Effects of strategy-updating cost on evolutionary spatial prisoner’s dilemma game

Liu, Run-Ran; Jia, Chun-Xiao; Rong, Zhihai

doi:10.1016/j.amc.2020.125445

Cited by 4 publications

(1 citation statement)

References 79 publications

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“…It keeps its strategy if it earned more than its neighbors or if a neighbor using its same strategy earned more. Accordingly, the model uses the original strategy update method of the spatial prisoner's dilemma [17] instead of more-recent novel conceptualizations of the update dynamics [89][90][91].…”

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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Environmental-based defensive promotes cooperation in the prisoner’s dilemma game

Gao

Pan

2021

Applied Mathematics and Computation

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Two-stage strategy update rule based on learning cost in weak prisoner’s dilemma

Gao,

Pan,

2024

Chaos: An Interdisciplinary Journal of Nonlinear Science

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When players are dissatisfied with their actual payoffs, they will change the actuality by learning strategy of neighbors. The more effort players put in, the more likely they are to succeed in learning. Inspired by this, this paper proposes a two-stage strategy update rule based on learning cost. The players first decide whether to learn strategy according to the updating willingness. If the players imitate the strategy of neighbors, they need to pay the learning cost. Results show that for the well-mixed population, if the updating willingness is homogeneous and remains unchanged, reducing the updating willingness or increasing the learning cost can extend the life cycle of cooperators. If the updating willingness is heterogeneous and dynamically adjusted based on the difference between the actual payoff and the expected payoff, increasing aspiration value and learning cost promotes cooperation. For the structured population, if the updating willingness is homogeneous and remains unchanged, the moderate learning cost is beneficial for cooperators to resist the temptation of defection, and reducing updating willingness makes the system maintain cooperation within a larger parameter range. If the updating willingness is heterogeneous and dynamically adjusted, the larger learning cost and the appropriate aspiration value promote cooperation. This study highlights the complex dynamics of cooperation in paid strategy learning, contributing to the theory of cooperation in the evolutionary game.

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Effects of strategy-updating cost on evolutionary spatial prisoner’s dilemma game

Cited by 4 publications

References 79 publications

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

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

Environmental-based defensive promotes cooperation in the prisoner’s dilemma game

Two-stage strategy update rule based on learning cost in weak prisoner’s dilemma

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