Diffusion sustains cooperation via forming diverse spatial patterns in prisoner's dilemma game

Liu, Yan-Ping; Wang, Lin; Zhang, Feng; Wang, Ruiwu

doi:10.1016/j.amc.2020.125077

Cited by 3 publications

(3 citation statements)

References 49 publications

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“…Te model begins with cooperators located at the primenumbered values of Ulam's spiral, while defectors are located at composite values of Ulam's spiral. Given evidence that the initial fraction of cooperators [92] and the spatial pattern of cooperators [93] infuence the evolution of cooperation in the spatial prisoner's dilemma, it warrants mentioning that seeding the model with cooperators at the prime-number locations of Ulam's spiral results in a constant fraction and fxed pattern of cooperators (at g � 1) for any given value of n.…”

Section: Methodsmentioning

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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Section: Methodsmentioning

confidence: 99%

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

Johnson

2023

Complexity

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“…Over the past two decades, network science has made huge progresses that help us to cope with some pending and challenging problems, such as social evolution dynamics [5,6], traffic jam [7,8] and epidemic spreading [9,10]. Taking the complex network and game dynamics as a universal framework, where networks stipulate the population topology and games depict interactions between individuals, and combining other approaches of social science and statistical physics such as Monte Carlo (MC) simulation and mean-field approximation, evolutionary game theory (EGT) has become an important method to study the evolution of pro-social behavior and collective cooperation [11].…”

Section: Introductionmentioning

confidence: 99%

“…In recent years, formation and evolution of trust has attracted the great attention in the field of theoretical economics [12,13], behavioral economics [14,15], social psychology [16] and even cognitive neuroscience [17]. However, based on the networked population, previous studies often focus on the traditional game models such as the snowdrift game (SDG) [18][19][20], prisoner's dilemma game (PDG) [21][22][23] and public goods game(PGG) [24][25][26], while the trust game in the networked population has drawn the less concern, especially for researchers in the field of EGT and network science.…”

Section: Introductionmentioning

confidence: 99%

Costly reputation building still promotes the collective trust within the networked population

Xia

Hu²,

Zhao³

2022

New J. Phys.

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Trust is of vital importance to economic development, social harmony, political stability and cultural succession in the real world, and then understanding how trust emerges and evolves in a selfish population has long been a significant and challenging issue. From the perspective of trustees, we investigate how reputation building and cost for trustees with dynamic adaptive reputation affect the evolution of trust. Trustees can spend specific funds or costs to build or maintain their reputation, which then enhances their own social competitiveness during the trust evolution. Considering the heterogeneity of individual cost, sigmoid function is used to describe the relationship between reputation and cost. It is found that trust and trustworthiness could still emerge and persist even if reputation building is costly. Meanwhile, the moderate level of willingness to build the reputation or the middle reputation cost is more conducive to the evolution of trust, otherwise it could result in the deterioration of trust behaviors among agents. The current results are helpful to illustrate the evolution of trust and cooperation within the networked population.

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Islands of cooperation emerge by stigmergic interactions in iterated spatial games

Zambonelli,

Bergenti,

Mariani

et al. 2024

PLoS ONE

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This article focuses on the emergence of cooperation in societies of self-interested agents. In particular, it introduces a mechanism based on indirect—stigmergic—interactions between agents moving in an environment, to express the likeliness of finding cooperative partners. On the one hand, agents that find themselves cooperating with others emit pheromones in their current location, expressing the presence of agents willing to cooperate. On the other hand, agents that sense pheromones tend to move towards regions with a higher pheromone concentration. Results show that this mechanism leads to the emergence of spatial regions where cooperation can be effectively sustained, and in which agents can overall get better payoffs than those agents not taking into account pheromones in their choices.

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Diffusion sustains cooperation via forming diverse spatial patterns in prisoner's dilemma game

Cited by 3 publications

References 49 publications

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

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

Costly reputation building still promotes the collective trust within the networked population

Islands of cooperation emerge by stigmergic interactions in iterated spatial games

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