Abstract
Under certain circumstances such as lack of information or bounded rationality, human players can take decisions on which strategy to choose in a game on the basis of simple opinions. These opinions can be modified after each round by observing own or others payoff results but can be also modified after interchanging impressions with other players. In this way, the update of the strategies can become a question that goes beyond simple evolutionary rules based on fitness and become a social issue. In this work, we explore this scenario by coupling a game with an opinion dynamics model. The opinion is represented by a continuous variable that corresponds to the certainty of the agents respect to which strategy is best. The opinions transform into actions by making the selection of an strategy a stochastic event with a probability regulated by the opinion. A certain regard for the previous round payoff is included but the main update rules of the opinion are given by a model inspired in social interchanges. We find that the fixed points of the dynamics of the coupled model are different from those of the evolutionary game or the opinion models alone. Furthermore, new features emerge such as the independence of the fraction of cooperators with respect to the topology of the social interaction network or the presence of a small fraction of extremist players.
Highlights
Evolutionary game theory has been introduced as a framework to study the processes of selection of genes or behaviors in biological and social systems [1,2,3]
We provide an example with a simple model that shows how these ideas can be implemented in practice and how the dynamic and stationary predictions of evolutionary game theory can dramatically change due to the coupling between opinion and games
Let us start by considering a mean-field situation in which in each time step a randomly selected agent interacts with a group formed by four other agents chosen at random
Summary
Evolutionary game theory has been introduced as a framework to study the processes of selection of genes or behaviors in biological and social systems [1,2,3]. In the abstract representation of Equation (1), the addition of a variable of opinion can be modeled as dxi dt dwj ~h(~w,~x), dt where the index describing the opinion j can be continuous or, as in this example, discrete, wj represents the fractions of individuals holding opinion j, g() is a function that relates the opinion j with the probability of playing strategy i and the function h() describes the evolution of the opinions given the state of the system and the outcome of the game.
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