Compleat Strategyst

Compleat Strategyst

J. D. Williams · 2012

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1. Saddle Point As Stable Solution

   In a two-person zero-sum game, inspect the payoff matrix for an entry that is simultaneously the minimum of its row and the maximum of its column; if one exists, both players should play that pure strategy, since neither can gain by deviating. When this saddle point exists, the game is strictly determined and no randomizing is needed.

2. Assume A Maximally Competent Opponent

   Strategy in zero-sum games should be computed against an adversary assumed to be rational and playing as well as possible, not against their likely mistakes. Solving for the opponent's best response yields a strategy that guarantees a secured value even if they play perfectly, so errors by a weaker opponent can only help you.

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