Split or steal or gift: Nash equilibria under altruistically extended payoffs

Incentives for cooperation can come from different conceptual directions, beyond the “sticks and carrots” duality. This paper looks into potential, altruistic extensions of the payoff structure known from the prisoner's dilemma in game theory. The illustration of the payoff extensions happens through the derived game “split or steal”. The notion of altruism has been frequently and increasingly channeled into game theory previously, yet no attempts were found where it affects the design of the payoff matrix directly and explicitly. The aim of this paper is to show that the original payoffs of the game “split or steal”, and of the prisoner's dilemma more broadly, do not cover the full spectrum of human behavior in the strategic dimension of the situation, and that an altruistic adjustment, the “giving as a gift” option, gives space to corresponding incentives. The results are interpreted to be applicable to a number of real-life situations, complex, as well as competitive, both in the corporate and the governmental sphere.

Keywords: game theory, Nash equilibrium, altruism, gift giving, reward scheme