Abstract
Infinite multistage games G with games Γ(·) played on each stage are considered. The definition of path and trajectory in graph tree are introduced. For infinite multistage games G a regularization procedure is introduced and in the regularizied game a strong Nash Equilibrium (coalition proof) is constructed. The approach considered in this paper is similar to one used in the proof of Folk theorems for infinitely repeated games. The repeated n-person "Prisoner's Dilemma" game is considered, as a special case. For this game a strong Nash Equilibrium is found.
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