Abstract
Cooperation, both intraspecific and interspecific, is a well-documented phenomenon in nature that is not well understood. Evolutionary game theory is a powerful tool to approach this problem. However, it has important limitations. First, very often it is not obvious which game is more appropriate to use. Second, in general, identical payoff matrices are assumed for all players, a situation that is highly unlikely in nature. Third, slight changes in these payoff values can dramatically alter the outcomes. Here, I use an evolutionary spatial model in which players do not have a universal payoff matrix, so no payoff parameters are required. Instead, each is equipped with random values for the payoffs, fulfilling the constraints that define the game(s). These payoff matrices evolve by natural selection. Two versions of this model are studied. First is a simpler one, with just one evolving payoff. Second is the “full” version, with all the four payoffs evolving. The fraction of cooperator agents converges in both versions to nonzero values. In the case of the full version, the initial heterogeneity disappears and the selected game is the “Stag Hunt.”
Highlights
Mutualism, symbiotic relations, and altruistic behavior are ubiquitous in nature [1, 2]
All the agents that have a temptation T < 1/2 = R are marked in gray. Notice that they are a subset of the C agents
The simplest version of this evolving payoffs model produces the evolution of cooperation
Summary
Symbiotic relations, and altruistic behavior are ubiquitous in nature [1, 2]. 2 × 2 games, that is, 2 players making a choice between 2 alternatives to cooperate (C) or to defect (D), are useful to model very different individuals, from viruses [6] to humans [7, 8]. Their application to diverse ecological issues is quite common [9, 10]. I analyze the “full” version in which all the four payoffs are evolving variables (i.e., with no payoff parameters) This introduces unexpected remarkable changes: first, the natural selection process yields a homogeneous or almost homogeneous distribution of payoff matrices. These payoff matrices correspond, in the great majority of cases, to the SH game
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