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.