‘Supergame’ is the original name for situations where the same game is played repetitively, and players are interested in their long run average pay-off. Repeated game is used for more general models, and we refer the reader to that article for those. For the supergame to be well defined, one has to specify the information players receive after each stage: it is assumed that a lottery, depending on the pure strategy choices of all players in the last stage, will select for each player his pay-off and a signal. The lottery stands for the compound effect of all moves of nature in the extensive form of the game, while the signals stand for a new datum – an information partition for each player on the terminal nodes of this extensive form. It is assumed that this information partition describes all information available to the player at the end of the game – in particular, he is not informed (except possibly through the signal) of his own pay-off. The motivation for this degree of generality in the model is discussed in the entry on REPEATED GAMES. The present article is quite brief; a more thorough survey may be found in a lecture by the author at the International Congress of Mathematicians (1986) in Berkeley, which will appear in the Proceedings of that Congress, under the title ‘Repeated Games’, together with a bibliography.
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