Interaction between games give rise to the evolution of moral norms of cooperation

Abstract

In many biological populations, such as human groups, individuals face a complex strategic setting, where they need to make strategic decisions over a diverse set of issues and their behavior in one strategic context can affect their decisions in another. This raises the question of how the interaction between different strategic contexts affects individuals’ strategic choices and social norms? To address this question, I introduce a framework where individuals play two games with different structures and decide upon their strategy in a second game based on their knowledge of their opponent’s strategy in the first game. I consider both multistage games, where the same opponents play the two games consecutively, and reputation-based model, where individuals play their two games with different opponents but receive information about their opponent’s strategy. By considering a case where the first game is a social dilemma, I show that when the second game is a coordination or anti-coordination game, the Nash equilibrium of the coupled game can be decomposed into two classes, a defective equilibrium which is composed of two simple equilibrium of the two games, and a cooperative equilibrium, in which coupling between the two games emerge and sustain cooperation in the social dilemma. For the existence of the cooperative equilibrium, the cost of cooperation should be smaller than a value determined by the structure of the second game. Investigation of the evolutionary dynamics shows that a cooperative fixed point exists when the second game belongs to coordination or anti-coordination class in a mixed population. However, the basin of attraction of the cooperative fixed point is much smaller for the coordination class, and this fixed point disappears in a structured population. When the second game belongs to the anti-coordination class, the system possesses a spontaneous symmetry-breaking phase transition above which the symmetry between cooperation and defection breaks. A set of cooperation supporting moral norms emerges according to which cooperation stands out as a valuable trait. Notably, the moral system also brings a more efficient allocation of resources in the second game. This observation suggests a moral system has two different roles: Promotion of cooperation, which is against individuals’ self-interest but beneficial for the population, and promotion of organization and order, which is at both the population’s and the individual’s self-interest. Interestingly, the latter acts like a Trojan horse: Once established out of individuals’ self-interest, it brings the former with itself. Importantly, the fact that the evolution of moral norms depends only on the cost of cooperation and is independent of the benefit of cooperation implies that moral norms can be harmful and incur a pure collective cost, yet they are just as effective in promoting order and organization. Finally, the model predicts that recognition noise can have a surprisingly positive effect on the evolution of moral norms and facilitates cooperation in the Snow Drift game in structured populations.

Evolution as a result of resource flow in ecosystems: Ecological dynamics can drive evolution

“…While the framework can readily be used to consider any interaction, as an example, I study the evolution of cooperation in public goods game, a classic problem in evolutionary game theory [ 20 , 26 – 30 ] and experimental economics [ 31 – 33 ] and of interest in a wide range of issues from strategic interactions between animals and humans [ 15 , 26 – 28 , 31 , 34 – 37 ] to common resource management [ 38 , 39 ]. I show that the evolution of cooperation is no longer a puzzle in this framework.…”

Cooperation dynamics in multiple correlated games: A review

“…in the fluctuation of payoffs [14,15,[20][21][22], the two or more evolutionary games played in parallel within oneshot interaction [23,24] or the repeated interactions [17], the occurrence of crosstalk, where an individual's behavior in one game will affect his action in the other game [16], the multistage games with different payoff structures exhibiting interdependence [25,26]. There may be definite or implicit stakes between different game scenarios, and regardless of the specific form of correlation between different games, ultimately it manifests as a reciprocal influence between payoffs and strategies, leading to changes in evolutionary dynamics.…”

“…Venkateswaran et al [42] studied multiple games with multiplayer, they showed that the combined dynamics cannot be captured by only single-game dynamics if the game has more than two strategies. Salahshour [25] set up the reputation-building mechanism and decisionmaking mechanism at different games, which provided a new way to solve the problem of self-reference in the indirect reciprocity model.…”