多段階ゲームの構成とダイナミックプログラミングの手法によるゲーム行動の分析について

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In a matrix game situation, the selection of strategies, one by each player, determines a play a, and to this strategy complex utility function to each player is defined. Therefore, a matrix game could be considered as a function Γ which defines one to one correspondence between strategy complex and utility vector U. U=Γ(α) In the report, the author expands the above definition of matrix game by incorporating scalar vector x and transformation matrix R. Now, a matrix game is redefined as U=x・R x=Γ(α) Then, the N-stage finite multi-stage matrix game is constructed by using another transformation H. U_n=x_n・R_n R_n=H(R_<n-1>, x_<n-1>) x_n=Γ(α) n=1, 2, ..., N As a model of players decisional game behavior in this multi-stage game situation, we can preliminarily consider that they will make a sequence of optimum decisions which will maximize some evaluation function of the game. For instance, they may play the game to make the total joint gain maximum. In this case, the evaluation function is able to be defined as [numerical formula] Now, because of additive W, we are able to apply the Dynamic Programming method, and are able to have the recurrence relation [numerical formula] The numerical solution of the above functional equation is the optimum policy which designates an optimum decision for each stage of the game, and maximizes the evaluation function. Now, we may shift the analytical first stage to an actual later stage, or we may replace the evaluation function by another strategic nature, and in this way, we will be able to analyze an actual dynamic human game behavior more in detail.
帯広畜産大学の論文
1979-03-20

著者

中原淳一
帯広畜産大学心理学研究室

多段階ゲームの構成とダイナミックプログラミングの手法によるゲーム行動の分析について

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