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Definition and properties of cooperative equilibria in a two-player game of infinite duration. (English) Zbl 0548.90098

A two-player multistage game, with an infinite number of stages is considered. The concepts of overtaking and weakly-overtaking pay-off sequences are introduced. The class of strategies considered consists of memory strategies, which are based on past history of the control and the initial state from where the game has been played. Weak equilibria are defined in this class of strategies. It is shown how such equilibria can be constructed by composing into a trigger strategy a nominal cooperative control sequence and two threat strategies representing the announced retaliation by each player in the case where the other player does not play according to the nominal control. When the threats consist of a feedback equilibrium pair, the resulting cooperative equilibrium is perfect. Another result shows that, if each player can use a most effective threat based on a saddle-point feedback strategy, then any weak equilibrium in the class of memory strategies is in some sense related to this particular kind of equilibrium in the class of trigger strategies.

MSC:

91A15 Stochastic games, stochastic differential games
91A12 Cooperative games
91A05 2-person games
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