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Király B, Varga T, Szabó G, Garay J. Evolutionarily stable payoff matrix in hawk-dove games. BMC Ecol Evol 2024; 24:65. [PMID: 38769504 PMCID: PMC11107024 DOI: 10.1186/s12862-024-02257-8] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/05/2024] [Accepted: 05/15/2024] [Indexed: 05/22/2024] Open
Abstract
BACKGROUND Classical matrix game models aim to find the endpoint of behavioural evolution for a set of fixed possible interaction outcomes. Here, we introduce an evolutionary model in which not only the players' strategies but also the payoff matrix evolves according to natural selection. RESULTS We start out from the hawk-dove matrix game and, in a way that is consistent with the monomorphic model setup of Maynard Smith and Price, introduce an evolving phenotypic trait that quantifies fighting ability and determines the probability of winning and the cost of losing escalated hawk-hawk fights. We define evolutionarily stable phenotypes as consisting of an evolutionarily stable strategy and an evolutionarily stable trait, which in turn describes a corresponding evolutionarily stable payoff matrix. CONCLUSIONS We find that the maximal possible cost of escalating fights remains constant during evolution assuming a separation in the time scales of fast behavioural and slow trait selection, despite the fact that the final evolutionarily stable phenotype maximizes the payoff of hawk-hawk fights. Our results mirror the dual nature of Darwinian evolution whereby the criteria of evolutionary success, as well as the successful phenotypes themselves, are a product of natural selection.
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Affiliation(s)
- Balázs Király
- Institute of Technical Physics and Materials Science, HUN-REN Centre for Energy Research, Konkoly-Thege Miklós út 29-33., Budapest, H-1121, Hungary.
| | - Tamás Varga
- Bolyai Institute, University of Szeged, Aradi vértanúk tere 1., Szeged, H-6720, Hungary
| | - György Szabó
- Institute of Technical Physics and Materials Science, HUN-REN Centre for Energy Research, Konkoly-Thege Miklós út 29-33., Budapest, H-1121, Hungary
- Institute of Evolution, HUN-REN Centre for Ecological Research, Konkoly-Thege Miklós út 29-33., Budapest, H-1121, Hungary
| | - József Garay
- Institute of Evolution, HUN-REN Centre for Ecological Research, Konkoly-Thege Miklós út 29-33., Budapest, H-1121, Hungary
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Abstract
Reputation and reciprocity are key mechanisms for cooperation in human societies, often going hand in hand to favor prosocial behavior over selfish actions. Here we review recent researches at the interface of physics and evolutionary game theory that explored these two mechanisms. We focus on image scoring as the bearer of reputation, as well as on various types of reciprocity, including direct, indirect, and network reciprocity. We review different definitions of reputation and reciprocity dynamics, and we show how these affect the evolution of cooperation in social dilemmas. We consider first-order, second-order, as well as higher-order models in well-mixed and structured populations, and we review experimental works that support and inform the results of mathematical modeling and simulations. We also provide a synthesis of the reviewed researches along with an outlook in terms of six directions that seem particularly promising to explore in the future.
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Affiliation(s)
- Chengyi Xia
- School of Artificial Intelligence, Tiangong University, Tianjin 300384, China
| | - Juan Wang
- School of Electrical Engineering and Automation, Tianjin University of Technology, Tianjin 300384, China.
| | - Matjaž Perc
- Faculty of Natural Sciences and Mathematics, University of Maribor, Koroška cesta 160, 2000 Maribor, Slovenia; Department of Medical Research, China Medical University Hospital, China Medical University, Taichung 404332, Taiwan; Alma Mater Europaea, Slovenska ulica 17, 2000 Maribor, Slovenia; Complexity Science Hub Vienna, Josefstädterstraße 39, 1080 Vienna, Austria
| | - Zhen Wang
- Center for OPTical IMagery Analysis and Learning (OPTIMAL), Northwestern Polytechnical University, Xian 710072, China.
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Garay J, Móri TF. Best Reply Player Against Mixed Evolutionarily Stable Strategy User. Bull Math Biol 2021; 84:23. [PMID: 34951688 PMCID: PMC8709824 DOI: 10.1007/s11538-021-00980-7] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/11/2021] [Accepted: 11/25/2021] [Indexed: 11/26/2022]
Abstract
We consider matrix games with two phenotypes (players): one following a mixed evolutionarily stable strategy and another one that always plays a best reply against the action played by its opponent in the previous round (best reply player, BR). We focus on iterated games and well-mixed games with repetition (that is, the mean number of repetitions is positive, but not infinite). In both interaction schemes, there are conditions on the payoff matrix guaranteeing that the best reply player can replace the mixed ESS player. This is possible because best reply players in pairs, individually following their own selfish strategies, develop cycles where the bigger payoff can compensate their disadvantage compared with the ESS players. Well-mixed interaction is one of the basic assumptions of classical evolutionary matrix game theory. However, if the players repeat the game with certain probability, then they can react to their opponents’ behavior. Our main result is that the classical mixed ESS loses its general stability in the well-mixed population games with repetition in the sense that it can happen to be overrun by the BR player.
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Affiliation(s)
- József Garay
- Institute of Evolution, Centre for Ecological Research, Konkoly-Thege Miklós út 29-33, Budapest, 1121, Hungary.
- ELKH-ELTE Theoretical Biology and Evolutionary Ecology Research Group, Loránd Eötvös University, Pázmány Péter sétány 1/c, Budapest, 1117, Hungary.
| | - Tamás F Móri
- Alfréd Rényi Institute of Mathematics, Reáltanoda u. 13-15, Budapest, 1053, Hungary
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Kayser K, Lampert A. Survivor's dilemma: The evolution of cooperation in volatile environments. J Theor Biol 2021; 516:110603. [PMID: 33508324 DOI: 10.1016/j.jtbi.2021.110603] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/10/2020] [Revised: 12/02/2020] [Accepted: 01/21/2021] [Indexed: 11/25/2022]
Abstract
The volatility of an environment significantly impacts cooperative behavior. In environments where viability-threatening events occur on a shorter timescale than reproduction, it is reasonable to measure the costs and benefits of cooperation in terms of their direct effect on survival probability. Then, the number of offspring increases with lifespan. With such a model, is it possible for cooperation to be evolutionarily stable, and how does cooperation depend on the benefit and cost of such interactions, and the volatility of the environment? In this paper, we develop an N-player survivor's dilemma in which prisoner's dilemma payoffs in an iteration are survival rates, and expected lifespan is the measure of reproductive fitness. We investigate cost, benefit, and volatility parameter ranges where various cooperative behaviors may occur. We observe that free-riding results in indirect punishment as the cheated partner's early death leaves the defector vulnerable. For 2- and 3-player versions of the game, we identify parameter regions where the repeated game becomes equivalent to a Harmony, Stag Hunt, or Prisoner's Dilemma static game and discuss evolutionary stability. We find that with two individuals, the initial fraction of cooperators necessary for cooperation to be selected for decreases as the benefit to cost ratio increases and as environmental volatility decreases. With the presence of a third individual, there also exists a parameter region where cooperation can invade an initially all-defecting population.
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Affiliation(s)
- Kirk Kayser
- Department of Mathematics and Actuarial Science, Otterbein University, Westerville, OH 43081, USA
| | - Adam Lampert
- School of Human Evolution and Social Change, Arizona State University, Tempe, AZ 85287, USA; Simon A. Levin Mathematical, Computational and Modeling Science Center, Arizona State University, Tempe, AZ 85287, USA
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Garay J, Garay BM, Varga Z, Csiszár V, Móri TF. To save or not to save your family member's life? Evolutionary stability of self-sacrificing life history strategy in monogamous sexual populations. BMC Evol Biol 2019; 19:147. [PMID: 31324139 PMCID: PMC6642471 DOI: 10.1186/s12862-019-1478-0] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/27/2019] [Accepted: 07/16/2019] [Indexed: 11/10/2022] Open
Abstract
BACKGROUND For the understanding of human nature, the evolutionary roots of human moral behaviour are a key precondition. Our question is as follows: Can the altruistic moral rule "Risk your life to save your family members, if you want them to save your life" be evolutionary stable? There are three research approaches to investigate this problem: kin selection, group selection and population genetics modelling. The present study is strictly based on the last approach. RESULTS We consider monogamous and exogamous families, where at an autosomal locus, dominant-recessive alleles determine the phenotypes in a sexual population. Since all individuals' survival rate is determined by their altruistic family members, we introduce a new population genetics model based on the mating table approach and adapt the verbal definition of evolutionary stability to genotypes. In general, when the resident is recessive, a homozygote is an evolutionarily stable genotype (ESG), if the number of survivors of the resident genotype of the resident homozygote family is greater than that of non-resident heterozygote survivors of the family of the resident homozygote and mutant heterozygote genotypes. Using the introduced genotype dynamics we proved that in the recessive case ESG implies local stability of the altruistic genotype. We apply our general ESG conditions for self-sacrificing life history strategy when the number of new-born offspring does not depend on interactions within the family and the interactions are additive. We find that in this case our ESG conditions give back Hamilton's rule for evolutionary stability of the self-sacrificing life history strategy. CONCLUSIONS In spite of the fact that the kidney transplantations was not a selection factor during the earlier human evolution, nowadays "self-sacrificing" can be observed in the live donor kidney transplantations, when the donor is one of the family members. It seems that selection for self-sacrificing in family produced an innate moral tendency in modulating social cognition in human brain.
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Affiliation(s)
- József Garay
- MTA Centre for Ecological Research, Evolutionary Systems Research Group, Klebelsberg Kuno u. 3, Tihany, H-8237, Hungary. .,MTA-ELTE Research Group in Theoretical Biology and Evolutionary Ecology and Department of Plant Systematics, Ecology and Theoretical Biology, ELTE Eötvös Loránd University, Pázmány P. s. 1/C, Budapest, H-1117, Hungary.
| | - Barnabás M Garay
- Faculty of Information Technology and Bionics, Pázmány Péter Catholic University, Práter u. 50/A, Budapest, H-1083, Hungary
| | - Zoltán Varga
- Department of Mathematics, Szent István University, Páter K. u. 1, Gödöllő, H-2103, Hungary
| | - Villő Csiszár
- Department of Probability Theory and Statistics, Eötvös Loránd University, Pázmány P. s. 1/C, Budapest, H-1117, Hungary
| | - Tamás F Móri
- Department of Probability Theory and Statistics, Eötvös Loránd University, Pázmány P. s. 1/C, Budapest, H-1117, Hungary
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Garay J, Varga Z, Móri TF, López I, Gámez M, Gallego JR, Cabello T. Opportunistic random searcher versus intentional search image user. Sci Rep 2018; 8:3336. [PMID: 29463915 PMCID: PMC5820282 DOI: 10.1038/s41598-018-21563-y] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/26/2017] [Accepted: 02/06/2018] [Indexed: 11/30/2022] Open
Abstract
We consider two types of optimal foragers: a random searcher and a search image user. A search image user can find its desired prey with higher and undesired prey with lower probability than a random searcher. Our model considers the density-dependent travelling time and the time duration of reproduction (oviposition). In the framework of optimal foraging theory for one predator-two prey systems, we find that there are ranges of prey densities in which the search image user has a higher net energy intake, and there are other ranges of prey densities in which the random searcher has higher net energy intake. The damsel bug Nabis pseudoferus Remane (Hemiptera: Nabidae) is a generalist predator rather than an omnivore. This species has a wide range of arthropod prey (predominantly insects and mites). Several aspects of the biology of this species have been studied, especially its cannibalistic behaviour, which is a quite important feature because N. pseudoferus is often used as a biological control agent against lepidopteran pests in greenhouse crops. Experimentally, we found that Nabis is a search image user in the above sense.
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Affiliation(s)
- József Garay
- MTA-ELTE Theoretical Biology and Evolutionary Ecology Research Group and Department of Plant Systematics, Ecology and Theoretical Biology, Eötvös Loránd University, Pázmány Péter sétány1/c, H-1117, Budapest, Hungary.
- MTA Centre for Ecological Research, Evolutionary Systems Research Group., Klebelsberg Kuno utca 3, Tihany, 8237, Hungary.
| | - Zoltán Varga
- Department of Mathematics, Szent István University, Páter K. u. 1.H-2103, Gödöllő, Hungary
| | - Tamás F Móri
- Department of Probability Theory and Statistics, L. Eötvös University, Pázmány Péter sétány1/c, H-1117, Budapest, Hungary
| | - Inmaculada López
- Department of Mathematics, University of Almería. La Cañada de San Urbano, 04120, Almería, Spain
| | - Manuel Gámez
- Center for Agribusiness Biotechnology Research, Almería University, Ctra. Sacramento s/n, ES-04120, Almería, Spain
| | - Juan R Gallego
- Center for Agribusiness Biotechnology Research, Almería University, Ctra. Sacramento s/n, ES-04120, Almería, Spain
| | - Tomás Cabello
- Center for Agribusiness Biotechnology Research, Almería University, Ctra. Sacramento s/n, ES-04120, Almería, Spain
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Garay J, Cressman R, Xu F, Varga Z, Cabello T. Optimal Forager against Ideal Free Distributed Prey. Am Nat 2015; 186:111-22. [PMID: 26098343 DOI: 10.1086/681638] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/03/2022]
Affiliation(s)
- József Garay
- Hungarian Academy of Sciences-Eötvös University (MTA-ELTE) Theoretical Biology and Evolutionary Ecology Research Group; and Department of Plant Systematics, Ecology and Theoretical Biology, Eötvös University, Pázmány Péter sétány 1/c, H-1117 Budapest, Hungary
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Kingma SA, Santema P, Taborsky M, Komdeur J. Group augmentation and the evolution of cooperation. Trends Ecol Evol 2014; 29:476-84. [PMID: 24996259 DOI: 10.1016/j.tree.2014.05.013] [Citation(s) in RCA: 79] [Impact Index Per Article: 7.9] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/18/2013] [Revised: 05/02/2014] [Accepted: 05/30/2014] [Indexed: 11/24/2022]
Abstract
The group augmentation (GA) hypothesis states that if helpers in cooperatively breeding animals raise the reproductive success of the group, the benefits of living in a resulting larger group--improved survival or future reproductive success--favour the evolution of seemingly altruistic helping behaviour. The applicability of the GA hypothesis remains debatable, however, partly owing to the lack of a clear conceptual framework and a shortage of appropriate empirical studies. We conceptualise here the GA hypothesis and illustrate that benefits of GA can accrue via different evolutionary mechanisms that relate closely to well-supported general concepts of group living and cooperation. These benefits reflect several plausible explanations for the evolutionary maintenance of helping behaviour in cooperatively breeding animals.
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Affiliation(s)
- Sjouke A Kingma
- School of Biological Sciences, University of East Anglia, Norwich, UK; Behavioural Ecology and Self-Organization Group, Centre for Ecological and Evolutionary Studies, University of Groningen, Groningen, The Netherlands; Max Planck Institute for Ornithology, Vogelwarte Radolfzell, Radolfzell, Germany.
| | - Peter Santema
- Behavioural Ecology and Self-Organization Group, Centre for Ecological and Evolutionary Studies, University of Groningen, Groningen, The Netherlands; Department of Zoology, University of Cambridge, Cambridge, UK
| | - Michael Taborsky
- Department of Behavioral Ecology, Institute of Ecology and Evolution, University of Bern, Hinterkappelen, Switzerland
| | - Jan Komdeur
- Behavioural Ecology and Self-Organization Group, Centre for Ecological and Evolutionary Studies, University of Groningen, Groningen, The Netherlands
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Garay J, Csiszár V, Móri TF. Under multilevel selection: "when shall you be neither spiteful nor envious?". J Theor Biol 2014; 340:73-84. [PMID: 24041593 DOI: 10.1016/j.jtbi.2013.08.031] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/09/2013] [Revised: 08/13/2013] [Accepted: 08/26/2013] [Indexed: 11/20/2022]
Abstract
In this paper, we study the egalitarianism-game in multilevel selection situation. The individuals form reproductive groups. In each group, an egalitarianism-game determines the number of juveniles of different phenotypes (spiteful, envious, neutral and donator). Before the juveniles form the next reproductive group, they have to survive either predators' attacks or a fight between two groups. We adopt the ESS definition of Maynard Smith to multilevel selection. Based on the "group size advantage" assumption (which claims that each juvenile's survival rate depends on the size of his own group, supposing that either the survival rate under predators' attacks is higher in larger groups, or in inter-group aggression usually the larger group wins) we found that when the survival probability has a massive effect on the average fitness, then "group fitness maximizing behavior" (in our case, either neutral or donator) has evolutionary advantage over "competitive behavior" (in our case, either spiteful or envious).
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Affiliation(s)
- József Garay
- Research Group of Theoretical Biology and Ecology of the Hungarian Academy of Sciences, Department of Plant Systematics, Ecology and Theoretical Biology, L. Eötvös University, Pázmány Péter sétány 1/c, H-1117 Budapest, Hungary.
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