Games with randomly disturbed payoffs: A new rationale for mixed-strategy equilibrium points

@article{harsanyi-73, abstract = {Equilibrium points in mixed strategies seem to be unstable, because any player can deviate without penalty from his equilibrium strategy even if he expects all other players to stick to theirs. This paper proposes a model under which most mixed-strategy equilibrium points have full stability. It is argued that for any gameGamma the players' uncertainty about the other players' exact payoffs can be modeled as a disturbed gameGamma *, i.e., as a game with small random fluctuations in the payoffs. Any equilibrium point inGamma, whether it is in pure or in mixed strategies, can ldquoalmost alwaysrdquo be obtained as a limit of a pure-strategy equilibrium point in the corresponding disturbed gameGamma * when all disturbances go to zero. Accordingly, mixed-strategy equilibrium points are stable — even though the players may make no deliberate effort to use their pure strategies with the probability weights prescribed by their mixed equilibrium strategies — because the random fluctuations in their payoffs willmake them use their pure strategies approximately with the prescribed probabilities.}, author = {Harsanyi, John C. }, citeulike-article-id = {505409}, journal = {International Journal of Game Theory}, keywords = {410-3, game\_theory, tartumicro}, month = {December}, number = {1}, pages = {1--23}, posted-at = {2006-02-14 20:58:13}, priority = {2}, publisher = {Physica Verlag, An Imprint of Springer-Verlag GmbH}, title = {Games with randomly disturbed payoffs: A new rationale for mixed-strategy equilibrium points}, volume = {2}, year = {1973} }

TY - JOUR ID - harsanyi-73 L3 - citeulike-article-id:505409 TI - Games with randomly disturbed payoffs: A new rationale for mixed-strategy equilibrium points JF - International Journal of Game Theory VL - 2 IS - 1 SP - 1 EP - 23 PB - Physica Verlag, An Imprint of Springer-Verlag GmbH N2 - Equilibrium points in mixed strategies seem to be unstable, because any player can deviate without penalty from his equilibrium strategy even if he expects all other players to stick to theirs. This paper proposes a model under which most mixed-strategy equilibrium points have full stability. It is argued that for any gameGamma the players' uncertainty about the other players' exact payoffs can be modeled as a disturbed gameGamma *, i.e., as a game with small random fluctuations in the payoffs. Any equilibrium point inGamma, whether it is in pure or in mixed strategies, can ldquoalmost alwaysrdquo be obtained as a limit of a pure-strategy equilibrium point in the corresponding disturbed gameGamma * when all disturbances go to zero. Accordingly, mixed-strategy equilibrium points are stable — even though the players may make no deliberate effort to use their pure strategies with the probability weights prescribed by their mixed equilibrium strategies — because the random fluctuations in their payoffs willmake them use their pure strategies approximately with the prescribed probabilities. KW - 410-3 KW - game_theory KW - tartumicro AU - Harsanyi, John PY - 1973/12// ER -