Title: An evolutionary game with environmental feedback and players' opinions

Abstract: Evolutionary games are a developing sub-field of game theory. This branch of game theory is used in the study of the adaptation of large, but finite, populations of agents to changes in the environment. It assumes that each agent has no significant influence on the system. Many scientific areas use the theory of evolutionary games. In particular, it is used in biology, medicine and the modelling of wireless networks. In this paper we study an evolutionary game with two levels of interaction between population agents. At the first level, changes in the population state depend on changes in the environment and on increasing or decreasing the resources available to the agents. At the second level, the populations state changes according to how the agents evaluate the state of the environment. These levels form a hierarchical structure. A change in one parameter of the system, which is responsible for the state of the environment, the population or the opinions of the agents, causes a change in the other elements of the system. The study involves the analysis of a modified evolutionary game taking into account the influence of the environment and the opinions of the agents. It also involves the development of computational methods in MATLAB and two sets of numerical experiments.