The Reconsideration of the Altruistic Decision Based on the Notion of the Bounded Rationality

Abstract

This study proposes that there are two main problems which several works challenging the issue of cooperation have not assumed. Firstly, those works basically employ the best decision that every player knows all information regarding the payoff matrix, and selects the strategy of the highest payoff. Secondly, as Ohdaira and Terano also insist, when we represent specific tendering based on the model of game theory, we confront the restriction that a player can submit only a move in a match. Considering those issues, this paper enhances Ohdaira's previous discussion of the altruistic decision by newly introducing the notion of the bounded rationality which is essential for recognizing the decision with some compromise in limited information. Utilizing the model of match between two groups with the evolutionary process, this study shows that each group establishes cooperation of a high level in comparison with the previous study employing the second-best decision. In addition, showing the detailed sensitivity analysis regarding the probability of the rational decision and the probability of mutation in the evolutionary process, this paper also reveals that the small probabilistic rational decision (a little selection of the strategy of the first grade) has an effect on the rapid collapse of cooperation, while the growth of defection does not keep pace with the rate of that collapse. Moreover, this study exhibits that the change of the probability of mutation in the evolutionary process has a moderate effect on the speed of the collapse of cooperation.