Altruistic Duality in Evolutionary Game Theory

Through the modeling of ecosystems, evolutionary game theory brings such diverse fields as biology, ecology, economics and sociology under the umbrella of mathematical sciences [1, 2, 3]. One central objective of evolutionary game theory is to understand the workings of cooperative behavior among the individuals in an ecosystem. Since the publication of the work by Axelrot on the prisoner’s dilemma [4], it is generally understood that the concept of altruism holds a key to the emergence of cooperative behavior. While egoism, defined as the drive toward maximization of individual payoffs, is a cornerstone of game theory, casual observation reveals that altruism is just as universal a feature as egoism in systems consisting of like individuals. Altruism has obtained mathematical expression in the work of Bester and Güth [5], in which altruistic behavior is shown to become evolutionarily stable in certain situations through the enhancement of fitness of a majority of individuals in a system. While their mathematical treatment is general and elegant, it is formulated in static and descriptive language. Bringing in dynamics to the model would give it more predictive power.