On Altruism and Spite in Bimatrix Games

TL;DR

This paper explores how altruism and spite influence bimatrix games, analyzing their impact on the complexity and approximation of Nash equilibria through theoretical and experimental methods.

Contribution

It introduces the study of algorithmic implications of altruism and spite in bimatrix games, including complexity, equilibrium quality, and learning opponent behavior.

Findings

Altruism and spite alter the complexity of finding Nash equilibria.

Experimental results show effects of altruism/spite on equilibrium approximation.

Potential to learn and exploit opponent's altruistic/spiteful tendencies.

Abstract

One common assumption in game theory is that any player optimizes a utility function that takes into account only its own payoff. However, it has long been observed that in real life players may adopt an altruistic or even spiteful behaviour. As such, there are numerous attempts in the economics literature that strive to explain the fact that players are not entirely selfish, but most of these works do not focus on the algorithmic implications of altruism or spite in games. In this paper, we relax the aforementioned ``self-interest'' assumption, and initiate the study of algorithmic aspects of bimatrix games -- such as the complexity and the quality of their (approximate) Nash equilibria -- under altruism or spite. We provide both a theoretical and an experimental treatment of these topics. Moreover, we demonstrate the potential for learning the degree of an opponent's altruistic/spiteful behaviour, and employing this for opponent selection and transfer of knowledge in bimatrix games.