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Cuaresma DCN, Chiba E, Tubay JM, Rabajante JF, Gavina MKA, Yoshimura J, Ito H, Okabe T, Morita S. Optimal strategies and cost-benefit analysis of the [Formula: see text]-player weightlifting game. Sci Rep 2022; 12:8482. [PMID: 35589925 PMCID: PMC9120137 DOI: 10.1038/s41598-022-12394-z] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/05/2022] [Accepted: 04/27/2022] [Indexed: 11/08/2022] Open
Abstract
The study of cooperation has been extensively studied in game theory. Especially, two-player two-strategy games have been categorized according to their equilibrium strategies and fully analysed. Recently, a grand unified game covering all types of two-player two-strategy games, i.e., the weightlifting game, was proposed. In the present study, we extend this two-player weightlifting game into an [Formula: see text]-player game. We investigate the conditions for pure strategy Nash equilibria and for Pareto optimal strategies, expressed in terms of the success probability and benefit-to-cost ratio of the weightlifting game. We also present a general characterization of [Formula: see text]-player games in terms of the proposed game. In terms of a concrete example, we present diagrams showing how the game category varies depending on the benefit-to-cost ratio. As a general rule, cooperation becomes difficult to achieve as group size increases because the success probability of weightlifting saturates towards unity. The present study provides insights into achieving behavioural cooperation in a large group by means of a cost-benefit analysis.
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Affiliation(s)
- Diane Carmeliza N. Cuaresma
- Graduate School of Science and Technology, Shizuoka University, Hamamatsu, Shizuoka 423-8561 Japan
- Institute of Mathematical Sciences and Physics, College of Arts and Sciences, University of the Philippines Los Baños, 4031 Laguna, Philippines
| | - Erika Chiba
- Graduate School of Informatics, Nagoya University, Furo-cho, Chikusa-ku, Nagoya, 464-8601 Japan
| | - Jerrold M. Tubay
- Institute of Mathematical Sciences and Physics, College of Arts and Sciences, University of the Philippines Los Baños, 4031 Laguna, Philippines
| | - Jomar F. Rabajante
- Institute of Mathematical Sciences and Physics, College of Arts and Sciences, University of the Philippines Los Baños, 4031 Laguna, Philippines
| | - Maica Krizna A. Gavina
- Institute of Mathematical Sciences and Physics, College of Arts and Sciences, University of the Philippines Los Baños, 4031 Laguna, Philippines
| | - Jin Yoshimura
- Graduate School of Science and Technology, Shizuoka University, Hamamatsu, Shizuoka 423-8561 Japan
- Department of International Health and Medical Anthropology, Institute of Tropical Medicine, Nagasaki University, Nagasaki, 852-8523 Japan
- Department of Biological Sciences, Tokyo Metropolitan University, Hachioji, Tokyo, 192-0397 Japan
- The University Museum, University of Tokyo, Bunkyo-ku, Tokyo, 113-0033 Japan
| | - Hiromu Ito
- Department of International Health and Medical Anthropology, Institute of Tropical Medicine, Nagasaki University, Nagasaki, 852-8523 Japan
| | - Takuya Okabe
- Graduate School of Integrated Science and Technology, Shizuoka University, Hamamatsu, Shizuoka 423-8561 Japan
| | - Satoru Morita
- Graduate School of Science and Technology, Shizuoka University, Hamamatsu, Shizuoka 423-8561 Japan
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