Relationship between aggregation of rewards and the possibility of polymorphism in continuous snowdrift games.
The existence of intra-population variations in cooperation level has often been reported by some empirical studies. Evolutionary conditions of polymorphism in cooperation have been investigated by using a framework of the continuous snowdrift game. However, our insights from this framework have been limited because of an assumption that the cooperative reward is a function of total amount of investments within an interacting group. In many cases, payoffs may actually depend on the interactions between the effects of such investments, such as members share the sum of beneficial effects that are individually produced from their own investments. Alternatively, payoffs may depend multiplicatively on investment, such as when investments are complementary. In the present paper, we investigated the influence of such difference on the evolution of cooperation with respect to three aspects of the aggregating process of individuals' contributions for reward, i.e. (i) additive or multiplicative, (ii) aggregation of either investments or effects, and (iii) promotion of advantage or suppression of disadvantage. We analytically show that the possibilities of the emergence of polymorphism are different depending on the type of aggregation process classified from these three aspects. Polymorphism of cooperation level never emerges unless the aggregation process is the aggregation of investment or the multiplicative aggregation of effect with suppression of disadvantage. Our results show the necessary condition for the emergence of polymorphic cooperation levels that are observed in various taxonomic groups.
Center for Ecological Research, Kyoto University, Hirano 2-509-3, Otsu 520-2113, Japan. Electronic address: hmito@outlook.com.
Koichi
K
Ito
Department of Evolutionary Studies of Biosystems, School of Advanced Sciences, The Graduate University for Advanced Studies (SOKENDAI), Shonan Village, Hayama, Kanagawa 240-0193, Japan.
Hisashi
H
Ohtsuki
Center for Ecological Research, Kyoto University, Hirano 2-509-3, Otsu 520-2113, Japan.
Atsushi
A
Yamauchi
D000465:Algorithms; D005075:Biological Evolution; D003299:Cooperative Behavior; D019143:Evolution, Molecular; D005716:Game Theory; D008962:Models, Theoretical; D010641:Phenotype; D011157:Population Dynamics; D000068956:Prisoner Dilemma; D011336:Probability; D012201:Reward; D012641:Selection, Genetic
Adaptive dynamics; Common good; Variance in cooperation