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Imitation-Induced Criticality: Network Reciprocity and Psycho-logical Reward

The nodes of a regular two-dimensional lattice play a game based on the joint action of two distinct levels. At the first step of the game, using a random prescription half players are assigned the cooperation and half the defection state. At the bottom level the strategy choice is done on the mere basis of imitation according to the homo imitans principle, generating a form of collective intelligence that makes the system sensitive to the criteria determining the strategy choice adopted at the top level. The units of the top level, in fact, play the prisoner's dilemma game and are allowed to update their strategy either by selecting the strategy of the most successful nearest neighbor, success model, or merely on the basis of the criterion of the best financial benefit, selfishness model. The intelligence emerging from imitation-induced criticality leads in the former case to the extinction of defection and in the latter case to the extinction of cooperation. The former case is interpreted as a form of network reciprocity enhanced by the imitation-induced criticality and contributing to the evolution towards cooperation. We perturb the selfishness model with a form of morality pressure, exerted by a psychological reward Lambda for cooperation, to establish the sensitivity of collective intelligence to morality. We find that when Lambda gets a crucial value Lambda-c, exceeding the temptation to cheat, the system makes a transition from the supercritical defection state to the critical regime, with the warning that an excess of morality and religion pressure may annihilate the criticality-induced resilience of the system.