ABSTRACT
When a game is repeated many times, it seems that some sort of "cooperative" behavior might be induced: if a player deviates from a particular strategy at some point in order to increase his own payoff, the other players may be able to act in such a way that he is penalized in every subsequent play of the game. To formalize these ideas, let G be a game in strategic form (see Definition 2.3). The supergame G* of G 87is then the game each play of which consists of an infinite sequence of plays of G. One might then expect that the outcomes in G* generated by noncooperative solution concepts (i.e. ones in which it is assumed that contracts cannot be enforced) are related to the outcomes in G generated by cooperative solution concepts (where it is assumed that contracts can be enforced). To examine this question, use the following notations for G:
N ={l,...,n} is the set of players,
Σi is the (finite) set of strategies of player i; σi is an element of Σi and σ = (σ1,σ2,...,σn) ∈ x Σi = Σ, and https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780429042034/4eff4487-a367-4138-a35f-94df68001ede/content/inline36.tif" xmlns:xlink="https://www.w3.org/1999/xlink"/>
h: Σ → EN is the vector of players' payoff functions.
