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The outbreak of cooperation among success-driven individuals under noisy conditions

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According to Thomas Hobbes' Leviathan [1651; 2008 (Touchstone, New York), English Ed], "the life of man [is] solitary, poor, nasty, brutish, and short," and it would need powerful social institutions to establish social order. In reality, however, social cooperation can also arise spontaneously, based on local interactions rather than centralized control. The self-organization of cooperative behavior is particularly puzzling for social dilemmas related to sharing natural resources or creating common goods. Such situations are often described by the prisoner's dilemma. Here, we report the sudden outbreak of predominant cooperation in a noisy world dominated by selfishness and defection, when individuals imitate superior strategies and show success-driven migration. In our model, individuals are unrelated, and do not inherit behavioral traits. They defect or cooperate selfishly when the opportunity arises, and they do not know how often they will interact or have interacted with someone else. Moreover, our individuals have no reputation mechanism to form friendship networks, nor do they have the option of voluntary interaction or costly punishment. Therefore, the outbreak of prevailing cooperation, when directed motion is integrated in a game-theoretical model, is remarkable, particularly when random strategy mutations and random relocations challenge the formation and survival of cooperative clusters. Our results suggest that mobility is significant for the evolution of social order, and essential for its stabilization and maintenance.
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... Remarkably, as an important reference and an enlightening attempt, Helbing et al. soon conceive an elaborate model embedded with profit-maximization-driven migration [22]. By means of the so-called cost-free fictitious interaction, for the first time, they spark an explosion of cooperation by deterministic migration in a noisy environment where defection completely dominates. ...
... By comparison, so far, it is not difficult to find that Helbing et al. mainly focus on where to move [22], nevertheless others give more weight to when to leave [24][25][26][27][28][29][30], resulting in the biggest gap between them. In either case, however, existing literatures have more or less imposed an aversion to defection during migration. ...
... Compared with existing work, this operation seems to be more strategy-neutral. Therefore, migration in this article is often risky due to the absence of optimal relocation as generated by the success-driven migration [22], which constitutes the most striking feature of this design. n s i denotes the number of strategy s i , n i the size of i's neighborhood excluding unoccupied vacancies, and π a the average payoff of i's neighborhood before the current iteration. ...
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... Within an adaptive migration model, agents move to more favourable regions of the network in order to boost their payoff. The foundational example here is Helbing and Yu (2009), whose model was a lattice containing more sites than agents. Each agent was given knowledge of the payoff that would ensue by moving to an empty site within a Moore neighbourhood of range M . ...
... This knowledge takes diverse forms, e.g., the neighbourhood (Santos et al., 2006b), strategy (Zimmermann et al., 2004) or reputation (Fu et al., 2008) of a network neighbour. In the case of adaptive migration, agents are ascribed with knowledge of the potential payoff from moving to unoccupied slots of the lattice (Helbing and Yu, 2009). This knowledge is then applied during the network update phase of the model to guide the agent's rewiring strategy. ...
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... The research in this field is focused on the proportion and distribution of the number of nodes in different states [6,7]. Accordingly, scholars have tried to understand the evolution of cooperation in terms of social connections, such as the migration of individuals [8], dynamic networks [9,10], and temporal networks [11]. In real interaction scenarios, such as narrow altruism [12], preference for fairness [13,14], individual emotions [15,16], disease transmission dynamics [17] and biological systems [18], numerous examples demonstrate individuals adaptively adjusting their strategies based on the reactions of their opponents. ...
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... Organisms usually have the ability to change their neighbors by traveling to different locations. To account for this, models have introduced mobility in a variety of forms: random dispersal [24][25][26][27][28][29], moving away from unfavorable locations [30][31][32][33], and successdriven mobility where individuals tend towards locations with greater benefits [34][35][36][37]. ...
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... Promoting cooperation between individuals will make a society flourish. To that end, mechanisms such as migration [7], reputation [8], rewarding the cooperators [9] or punishing the defectors has been studied throughout different games or dilemmas. Punishing can be done either by social exclusion [10] or by a monetary fine [11]. ...
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