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8.10.1. Definition
We now turn to a study of finitely repeated games. The formal description of a finitely repeated game is very similar to that of an infinitely repeated game: for any positive integer 
a - period finitely repeated game of the strategic game 
is an extensive game with perfect information that satisfies the conditions in Definition 137.1 when the symbol 
is replaced by . We restrict attention to the case in which the preference relation 
of each player 
in the finitely repeated game is represented by the function 
, where 
is a payoff function that represents ’s preferences in the constituent game. We refer to this game as the -period repeated game of 
8.10.2 Nash Equilibrium
The intuitive argument that drives the folk theorems for infinitely repeated games is that a mutually desirable outcome can be supported by a stable social arrangement in which a player is deterred from deviating by the threat that he will be "punished" if he does so. The same argument applies, with modifications, to a large class of finitely repeated games. The need for modification is rooted in the fact that the outcome in the last period of any Nash equilibrium of any finitely repeated game must be a Nash equilibrium of the constituent game, a fact that casts a shadow over the rest of the game. This shadow is longest in the special case in which every player's payoff in every Nash equilibrium of the constituent game is equal to his minmax payoff (as in the Prisoner's Dilemma). In this case the intuitive argument behind the folk theorems fails: the outcome in every period must be a Nash equilibrium of the constituent game, since if there were a period in which the outcome were not such an equilibrium then in the last such period some player could deviate with impunity. The following result formalizes this argument.
Proposition 155.1. If the payoff profile in every Nash equilibrium of the strategic game 
is the profile 
of minmax payoffs in , then for any value of the outcome 
of every Nash equilibrium of the - period repeated game of has the property that 
is a Nash equilibrium of for all 
.
Список использованной литературы
[1]. "A Course in Game Theory". Martin J. Osborne, Ariel Rubinstein. The MIT Press
Cambridge, Massachusetts, London, England, 1994
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| The Structure of Subgame Perfect Equilibria Under the Discounting Criterion | | | Decide if the following sentences are true of false. Work in pairs. Use the phrases from Appendix 5. |