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Опубликовано на портале: 30-01-2007George J. Mailath, Larry Samuelson, Jeroen M. Swinkels Econometrica. 1993. Vol. 61. No. 2. P. 273-302.
Different extensive form games with the same reduced normal form can have different information sets and subgames. This generates a tension between a belief in the strategic relevance of information sets and subgames and a belief in the sufficiency of the reduced normal form. We identify a property of extensive form information sets and subgames which we term strategic independence. Strategic independence is captured by the reduced normal form, and can be used to define normal form information sets and subgames. We prove a close relationship between these normal form structures and their extensive form namesakes. Using these structures, we are able to motivate and implement solution concepts corresponding to subgame perfection, sequential equilibrium, and forward induction entirely in the reduced normal form, and show close relations between their implications in the normal and extensive form.
Опубликовано на портале: 30-01-2007Eric van Damme, Hans Carlsson Econometrica. 1993. Vol. 61. No. 5. P. 989-1018.
A global game is an incomplete information game where the actual payoff structure is determined by a random draw from a given class of games and where each player makes a noisy observation of the selected game. For 2 x 2 games, it is shown that, when the noise vanishes, iterated elimination of dominated strategies in the global game forces the players to conform to J. C. Harsanyi and R. Selten's risk dominance criterion.
Опубликовано на портале: 22-01-2007Ehud Lehrer, Ehud Kalai Econometrica. 1993. Vol. 61. No. 5. P. 1019-1045.
Subjective utility maximizers, in an infinitely repeated game, will learn to predict opponents' future strategies and will converge to play according to a Nash equilibrium of the repeated game. Players' initial uncertainty is placed directly on opponents' strategies and the above result is obtained under the assumption that the individual beliefs are compatible with the chosen strategies. An immediate corollary is that, when playing a Harsanyi-Nash equilibrium of a repeated game of incomplete information about opponents' payoff matrices, players will eventually play a Nash equilibrium of the real game, as if they had complete information.