An axiomatic system of social motivations in dyadic relation: Potential existence of altruism and egalitarianism

The purpose of this paper is to deduce axiomatically a bilateral evaluation function that has various meanings on caring about the other e.g. equalitarian, maximin, competition etc. The evaluation function of one's and the other's payoffs looks like a little complicated including absolute value, but the function can be deduced from very simple axioms. Concretely speaking, the axioms are (1) comparable payoffs between actors and (2) positive affine transformation constancy on payoffs and evaluations respectively. These two axioms look like not including equality, but the evaluation function from the axioms includes equality. Because increasing affine transformation keeps the order property of payoffs. By the way the equality is defined as-|x-y| where x is one's payoff and y is the other's payoff. Then the asymmetric property of absolute value of equality originates from the asymmetric property of the order of payoffs.