Natural selection between two games with environmental feedback

Author:

Yuan Hairui1,Meng Xinzhu1,Li Zhenqing2

Affiliation:

1. College of Mathematics and Systems Science, Shandong University of Science and Technology, Qingdao 266590, P. R. China

2. State Key Laboratory of Vegetation and Environmental Change, Institute of Botany, Chinese Academy of Sciences, Beijing 100093, P. R. China

Abstract

Evolutionary game theory has extensively investigated situations in which several games are competing against each other at the same time, but the model only assumes symmetric interactions in homogeneous environments. Now, the population is considered in heterogeneous environments, individuals in the population occupy a different quality of patches, and individual fitness depends not only on the interaction between individuals, but also on the quality of the environment. Here, by establishing a mathematical framework, we analyze the natural selection between two strategies and two games in heterogeneous environments. Furthermore, we analyze the natural selection of Prisoner’s Dilemma and Hawk–Dove games theoretically to demonstrate the dynamics of cooperators and defectors in their choice of environment and their respective games. As expected, the distribution of games and strategies changes with time. Based on different initial population compositions, we also discuss the invasion problem of games from different perspectives. To one’s surprise, we can find that good quality patches attract all individuals; the long-term dynamics in invariant rich environments is the same as the dynamics of symmetric interactions in homogeneous environments.

Funder

Shandong Provincial Natural Science Foundation of China

Taishan Scholar Project of Shandong Province

Publisher

World Scientific Pub Co Pte Ltd

Subject

Applied Mathematics,Modelling and Simulation

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