The co-evolution of networks and prisoner’s dilemma game by considering sensitivity and visibility

Abstract

Strategies adopted by individuals in a social network significantly impact the network, and they strongly affect relationships between individuals in the network. Links between individuals also heavily influence their levels of cooperation. Taking into account the evolution of each individual’s connection, we explore how sensitivity and visibility affect the prisoner’s dilemma game. The so-called ‘sensitivity’ and ‘visibility’ respectively present one’s self-protection consciousness and the ability of gaining information. We find that at moderate levels of player sensitivity cooperative behavior increases, but that at high levels it is inhibited. We also find that the heterogeneity of the weight of individuals at the end of the game is higher when sensitivity and visibility are increased, but that the successful-defection-payoff has less impact on the weight of individuals and on the relationship between the heterogeneity of the weight of individuals and the density of cooperators. This framework can be used to clarify the interaction mechanism between the micro-level of individual behavior and the macro-level of individual co-evolutionary processes.

A further analysis of the role of heterogeneity in coevolutionary spatial games

“…Studies on weighted networks have attracted much attention as such networks enable the representation of the strength of each connection, which is essential information in a wide range of real-world scenarios including biological networks and social media. Recently, both the Prisoner's Dilemma and the Optional Prisoner's Dilemma games have been explored in the context of dynamic weighted networks, which lead to a coevolutionary scenario where not only the game strategies, but also the link weights, evolve over time [32,33,34,35,36]. Moreover, it has been shown that the use of dynamic weighted networks can increase heterogeneity of states (i.e., the number of possible utilities in the network), which in turn induces the promotion of cooperation.…”

Rethinking network reciprocity over social ties: local interactions make direct reciprocity possible and pave the rational way to cooperation

“…Optional participation is known to relax social dilemmas when a baseline payoff is granted to loners, 11,26 whereas link disconnection has been recently considered. 27 Our link inhibition is temporary and grants no profit to C's. We prefer abstention rather than forcing retaliation-cooperators defecting neighboring exploiters-because this is more connatural to the C mood.…”

“…Reciprocity is implemented by allowing C's to selectively abstain from playing for a few game rounds with exploiting neighbors. 11,26,27 So doing, C's reduce exploitation risks-with respect to unconditional C's-and, at the same time, communicate their mood, thus increasing their chances to reciprocate cooperation in future interactions. We name this new mechanism for the social evolution of cooperation networked rational reciprocity.…”

Aplicación De Un Modelo De Teoría Evolutiva De Juegos en Procesos De Cooperación

“…Como se puede apreciar, si los jugadores deciden cooperar entre ellos, van a obtener una recompensa (R), pero, si un jugador decide cooperar y el otro lo traiciona, quien coopera obtendrá en pago del bobo (S) y el traidor mayor pago dentro del juego (T) (Li, Ma, Mei , Tian, & Stanley, 2017) considerando esto, la solución clásica del dilema del prisionero se da cuando los jugadores deciden no cooperar obteniendo un pago P. Si bien es cierto, y como ya se expuso con anterioridad, la cooperación entre las partes (pago R) es, en un sentido empírico, la actitud estratégica más conveniente para los jugadores, considerando que R>P.…”