NASH EQUILIBRIUM COMBINATIONS OF (PURE OR MIXED) STRATEGIES

A combination of pure or mixed strategies s1 for agent A1, s2 for agent A2, . . . , sn for agent An is a (non-cooperative) Nash equilibrium combination iff while keeping the strategies of the other agents fixed, no single agent Ai could unilaterally increase the utility (or, in cases involving mixed strategies, expected utility) to her of the combination by choosing a different pure or mixed strategy from among the strategies available to her. Where <s1, s2, . . . , sn> is a combination of strategies that is a Nash equilibrium, we will say that each strategy in the combination is a Nash equilibrium component strategy.

THE BIG IDEA: In a two-person strategic interaction, a Nash equilibrium combination of strategies is such that each agent's component strategy is that agent's best reply to the other agent's best reply to it.