 Individually rational payoff in a repeated game

A payoff vector in a repeated game is individually rational when it gives every player at least that player's minmax payoff. It is strictly individually rational when every inequality is strict. These comparisons use each player's own payoff scale.

For a two-player finite stage game, the minimax theorem identifies this bound with the player's maximum guaranteed expected payoff. For example, in a prisoner's dilemma with $T=5,R=3,P=1,S=0$, defection guarantees $1$, and the cooperative payoff vector $(3,3)$ is strictly individually rational. This does not by itself prove that cooperation is an equilibrium under any specified horizon or monitoring rule.

With several opponents, the permitted correlation in their punishment strategies matters: a minmax over independent opposing mixed strategies need not equal the player's maximin guarantee against a coordinated coalition. Therefore one must state the repeated-game information and punishment conventions before interpreting the bound as an enforceable guarantee. This use is distinct from the participation constraints called individual rationality in mechanism design.