Stability of essential strategy in two-person zero-sum games

A two-person zero sum game has a (finite) payoff matrix T whose rows and columns are the pure strategies (i.e. moves) for player I and player II respectively. The element (i, j) of T is a payoff to player I, resulting from player I selecting the i^th row and player II selecting the j^th column. Both players are rational and conservative (they minimize the worst possible loss to them). Players independently pick a strategy, and the game is played many times. It is well known that both players do possess optimal mixed strategies which provide a random mixture of pure strategies. A pure strategy is called essential if and only if it has a non-zero probability at equilibrium. Synonyms for the essential pure strategy include relevant strategy, good strategy, and worthwhile strategy. We present a necessary and sufficient condition for the stability of any essential strategy, that is the strategy remains essential with respect to any changes in the payoff of the strategy.