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Theory of conditional games by Wynn C. Stirling

The book is about game theory which is based on the mathematical model described in 1944 by John von Neumann and Oskar Morgenstern. A finite strategic single-stage non-cooperative game is consisting of n (n>1) competing autonomous stakeholders (or players), each having a finite set of strategies, that is actions in a single-stage context. There are considered consequences (or outcomes) of players' actions and a preference ordering is defined for every stakeholder. There is no central authority to dictate the decisions of the players. Therefore, the problem is to solve n problems of 1-player constrained optimization, each player defining their own criteria of optimality. In many cases, a multistage game could be decomposed in a series of single-stage games. The Nash equilibrium is a constrained maximization problem of identification of a solution such as any single player acting alone by deviating from the solution, the benefit of the player would decrease. The conditioned Nash equilibrium is defined for conditioned cases using Bayes probabilities.