Appendix E: N-Person Nonzero Sum Games and Games With a Continuum of Strategies
Definition E.1 A collection of strategies is a pure Nash equilibrium for the game with payoff functions {ui(q1, . . ., qn)}, i = 1, . . ., N, if for each player i = 1, . . ., N, we have
A short hand way to write this is ui for all qi Qi, where q−i refers to all the players except the ith.
Definition E.2 Given payoff functions ui(q1, . . ., qn), a best response of player k, written qk = B Rk(q1, . . ., qk−1, qk+1, . . ., qn) is a value that satisfies
or . In other words, qk provides the maximum payoff for player k, given the values of the other player’s .
In general, we say that qk = B Rk(q−k) arg maxx
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