“対人選択ゲーム”における3人関係過程 I

Abstract

This paper is the first part of the report on an experiment with the three-person interpersonal choice game, conducted for the purpose of obtaining basic information concerning the dynamic aspects of the three-person game-playing processes, including the formation and the disintegration of coalitions.The rules of this game, symmetric over its three players, ask each of them simultaneously to choose on every trial between the two players besides himself (under conditions A and A+) or among the three players including himself (under conditions B, B+, C, C+). In this first report only the results with the conditions A and A+ are reported. The payoff to players (in game points only, no monetary payment given) on each trial consists of three components: the gain for being chosen, the cost for making a choice, and the special bonus for the two players who choose each other (given only under conditions with the plus sign). For details, see Tables 1 and 2.The Ss were college students, 7 triads each for conditions A and A+, and they were encouraged to make as many points as possible through instruction. Each triad was run for more than 210 trials. The choices made by the three players were fed back to them on every trial.In order to interpret the results we need to know the good strategies for playing this game, but the goodness of a strategy obviously depends on the motive each S may entertain for playing this game. We considered as the likely alternatives the motive of maximizing one's own gain and the motive of maximizing the difference in gain between his and the others'. Also, we thought it important to distinguish the span of strategies, between long-range strategies and short-range ones. As for the long-range strategy, it is undoubtedly recommendable under both motives to form a stable mutual choice relation (coalition) and to maintain it, although condition A+ supplies a stronger incentive to this strategy than A. As for the short-range strategies only the motive of maximizing the difference practically counts, and it provides an incentive to desert the coalition partner by shifting one's choice. The changes in the gain and the difference following defection and the expected immediate retaliation (the former coalition partner also shifting his choice) are depicted in Fig. 2, showing that condition A+ also provides a stronger incentive for defection. As a result, it is expected that the rate of coalition formation and disintegration will both be greater under condition A+ than under A, and the result confirmed this expectation.Other major results, obtained mostly by applying the analysis of covariation, a newly developed data analysis technique by Toda, are as follows: The longer a coalition is maintained, the greater the probability of its further continuation. The triad differences are large, but are fairly well represented by setting up four triad categories, αI, αII, βI and βII. Among triads belonging to αI, αII categories, the long range strategies appear popular, and βII triads show a definite favor for the short range ones. The effect of the condition difference upon the overall behavior of triads is far less significant than that of the difference in categories, or strategies employed by each triad.