily stable strategies for a finite population and a variable contest size, J. Theor. Biol., 132, 469-478, (1988)
[51] Schaffer, M, Are profit-maximisers the best survivors?, J. Econ. Behav. Organ., 12, 29-45, (1989)
[52] Staudigl, M, Stochastic stability in binary choice coordination games, Games Econ. Behav., 75, 372-401, (2012) · Zbl 1280.91023
[53] Topkis, D.M.: Supermodularity and Complementarity. Princeton University Press, Princeton (1998)
[54] Vega-Redondo, F, The evolution of Walrasian behavior, Econometrica, 65, 375-384, (1997) · Zbl 0874.90049
[55] Vives, X, Complementarities and games: new developments, J. Econ. Lit., 43, 437-479, (2005)
[56] Weidenholzer, S, Coordination games and local interactions: a survey of the game theoretic literature, Games, 1, 551-585, (2010) · Zbl 1311.91059
[57] Young, P, The evolution of conventions, Econometrica, 61, 57-84, (1993) · Zbl 0773.90101
[58] Young, P, An evolutionary model of bargaining, J. Econ. Theory, 59, 145-168, (1993) · Zbl 0778.90096
[59] Young, P, Conventional contracts, Rev. Econ. Stud., 65, 773-792, (1998) · Zbl 0913.90278
[60] Young, P.: Individual Strategy and Social Structure. Princeton University Press, Princeton (1998b)
[61] Damme, E; Weibull, JW, Evolution in games with endogenous mistake probabilities, J. Econ. Theory, 106, 296-315, (2002) · Zbl 1035.91006
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