Randomized matrix games in a finite population: Effect of stochastic fluctuations in the payoffs on the evolution of cooperation
| Autor: | Cong Li, Sabin Lessard |
|---|---|
| Rok vydání: | 2020 |
| Předmět: |
0106 biological sciences
0301 basic medicine Computer Science::Computer Science and Game Theory education.field_of_study Population size Population Prisoner Dilemma Prisoner's dilemma Expected value Covariance Biological Evolution 010603 evolutionary biology 01 natural sciences 03 medical and health sciences 030104 developmental biology Game Theory Order (exchange) Pairwise comparison Cooperative Behavior education Mathematical economics Ecology Evolution Behavior and Systematics Selection (genetic algorithm) Mathematics |
| Zdroj: | Theoretical Population Biology. 134:77-91 |
| ISSN: | 0040-5809 |
| DOI: | 10.1016/j.tpb.2020.04.006 |
| Popis: | A diffusion approximation for a randomized 2 × 2-matrix game in a large finite population is ascertained in the case of random payoffs whose expected values, variances and covariances are of order given by the inverse of the population size N . Applying the approximation to a Randomized Prisoner’s Dilemma (RPD) with independent payoffs for cooperation and defection in random pairwise interactions, conditions on the variances of the payoffs for selection to favor the evolution of cooperation, favor more the evolution of cooperation than the evolution of defection, and disfavor the evolution of defection are deduced. All these are obtained from probabilities of ultimate fixation of a single mutant. It is shown that the conditions are lessened with an increase in the variances of the payoffs for defection against cooperation and defection and a decrease in the variances of the payoffs for cooperation against cooperation and defection. A RPD game with independent payoffs whose expected values are additive is studied in detail to support the conclusions. Randomized matrix games with non-independent payoffs, namely the RPD game with additive payoffs for cooperation and defection based on random cost and benefit for cooperation and the repeated RPD game with Tit-for-Tat and Always-Defect as strategies in pairwise interactions with a random number of rounds, are studied under the assumption that the population-scaled expected values, variances and covariances of the payoffs are all of the same small enough order. In the first model, the conditions in favor of the evolution of cooperation hold only if the covariance between the cost and the benefit is large enough, while the analysis of the second model extends the results on the effects of the variances of the payoffs for cooperation and defection found for the one-round RPD game. |
| Databáze: | OpenAIRE |
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