Social Dilemmas with Continuous Traits

Author: Christoph Hauert

Traditionally in both classical as well as evolutionary game theory a finite set of discrete strategies is assumed a priori. When discussing the evolution of cooperation in social dilemmas, the simplest set of strategies consists of two types, cooperators and defectors. Cooperators provide benefits to other individuals at some cost to themselves. In contrast, defectors attempt free ride on the contributions of others. This leads to a classic conflict of interest between the individual's and the group (pair) performance - and hence the dilemma. The game dynamics then determines the relative frequencies of the different strategies in a population. The problem of cooperation has been extensively studied both for interactions in pairs as well as in larger groups.

From an evolutionary perspective, however, it is essential to understand the emergence of discrete strategies of cooperators and defectors, in particular, to justify these a priori assumptions. Since evolution is a gradual process, it is important to consider continuous variants of game theoretical metaphors for cooperative interactions such as the Prisoner's Dilemma or the Snowdrift game. The essential difference between the two games is that in the Prisoner's Dilemma the benefits of cooperation accrue exclusively to the other individuals whereas in the Snowdrift game the act of cooperation also provides some benefits to the cooperator itself.