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Ito H, Tanimoto J. Dynamic utility: the sixth reciprocity mechanism for the evolution of cooperation. ROYAL SOCIETY OPEN SCIENCE 2020; 7:200891. [PMID: 32968531 PMCID: PMC7481712 DOI: 10.1098/rsos.200891] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 06/05/2020] [Accepted: 07/07/2020] [Indexed: 06/11/2023]
Abstract
Game theory has been extensively applied to elucidate the evolutionary mechanism of cooperative behaviour. Dilemmas in game theory are important elements that disturb the promotion of cooperation. An important question is how to escape from dilemmas. Recently, a dynamic utility function (DUF) that considers an individual's current status (wealth) and that can be applied to game theory was developed. The DUF is different from the famous five reciprocity mechanisms called Nowak's five rules. Under the DUF, cooperation is promoted by poor players in the chicken game, with no changes in the prisoner's dilemma and stag-hunt games. In this paper, by comparing the strengths of the two dilemmas, we show that the DUF is a novel reciprocity mechanism (sixth rule) that differs from Nowak's five rules. We also show the difference in dilemma relaxation between dynamic game theory and (traditional) static game theory when the DUF and one of the five rules are combined. Our results indicate that poor players unequivocally promote cooperation in any dynamic game. Unlike conventional rules that have to be brought into game settings, this sixth rule is universally (canonical form) applicable to any game because all repeated/evolutionary games are dynamic in principle.
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Affiliation(s)
- Hiromu Ito
- Department of International Health and Medical Anthropology, Institute of Tropical Medicine, Nagasaki University, Nagasaki 852-8523, Japan
| | - Jun Tanimoto
- Department of Energy and Environmental Engineering, Interdisciplinary Graduate School of Engineering Sciences, Kyushu University, Fukuoka 816-8580, Japan
- Department of Advanced Environmental Science and Engineering, Faculty of Engineering Sciences, Kyushu University, Fukuoka 816-8580, Japan
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Ito H. Risk sensitivity of a forager with limited energy reserves in stochastic environments. Ecol Res 2019. [DOI: 10.1111/1440-1703.1058] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Affiliation(s)
- Hiromu Ito
- Department of General Systems Studies The University of Tokyo Tokyo Japan
- Department of International Health Institute of Tropical Medicine, Nagasaki University Nagasaki Japan
- Department of Environmental Sciences, Zoology University of Basel Basel Switzerland
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Ito H, Katsumata Y, Hasegawa E, Yoshimura J. The promotion of cooperation by the poor in dynamic chicken games. Sci Rep 2017; 7:43377. [PMID: 28233837 PMCID: PMC5324166 DOI: 10.1038/srep43377] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/01/2016] [Accepted: 01/23/2017] [Indexed: 11/09/2022] Open
Abstract
The evolution of cooperative behavior is one of the most important issues in game theory. Previous studies have shown that cooperation can evolve only under highly limited conditions, and various modifications have been introduced to games to explain the evolution of cooperation. Recently, a utility function basic to game theory was shown to be dependent on current wealth as a conditional (state) variable in a dynamic version of utility theory. Here, we introduce this dynamic utility function to several games. Under certain conditions, poor players exhibit cooperative behavior in two types of chicken games (the hawk-dove game and the snowdrift game) but not in the prisoner’s dilemma game and the stag hunt game. This result indicates that cooperation can be exhibited by the poor in some chicken games. Thus, the evolution of cooperation may not be as limited as has been suggested in previous studies.
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Affiliation(s)
- Hiromu Ito
- Department of International Health, Institute of Tropical Medicine, Nagasaki University, Nagasaki, 852-8523, Japan.,Graduate School of Science and Technology, Shizuoka University, Hamamatsu, 432-8561, Japan
| | - Yuki Katsumata
- Department of Mathematical and Systems Engineering, Shizuoka University, Hamamatsu, 432-8561, Japan
| | - Eisuke Hasegawa
- Laboratory of Animal Ecology, Department of Ecology and Systematics, Graduate School of Agriculture, Hokkaido University, Sapporo 060-8589, Japan
| | - Jin Yoshimura
- Graduate School of Science and Technology, Shizuoka University, Hamamatsu, 432-8561, Japan.,Department of Mathematical and Systems Engineering, Shizuoka University, Hamamatsu, 432-8561, Japan.,Department of Environmental and Forest Biology, State University of New York College of Environmental Science and Forestry, Syracuse, NY 13210, USA.,Marine Biosystems Research Center, Chiba University, Uchiura, Kamogawa, Chiba 299-5502, Japan
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