On the Bayesian decision making model of 2-person coordination game

Most of the conflict problems between 2 persons can be represented as a bi-matrix game, because players' utilities, in general, are non-zero sum and change according to the progress of game. In the bi-matrix game the equilibrium point set which satisfies the Pareto optimality can be a good bargaining or coordination solution. Under the condition of incomplete information about the risk attitudes of the players, the bargaining or coordination solution depends on additional elements, namely, the players' methods of making inferences when they reach a node in the extensive form of the game that is off the equilibrium path. So the investigation about the players' inference type and its effects on the solution is essential. In addition to that, the effect of an individual's aversion to risk on various solutions in conflict problems, as expressed in his(her) utility function, must be considered. Those kinds of incomplete information make decision maker Bayesian, since it is often impossible to get correct information for building a decision making model. In Bayesian point of view, this paper represents an analytic frame for guessing and learning opponent's attitude to risk for getting better reward. As an example for that analytic frame, 2 persons' bi-matrix game is considered. This example explains that a bi-matrix game can be transformed into a kind of matrix game through the players' implicitly cooperative attitude and the need of arbitration.