Evolution of emotions on networks leads to the evolution of cooperation in social dilemmas

Abstract

We show that the resolution of social dilemmas in random graphs and scale-free networks is facilitated by imitating not the strategy of better-performing players but, rather, their emotions. We assume sympathy and envy to be the two emotions that determine the strategy of each player in any given interaction, and we define them as the probabilities of cooperating with players having a lower and a higher payoff, respectively. Starting with a population where all possible combinations of the two emotions are available, the evolutionary process leads to a spontaneous fixation to a single emotional profile that is eventually adopted by all players. However, this emotional profile depends not only on the payoffs but also on the heterogeneity of the interaction network. Homogeneous networks, such as lattices and regular random graphs, lead to fixations that are characterized by high sympathy and high envy, while heterogeneous networks lead to low or modest sympathy but also low envy. Our results thus suggest that public emotions and the propensity to cooperate at large depend, and are in fact determined by, the properties of the interaction network.

Evolution of cooperation driven by the diversity of emotions

“…By using a genetic algorithm we have studied the evolutionary process of these quantities within the framework of Prisoner's Dilemma game. As this finding is different from the results in (Szolnoki et al 2011(Szolnoki et al , 2013, we have demonstrated that the emotional diversity of individuals can evolve to a state where diversity is maintained. Furthermore, this emotional diversity of individuals can result in the boost of cooperation.…”

“…In Section 2, we introduce the applied microscopic model and discuss some consequences of emotional diversity. The difference between references (Szolnoki et al, 2011;Szolnoki et al, 2013) and this study is that the emotional model in (Szolnoki et al 2011(Szolnoki et al , 2013 has two parameters (α, β), whereas we establish an emotional model with four parameters {W , D, α, β}, where two types of compassion and harshness attitude to a weaker one and two types of respect and envy attitude to a stronger one are considered. Our results are presented in Section 3, and in Section 4 we summarise the results and outline some biological implications of our findings.…”

“…Could the endogenous feelings produce altruistic behaviour? The studies in Szolnoki, Xie, Wang, andPerc (2011) andSzolnoki, Xie, Ye, andPerc (2013) have presented the idea that not strategies but rather emotions could be the subject of imitation during the evolutionary process. The emotional profile of each player is determined by two pivotal factors, namely how it behaves towards less and how towards more successful neighbours.…”

Layla and Majnun: a complex love story

“…There is a growing interest in using mathematics and computational methods in psychology [1][2][3][4][5][6][7][8][9][10]. Some mathematicians and psychologists have introduced mathematical models for romantic relationships [3,7,[11][12][13][14][15][16][17][18][19][20][21][22][23][24][25][26][27][28].…”

Time-Delay Induced Dimensional Crossover in the Voter Model

“…When a delay time is comparable to or larger than characteristic time scales, the time delay brings about rich phenomena. It leads to multistable synchronized states for phase oscillators [1][2][3][4][5][6][7], amplitude death for coupled limitcycle oscillators [8,9], stabilization of periodic orbits in chaotic systems [10], a resonant behavior in stochastic systems [11][12][13], dynamic instability in feedback control systems [14], a pattern formation in evolutionary game dynamics [15,16], and so on.In this Letter, we investigate the effects of time delay on the ordering dynamics in the context of the voter model (VM). The VM is a prototypical model for opinion dynamics [17][18][19][20][21][22].…”