A $2\times2$ $\varepsilon$-best response stochastic two-step game

Anastasia V. Raygorodskaya

Lomonosov Moscow State University

Abstract: 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, bimatrix games, best response.

UDC: 519.83
BBK: 22.173