Seeding the Spatial Prisoner’s Dilemma with Ulam’s Spiral
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 s...
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| Format: | Article |
| Language: | English |
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Wiley
2023-01-01
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| Series: | Complexity |
| Online Access: | http://dx.doi.org/10.1155/2023/1649440 |
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| author | Tim Johnson |
| author_facet | Tim Johnson |
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| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-5a95fc0e7cc34411ad51245414ee1d40 |
| institution | Kabale University |
| issn | 1099-0526 |
| language | English |
| publishDate | 2023-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Complexity |
| spelling | doaj-art-5a95fc0e7cc34411ad51245414ee1d402025-02-03T01:29:28ZengWileyComplexity1099-05262023-01-01202310.1155/2023/1649440Seeding the Spatial Prisoner’s Dilemma with Ulam’s SpiralTim Johnson0Atkinson Graduate School of ManagementUlam’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.http://dx.doi.org/10.1155/2023/1649440 |
| spellingShingle | Tim Johnson Seeding the Spatial Prisoner’s Dilemma with Ulam’s Spiral Complexity |
| title | Seeding the Spatial Prisoner’s Dilemma with Ulam’s Spiral |
| title_full | Seeding the Spatial Prisoner’s Dilemma with Ulam’s Spiral |
| title_fullStr | Seeding the Spatial Prisoner’s Dilemma with Ulam’s Spiral |
| title_full_unstemmed | Seeding the Spatial Prisoner’s Dilemma with Ulam’s Spiral |
| title_short | Seeding the Spatial Prisoner’s Dilemma with Ulam’s Spiral |
| title_sort | seeding the spatial prisoner s dilemma with ulam s spiral |
| url | http://dx.doi.org/10.1155/2023/1649440 |
| work_keys_str_mv | AT timjohnson seedingthespatialprisonersdilemmawithulamsspiral |