In a 2 player, non-zero sum game, when finding the security levels for both players, does one examine mixed strategies and find mixed Nash equilibria that provide the highest payout, or is one restricted to pure strategies?
I understand that the security level is supposed to be the highest payoff a player can assure himself acting unilaterally, but I'm not sure if mixed strategies can be included, because unless the game is played many times over, the mixed strategy concept doesn't really make sense.
Citing E.N. Barron's Game Theory: An Introduction (second edition) on P. 362, mixed strategies are used in calculating the security levels.
That makes sense; over time, a equilibrium mixed strategy will provide a given payoff regardless of the opponent's strategy. It doesn't address the issue of a game played once, in which case the idea of an expected payoff is somewhat unrealistic.