The Algebra of Assortative Encounters and the Evolution of Cooperation

This paper explores the quantitative relation between non-random, as- sortative matching and the maintenance of cooperative behavior under evo- lutionary dynamics. Section 2 develops an \algebra of assortative encoun- ters" and de¯nes an index of assortativity of encounters. This section then applies the index of assortativity to study population dynamics under the assumption that the type with the higher payo® increases its proportion in the population. Section 3 calculates the index of assortativity for games be- tween relatives where it is assumed that behavior of o®spring is determined by either cultural or genetical inheritance. This section shows the logical connection between the index of assortativity and Hamilton's theory of kin selection [5]. Section 4 explores the index of assortativity and population dynamics for a model in which players select their partners, using partially informative cues about each others' types.