反応依存的利得行列による2人ゲームの選択モデル
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概要
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In the first part, an attempt was made to construct an appropriate model of choice behavior in a two alternative choice situation so as to infer subjects' motives in the response dependent games (RDG) (Nakahara, 1967).The RDG in this experiment was a type of Prisoner's Dilemma game with one variable element of the payoff matrix contingent upon the subject's prior responses. The value of the variable element on the (n+1) th trial is determined both by its prior value and by the subject's response on the n th trial. The rules for the changing of the value of the variable element were: (1) when both subjects responded with a competitive choice, the value of the variable was decreased on the next trial: (2) when one or both subjects made a cooperative choice, the value of the variable was increased.Four possible models of choice behavior in such a RDG were considered, all assuming a Markov chain of the first order, and each implying a different motive on the part of the subjects. The four possible models were: (1) the Bimax model, implying a motive of coexistence and coprosperity; (2) the Nash model, implying a motive of securing minimum loss in any single situation taken separately; (3) the Minimax model, implying a motive of securing a minimum loss; and (4) the Max Difference model, implying a competitive motive.The payoff matrix in a RDG of this sort might display any one of the following five different types of trends in the trial sequences: (1) the A type, in which the variable would increase; (2) the B type, in which the variable would oscillate near the upper limit of the Prisoner's Dilemma structure (PDS); (3) the C type, in which the variable would fluctuate irregularly in the PDS; (4) the D type, in which the variable would oscillate near the lower limit of PDS; (5) the E type, in which the variable would decrease continuously.It is to be noted that the four models are based on both the subject's motives and the five types of mathematical structure of the RDG. In order to see the relation between the models and the above mentioned types, a computer simulation was developed with the results as follows: (1) the Bimax model led to the B type change; (2) the Nash model led to the D type; (3) the Max Difference model led to the E type. No correspondence was obtained with the remaing models and the types of change.The second part of this study was concerned with “relativity of choice”. The term “relativity of choice” was meant to indicate that the same choice behavior would be obtained in the five payoff matrices each element of which were multiplication by a constant of the corresponding element of the standard matrix.Five groups were used in the experiment. Each group was composed of five pairs of males and five pairs of females. Two hundred trials were run in each case.Subjects were all students of Osaka City University; they were not allowed to communicate in the experiment and were not informed about the terminating conditions. The monetary payoff to subjects was not done.The results showed that: (1) in a choice behavior situation of this kind of RDG, “relativity of choice” held independently of the actual Payoff matrix; (2) the percentages of each type of changes mentioned earlier were as follows: B type 10%; C type 12%; D type 66%; E type 12%. A type was not seen.Since the D type was most frequent, it was concluded that the subjects' choice behavior was usually based on the motive of securing a minimum loss an instantaneous situation (Nash model).
- 公益社団法人 日本心理学会の論文