4/23/2021 0 Comments Pioneers Of Nowak Board Game
In such cases, the threshold for establishing cooperation, based on the rule b c k, is quite high: the benefit from an altruistic act must be at least 36 times greater than its cost.
![]() We model this phenomenon by introducing game transitions into classical models of evolutionary dynamics. Interacting individuals receive payoffs from the games that they play, and these games can change based on past actions. We find that game transitions can significantly reduce the critical benefit-to-cost threshold for cooperation to evolve in social dilemmas. This result improves our understanding of when cooperators can thrive in nature, even when classical results predict a high critical threshold. Abstract The environment has a strong influence on a populations evolutionary dynamics. Driven by both intrinsic and external factors, the environment is subject to continual change in nature. ![]() Within this model, we study the evolution of cooperation in structured populations and find a simple rule: Weak selection favors cooperation over defection if the ratio of the benefit provided by an altruistic behavior, b, to the corresponding cost, c, exceeds k k, where k is the average number of neighbors of an individual and k captures the effects of the game transitions. Even if cooperation cannot be favored in each individual game, allowing for a transition to a relatively valuable game after mutual cooperation and to a less valuable game after defection can result in a favorable outcome for cooperation. In particular, small variations in different games being played can promote cooperation markedly. Our results suggest that simple game transitions can serve as a mechanism for supporting prosocial behaviors in highly connected populations. Understanding how such a trait can be maintained in a competitive world has long been a focal issue in evolutionary biology and ecology ( 2 ). The spatial distribution of a population makes an individual more likely to interact with neighbors than with those who are more distant. Population structures can affect the evolution of cooperation ( 3 9 ). In viscous populations, ones offspring often stay close to their places of birth. Relatives thus interact more often than 2 random individuals. Compared with the well-mixed setting, population viscosity is known to promote cooperation ( 10 ) although when the population density is fixed, local competition can cancel the cooperation-promoting effect of viscosity ( 11, 12 ). Past decades have seen an intensive investigation of the evolution of cooperation in graph-structured populations ( 6 9 ). One of the best-known findings is that weak selection favors cooperation if the ratio of the benefit provided by an altruistic act, b, to the cost of expressing such an altruistic trait, c, exceeds the average number of neighbors, k (i.e., b c k ) ( 6, 13 ). This simple rule strongly supports the proposition that population structure is one of the major mechanisms responsible for the evolution of cooperation ( 2 ). However, many realistic systems are highly connected, with each individual having many neighbors on average. For example, in a contact network consisting of students from a French high school, each student has 36 neighbors on average, meaning k 36 ( 14 ).
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