# The approximation of a strong perfect equilibrium in a discounted supergame

Article Abstract:

The possibility of close estimation of a semi-strict version of a strong perfect equilibrium (SPE) requiring a coalition with compensatory intra-relationships in a discounted supergame is examined. It is suggested that three conditions should exist for close estimation of semi-strict SPE. These are: coalition deviation should not positively affect one member without negatively affecting another member; only the grand coalition can deviate without negative effect on any of its members; and all of its continuing equilibria are relatively equal Pareto-wise. It is concluded that meeting the three conditions will make possible the approximation of a SPE in a discounted supergame.

Publication Name: The Journal of Mathematical Economics

Subject: Mathematics

ISSN: 0304-4068

Year: 1996

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# Computability and randomness of Nash equilibrium in infinite games

Article Abstract:

Problems that cannot be solved through algorithms abound in economic game theory, particularly in the case of infinite non-cooperative games, in which the focus is on the computation of Nash equilibrium strategies. Such unsolvability is true even when the game strategies and utility functions of the players are simple and rational. In the case of mixed strategies and parametric flexibility of the utility functions, the answer to the question of the existence of finitely or infinitely many equilibria is akin to that for the outcome of tosses of a fair coin.

Publication Name: The Journal of Mathematical Economics

Subject: Mathematics

ISSN: 0304-4068

Year: 1991

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# Similarity of games with incomplete information

Article Abstract:

The association of the Bayesian-Nash equilibria and player information in normal form games with payoff uncertainty is described. A partition model is used to distinguish the information from the accompanying payoff distribution. The model is analogous to a type model with absolutely continuous information. The closeness of equilibria, which is a measure of the degree of similarity of games containing incomplete information, rationalizes the use of finite player types in game-theory models.

Publication Name: The Journal of Mathematical Economics

Subject: Mathematics

ISSN: 0304-4068

Year: 1991

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