- 著者
-
中原 淳一
- 出版者
- 帯広畜産大学
- 雑誌
- 帯広畜産大学学術研究報告. 第II部, 人文・社会科学篇 (ISSN:03857735)
- 巻号頁・発行日
- vol.4, no.4, pp.217-225, 1976-02-25
Taxonomy of 2×2 games has been shown by Rapoport & Guyer. Later, Hamburger introduced a metric classification system of 2×2 games restricting his examination on separability of payoffs. If the classification system is a metrical one, then not only comparability of game behavior of strategicaly different games, but also quantitative analysis of game behavior is supposed to be possible by using the parameters of the system. Moreover, dynamic game methods should become a powerful experimental method for the study of interpersonal interaction processes, if the system contains metricaly related, psychologicaly meaningful games such as prisoner's dilemma game, chicken game and so on. Following the above preliminary considerations the author presented a new way of construction of the 2×2 game system. Itemized discussions are as follows : 1. A state vector is attributed for each player. The element of this vector is a potential payoff. A rectangular arrangement of these vectors makes a state matrix. The state matrix of a two-person game is shown as follow : [numerical formula] 2. Somewhat ad hoc payoff rules are applied to the state matrix, and the 2×2 payoff matrix is constructed as follow : [numerical formula] 3. Characteristics of games which are deducible from this parametric payoff matrix are discussed. 4. A symmetric case (α=β, x=y) is examined at first, and α is hypothesized to be a fixed parameter. In this case, game are quasi-chicken games if x>α, prisoner's dilemma game if α>x>α/2, quasi-coordination games if α/2>x>o, and pure coordination game if x=0. 5. An asymmetric case (a=β, x≠y) is considered next. In this case, if y>α>x, then column player's payoffs are always secured as positive, and also he can determine row player's payoff as positive or negative only by his own strategic choice. This game is called the absolute positive-negative control game. 6. Finally, several further extensions of the method are discussed.