On the Future Parameter

Abstract

1. IntroductionWhen people make decisions, whether consciously or subconsciously, the decisions are made according to some rule or principle. Let us call this the decision principle. There are various kinds of decision principles in decision theory that are derived from game theory, for example, Wald's maximin principle, the maximax principle, Hurwicz's optimism-pessimism index principle, and Savage's minimax regret principle, etc. (French, 1986; Takahashi, 1993). A random choice of alternatives is also one of the typical decision principles (Takahashi, 1997a).The minimax theorem proves that in a zero-sum two-person game, as long as one player chooses a strategy according to Wald's maximin principle, the same principle should be the optimal decision principle for the other player as well. However, in a non-zero-sum two-person game, despite the existence of the Nash equilibrium, even if both players choose their strategy in accordance with maximin principle, they will reach the Nash equilibrium point. On the contrary, an attempt to explain the Nash equilibrium solely by economic rationality has been unsuccessful (Kandori, 1997). Rather than explaining the economic rationality of the equilibrium, it is better to analyze path dependency when multiple equilibria exist.It has been said that the Japanese have no decision principles; however, this is highly doubtful-the Japanese have decision principles. If their behaviors were guided by decision principles, people and companies of Japan would be able to predict each other's actions, and any kind of social life would become impossible; however, this is the case. Indeed, their actions are being led by some kind of principle. The decision principle commonly observed in many Japanese companies appears to be different from typical decision principles in game and decision theories.Generally, a person's choice of strategy depends on the decision principle he or she adopts. When two people use different decision principles, it is difficult for a player to imagine or understand what kind of decision principle the opponent is using, particularly when the opponent's choice upsets the player's expectations. Therefore, it appears to non-Japanese people that the Japanese have no decision principle. However, they do have decision principles, although different from well-known typical principles. So then, what types of decision principles lead the Japanese people's actions? This paper proposes a hypothesis to answer this question.2. Prisoner's DilemmaThere exists a non-zero-sum two-person game having an unconvinced equilibrium. A particularly well-known example is the prisoner's dilemma. By associating not to and confessing to the prisoner's dilemma game is often generalized in the following cooperation/ game (Axelrod, 1984, pp. 7-8).(a) Each player must choose either (C) or defection (D).(b) Each player must make the choice without knowing what the opponent will do.(c) Regardless of the opponent's choice, yields a higher payoff than cooperation. However, if both players have defected, both get lower payoffs than if both had cooperated.The dilemma here is (c). In other words, two players (two prisoners in the classic version of prisoner's dilemma) faced the dilemma where despite mutual cooperation having more benefit than mutual defection, if both players yield to the temptation to sell out their opponent in a one-sided defection, the result will end in mutual defection.If the prisoner's dilemma game is played a known finite number of times, theoretically, the game will never end in cooperation (Axelrod, 1984; Luce 85 Raiffa, 1957). This is because as long as the number of moves is known and finite, on the last move, the game will result in mutual since there is no future; this is the same as playing the game once. On the next-to-last move, both players defect since they can expect mutual on the last move. …