title: Evolutionary dynamics of n-player games played by relatives.
abstract: One of the core concepts in social evolution theory is kin selection. Kin selection provides a perspective to understand how natural selection operates when genetically similar individuals are likely to interact. A family-structured population is an excellent example of this, where relatives are engaged in social interactions. Consequences of such social interactions are often described in game-theoretical frameworks, but there is a growing consensus that a naive inclusive fitness accounting with dyadic relatedness coefficients are of limited use when non-additive fitness effects are essential in those situations. Here, I provide a general framework to analyse multiplayer interactions among relatives. Two important results follow from my analysis. First, it is generally necessary to know the n-tuple genetic association of family members when n individuals are engaged in social interactions. However, as a second result, I found that, for a special class of games, we need only measures of lower-order genetic association to fully describe its evolutionary dynamics. I introduce the concept of degree of the game and show how this degree is related to the degree of genetic association.
authors.affiliation: Department of Evolutionary Studies of Biosystems, School of Advanced Sciences, The Graduate University for Advanced Studies (SOKENDAI), , Shonan Village, Hayama, Kanagawa 240-0193, Japan.
authors.forename: Hisashi
authors.initials: H
authors.lastname: Ohtsuki
mesh_terms: D000818:Animals; D005075:Biological Evolution; D005716:Game Theory; D005717:Games, Experimental; D005828:Genetics, Population / Q000379:methods*; D008954:Models, Biological; D012641:Selection, Genetic / Q000235:genetics*; D012919:Social Behavior
keywords: cooperation; family group; game theory; kin selection; relatedness