Impact of binary social status with hierarchical punishment on the evolution of cooperation in the spatial prisoner’s dilemma game

Xie, Yunya; Zhang, Shuhua; Zhang, Zhipeng; Bu, Hongyu

doi:10.1016/j.chaos.2019.109422

Cited by 8 publications

(1 citation statement)

References 38 publications

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“…Active mechanisms include those in which cooperative individuals behave conditionally to avoid free-riding-for instance, by determining whether to cooperate based on others' shared genes [43], reputations [44][45][46][47], tags [48], or wealth [49][50][51]. Such active mechanisms also include conditional behavior either to sanction defection (e.g., via punishment [14,[52][53][54][55][56][57][58][59], reciprocating defection with defection [36,60], or discontinuing play [61][62][63]) or to repay cooperation (e.g., via reciprocal altruism and rewards [60,64,65]). An adjacent literature, moreover, has recently generalized from the problem of cooperation to consider moral preferences more widely [66] and ofers a new active mechanism for study in the literature on cooperation.…”

Section: Introductionmentioning

confidence: 99%

Seeding the Spatial Prisoner’s Dilemma with Ulam’s Spiral

Johnson

2023

Complexity

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Ulam’s spiral reveals patterns in the prime numbers by presenting positive integers in a right-angled whorl. The classic spatial prisoner’s dilemma (PD) reveals pathways to cooperation by presenting a model of agents interacting on a grid. This paper brings these tools together via a deterministic spatial PD model that distributes cooperators at the prime-numbered locations of Ulam’s spiral. The model focuses on a narrow boundary game variant of the PD for ease of comparison with early studies of the spatial PD. Despite constituting an initially small portion of the population, cooperators arranged in Ulam’s spiral always grow to dominance when (i) the payoff to free-riding is less than or equal to 8/6 (≈1.33) times the payoff to mutual cooperation and (ii) grid size equals or exceeds 23 × 23. As in any spatial PD model, particular formations of cooperators spur this growth and here these formations draw attention to rare configurations in Ulam’s spiral.

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