Geodesic
A $2\times2$ $\varepsilon$-best response stochastic two-step game
Matematičeskaâ teoriâ igr i eë priloženiâ, Tome 2 (2010) no. 4, pp. 84-105.

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A $2\times2$ $\varepsilon$-best response repeated game, in which each player in each subsequent round chooses a pure strategy based on the result of a random test, is analyzed. The random test is generated by the player's arbitrary mixed strategy prescribing the player to choose his/her best response to his/her partner's previously chosen pure strategy with a high probability. The so defined decision making patterns (called $\varepsilon$-best response functions) are interpreted as the players' behavioral strategies. These strategies define a stochastic game, in which the expected benefits averaged over all the rounds act as the players' benefits. The game is analyzed in the two-step case. A classification of the Nash equilibrium points is provided, and the equilibrium values are compared with the average benefits gained through the deterministic usage of the players' best response pure strategies.
Keywords: repeated games, best response.
Mots-clés : bimatrix games 
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     title = {A $2\times2$ $\varepsilon$-best response stochastic two-step game},
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Anastasia V. Raygorodskaya. A $2\times2$ $\varepsilon$-best response stochastic two-step game. Matematičeskaâ teoriâ igr i eë priloženiâ, Tome 2 (2010) no. 4, pp. 84-105. http://geodesic.mathdoc.fr/item/MGTA_2010_2_4_a4/

[1] Vorobev N. N., Teoriya igr dlya ekonomistov-kibernetikov, Nauka, Moskva, 1985 | MR

[2] Neve Zh., Matematicheskie osnovy teorii veroyatnostei, Mir, Moskva, 1969 | MR | Zbl

[3] Axelrod R., The Evolution of Cooperation, Basic Books, 1984

[4] Fudenberg D., Kreps D. M., “Learning mixed equilibria”, Games and Econ. Behavior, 5 (1993), 320–367 | DOI | MR | Zbl

[5] Hofbauer J., Sigmund K., The Theory of Evolution and Dynamical Systems, Cambridge University Press, Cambridge, 1988 | MR | Zbl

[6] Kaniovski Yu. M., Kryazhimskiy A. V., Young H. P., “Learning equilibria in games played by heterogeneous populations”, Games and Economic Behavior, 31 (2000), 50–96 | DOI | MR | Zbl

[7] Kleimenov A. F., Kryazhimskiy A. V., “Minimum-noncooperative trajectories in repeated games”, Complex Dynamical Systems with Incomplete Information, eds. E. Reithmeier, G. Leitmann, Shaker Verlag, Aachen, 1999, 94–107

[8] Kryazhimskiy A. V., Osipov Yu. S., “On evolutionary-differential games”, Proc. of Steklov Math. Inst., 211, 1995, 257–287 | MR | Zbl

[9] Nowak M., Sigmund K., “The Alternating Prisoner's Dilemma”, J. Theor. Biol., 168 (1994), 219–226 | DOI

[10] Van der Laan G., Tieman X., “Evolutionary Game Theory and the Modeling of Economic Behavior”, De Economist, 146:1 (1998), 59–89 | DOI

[11] Weibull J., Evolutionary Game Theory, The M.I.T. Press, Cambridge, 1995 | MR