The Analysis of the Payment Matrix in a Game Against a Neutral Opponent

The study discusses the topic of playing against a neutral (unreasonable) opponent and evaluating his mixed strategy. The goal is to prove the importance of the emphasis in such games on the analysis of the payment matrix. The task is to demonstrate the possibilities of this analysis in choosing the optimal strategy against a neutral opponent. The methodology of the mathematical proof and the testing of statistical hypotheses were used. It has been proven that it is sufficient for the probabilities to fall within the boundaries within which the conditions for dominance are met. It has been proven that the analysis (of the payment matrix) provides information about the limits within which the empirically obtained probabilities of the states are reliable estimates of the real probabilities. The sources for obtaining the mixed strategy of the player are evaluated. The use of analytically obtained limits for estimating empirically obtained probabilities with the tools for testing statistical hypotheses is considered. The approach is recommended when choosing a strategy in situations where changing the strategy afterwards is either impossible or too expensive. The proposed analysis has a high practical utility for all persons making strategic decisions in the conditions of a game against a neutral opponent. The conclusion is that only on the basis of this analysis can an optimal strategy be selected, insensitive to the inaccuracy of the mixed strategy of the opponent.