�yInteraction Systems about Caring: Game Theoretic Analysis�z

MASAYOSHI MUTO

Caring about others is clearly one of the most important themes about social sciences. Yet social systems theory has not tackled it very well. Because social systems theory, for example Luhmann, has kept boundary of one�fs own interest and other�fs interest ambiguous. But in the present day we don�ft rely generally on existence of common interests so that we take it for granted that yours are yours and mine are mine. From this reality we should construct social systems theory with regard to caring about others.

Caring about others is relevant to interaction system. Because it is mutually that we care about others in everyday life. Therefore we adopt game theory as interaction system theory that clearly distinguishes between one�fs own interest and other�fs interest as payoff system.

On the other hand, in the social value theory (that has been developed in experimental social psychology) caring about others is regarded as ways of other regarding. Basically the ways of other regarding is expressed by the linear combination of one�fs own payoff and the other�fs payoff. 

Then the purpose of this research is to clear what ways of other-regarding can lead to Pareto-efficiency in any mutual interactions. We define a Way of Other-Regarding (=WOR) as evaluation of players�f objective payoffs (including own payoff). In this research we assume that all players take the same WOR. WOR include altruism, egoism and competition etc.

A WOR transforms players�f objective payoffs into subjective evaluations, so that �gevaluation matrix�h is generated. The matrix is, so to speak, �gpayoff matrix�h in evaluation level. We assume that each player chooses an action based on an evaluation matrix. Then pure Nash equilibria on an evaluation matrix may be realized as constant social states. Therefore, the research question here is to investigate whether in any games a WOR transforms Pareto-efficient actions on a payoff matrix into pure Nash equilibria on an evaluation matrix.

We show that such a WOR exists and it satisfies �gimpartiality�h which gives the same weight on each player�fs payoff including own payoff. 

Keywords caring about others, egalitarianism, impartiality