Unintended effects of caring: 2×2 symmetric game structure transformations through various mutual caring

The purpose of this paper is to clarify social effects of mutual caring, by using game theory. We treat only 2×2 symmetric games that are twelve types in all. We define "way of caring" by "altruistic" and "egalitarian" parameters. We pick up thirteen ways of caring, for example altruism, competition, egalitarianism etc. Caring about the other transforms objective payoff structure into subjective payoff structure. As a result of analyzing this transformation we obtain following findings. (1) Almost all the payoff-structures can be transformed into all the payoff-structures in 2×2 symmetric games by changing the values of "altruistic" and "egalitarian" parameters. (2) It depends on game type whether a way of caring causes Pareto-inefficiency or not. For example, "poor loser" in other words the anti-altruistic and egalitarian causes Pareto-inefficiency in prisoners' dilemmas and chicken games. (3) The most frequent about causing Pareto-inefficiency are "competition" and "sacrifice" (7 games in 12 games). The second most frequent is "anti-egalitarianism" (6 games). On the other hand "egalitarianism" is less frequent (2 games), so that "egalitarianism" is good not only in equality but also in Pareto-efficiency. In fact both "egoism" and " altruism" are least frequent (1 game) except "maxmin", "maxmax", and "sum-ranking" (0 games). We clarify the ranking of "ways of caring" about causing Pareto-inefficiency in 2×2 symmetric games.