Co-operation is pervasive in human societies, but the evolutionary origins of co-operation are still incompletely understood. One prominent hypothesis for explaining co-operation is kin selection, whereby individuals accrue fitness benefits by helping close relatives who share many of their genes. Evolutionary game theory has been used to study the evolution of co-operation and kin selection, but until now it has been technically challenging to analyse scenarios where the benefits scale nonlinearly with the number of co-operators, which can occur, e.g., when there are economies of scale in a group activity such as a hunt.
In a new paper led by Nadiah Kristensen, we present a new mathematical method for rigorously accounting for relatedness in evolutionary models with an arbitrary number of players and an arbitrary number of discrete strategies, e.g., co-operators and defectors. We demonstrate the method with an application to a game in which the benefit to individuals rises sharply once some threshold number of co-operators is passed, representing, e.g., a successful hunt. In addition to unconditional co-operators and unconditional defectors, we allow a cognitively advanced strategy: co-ordinated co-operators, who conduct a lottery prior to each game to ensure that the threshold number of co-operators is attained. We find that co-ordinated co-operation is favoured by kin selection. However, if we allow homophily to decline, as happened over the course of human evolution, co-ordinated co-operators can be invaded by another cognitively advanced strategy, the liar, who participates in lotteries but does not follow through on commitments to co-operate. For coordinated cooperation to resist invasion by liars, either some level of homophily must be maintained, or following through on the agreement after a lottery must be in players’ self interest.
Our approach will be broadly useful for exploring the evolution of co-operation in other scenarios involving cognitively advanced strategies that arise from leaps of insight into how the game works. Such scenarios could include, for example, the evolution of punishment and enforcement institutions.
Nadiah was until last year a Research Fellow in our lab, and she is now working at the University of Queensland. This paper was part of an ongoing collaboration with Hisashi Ohtsuki at The Graduate University for Advanced Studies in Japan.
Chisholm Lab 