Abstract

A method of reduction of a finite statistical game is described. The method allows to reduce the solution of this game to the solution of a statistical game with a “smaller” space of observations in that case if the optimal strategy is partly known for the statistician. In particular, this.situation arises if a given optimal strategy of the nature is checked. Considering some infinite-dimensional linear programming problems associated to the original game, we prove theorems about the connection between the solutions of the original and the reduced game. A complete analysis of 2 × 2-statistical games is given using the described reduction.

AMS I980 Subject Classifications:

• Primary: 49 D 05
• Secondary: 90 E 05

Keywords:

• Game theory
• statistic game
• reduction of statistical games