1
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Hu K, Wang P, He J, Perc M, Shi L. Complex evolutionary interactions in multiple populations. Phys Rev E 2023; 107:044301. [PMID: 37198848 DOI: 10.1103/physreve.107.044301] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/01/2022] [Accepted: 03/22/2023] [Indexed: 05/19/2023]
Abstract
In competitive settings that entail several populations, individuals often engage in intra- and interpopulation interactions that determine their fitness and evolutionary success. With this simple motivation, we here study a multipopulation model where individuals engage in group interactions within their own population and in pairwise interactions with individuals from different populations. We use the evolutionary public goods game and the prisoner's dilemma game to describe these group and pairwise interactions, respectively. We also take into account asymmetry in the extent to which group and pairwise interactions determine the fitness of individuals. We find that interactions across multiple populations reveal new mechanisms through which the evolution of cooperation can be promoted, but this depends on the level of interaction asymmetry. If inter- and intrapopulation interactions are symmetric, the sole presence of multiple populations promotes the evolution of cooperation. Asymmetry in the interactions can further promote cooperation at the expense of the coexistence of the competing strategies. An in-depth analysis of the spatiotemporal dynamics reveals loop-dominated structures and pattern formation that can explain the various evolutionary outcomes. Thus, complex evolutionary interactions in multiple populations reveal an intricate interplay between cooperation and coexistence, and they also open up the path toward further explorations of multipopulation games and biodiversity.
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Affiliation(s)
- Kaipeng Hu
- School of Statistics and Mathematics, Yunnan University of Finance and Economics, Kunming 650221, China
| | - Pengyue Wang
- School of Statistics and Mathematics, Yunnan University of Finance and Economics, Kunming 650221, China
| | - Junzhou He
- School of Statistics and Mathematics, Yunnan University of Finance and Economics, Kunming 650221, China
| | - Matjaž Perc
- Faculty of Natural Sciences and Mathematics, University of Maribor, 2000 Maribor, Slovenia
- Department of Medical Research, China Medical University Hospital, China Medical University, Taichung 404332, Taiwan
- Alma Mater Europaea, 2000 Maribor, Slovenia
- Complexity Science Hub Vienna, 1080 Vienna, Austria
- Department of Physics, Kyung Hee University, 26 Kyungheedae-ro, Dongdaemun-gu, Seoul, Republic of Korea
| | - Lei Shi
- School of Statistics and Mathematics, Yunnan University of Finance and Economics, Kunming 650221, China
- Interdisciplinary Research Institute of Data Science, Shanghai Lixin University of Accounting and Finance, Shanghai 201209, China
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2
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Fang Y, Perc M, Zhang H. A game theoretical model for the stimulation of public cooperation in environmental collaborative governance. ROYAL SOCIETY OPEN SCIENCE 2022; 9:221148. [PMID: 36405643 PMCID: PMC9653250 DOI: 10.1098/rsos.221148] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 09/07/2022] [Accepted: 10/19/2022] [Indexed: 06/16/2023]
Abstract
Digital technologies provide a convenient way for the public to participate in environmental governance. Therefore, by means of a two-stage evolutionary model, a new mechanism for promoting public cooperation is proposed to accomplish environmental collaborative governance. Interactive effects of government-enterprise environmental governance are firstly explored, which is the external atmosphere for public behaviour. Second, the evolutionary dynamics of public behaviour is analysed to reveal the internal mechanism of the emergence of public cooperation in environmental collaborative governance projects. Simulations reveal that the interaction of resource elements between government and enterprise is an important basis for environmental governance performance, and that governments can improve this as well as public cooperation by increasing the marginal governance propensity. Similarly, an increase in the government's fixed expenditure item of environmental governance can also significantly improve government-enterprise performance and public cooperation. And finally, the effect of government's marginal incentive propensity on public environmental governance is moderated by enterprises' marginal environmental governance propensity, so that simply increasing the government's marginal incentive propensity cannot improve the evolutionary stable state of public behaviour under the scenario where enterprises' marginal environmental governance propensity is low.
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Affiliation(s)
- Yinhai Fang
- College of Economics and Management, Nanjing Forestry University, Nanjing 210037, People's Republic of 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
| | - Hui Zhang
- College of Economics and Management, Nanjing Forestry University, Nanjing 210037, People's Republic of China
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3
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Pal S, Hilbe C. Reputation effects drive the joint evolution of cooperation and social rewarding. Nat Commun 2022; 13:5928. [PMID: 36207309 PMCID: PMC9547006 DOI: 10.1038/s41467-022-33551-y] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/27/2022] [Accepted: 09/22/2022] [Indexed: 11/28/2022] Open
Abstract
People routinely cooperate with each other, even when cooperation is costly. To further encourage such pro-social behaviors, recipients often respond by providing additional incentives, for example by offering rewards. Although such incentives facilitate cooperation, the question remains how these incentivizing behaviors themselves evolve, and whether they would always be used responsibly. Herein, we consider a simple model to systematically study the co-evolution of cooperation and different rewarding policies. In our model, both social and antisocial behaviors can be rewarded, but individuals gain a reputation for how they reward others. By characterizing the game’s equilibria and by simulating evolutionary learning processes, we find that reputation effects systematically favor cooperation and social rewarding. While our baseline model applies to pairwise interactions in well-mixed populations, we obtain similar conclusions under assortment, or when individuals interact in larger groups. According to our model, rewards are most effective when they sway others to cooperate. This view is consistent with empirical observations suggesting that people reward others to ultimately benefit themselves. Rewards can motivate people to cooperate, but the evolution of rewarding behavior is itself poorly understood. Here, a game-theoretic analysis shows that reputation effects facilitate the simultaneous evolution of cooperation and social rewarding policies.
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Affiliation(s)
- Saptarshi Pal
- Max Planck Research Group Dynamics of Social Behavior, Max Planck Institute for Evolutionary Biology, 24306, Plön, Germany.
| | - Christian Hilbe
- Max Planck Research Group Dynamics of Social Behavior, Max Planck Institute for Evolutionary Biology, 24306, Plön, Germany
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4
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Zhou X, Belloum A, Lees MH, van Engers T, de Laat C. Costly incentives design from an institutional perspective: cooperation, sustainability and affluence. Proc Math Phys Eng Sci 2022. [DOI: 10.1098/rspa.2022.0393] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/12/2022] Open
Abstract
Incentives are usually introduced by the regulator entity (third-party), to promote cooperation in a market. The implementation of incentives is always costly and thus might fail to be enforced sustainably. This work aims at exploring the effects of incentives from an institutional perspective, while coping with the scenario where the third-party is part of the system but not composed by players. The evolutionary game theory (EGT) framework is applied to identify the incentives that lead to pure cooperation. In contrast to traditional EGT, this paper introduces an elimination mechanism that can reduce the market size. The incentives identified in the EGT analysis are further examined in simulation experiments which measure the market size, affluence and sustainability. The findings show: (1) light punishment leads to a reduction of the market size, yet heavier punishment is beneficial to the market size and wealth; (2) mixed incentives will generally lead to different wealth of the third party and of the participants. While under moderate strength, the wealth of both parties is the same and their overall wealth is maximal; (3) for sustainability, pure punishment (resp. reward) is sustainable (resp. unsustainable), the sustainability of mixed incentives depends on both their strength and agents’ rationality level.
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Affiliation(s)
- Xin Zhou
- Informatics Institute, University of Amsterdam, Amsterdam,The Netherlands
| | - Adam Belloum
- Informatics Institute, University of Amsterdam, Amsterdam,The Netherlands
| | - Michael H. Lees
- Informatics Institute, University of Amsterdam, Amsterdam,The Netherlands
| | - Tom van Engers
- Faculty of Law, University of Amsterdam, Amsterdam,The Netherlands
| | - Cees de Laat
- Informatics Institute, University of Amsterdam, Amsterdam,The Netherlands
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5
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Liu L, Chen X. Indirect exclusion can promote cooperation in repeated group interactions. Proc Math Phys Eng Sci 2022. [DOI: 10.1098/rspa.2022.0290] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/12/2022] Open
Abstract
Social exclusion has been regarded as one of the most effective measures to promote the evolution of cooperation. In real society, the way in which social exclusion works can be direct or indirect. However, thus far there is no related work to explore how indirect exclusion influences the evolution of cooperation from a theoretical perspective. Here, we introduce indirect exclusion into the repeated public goods game where the game organizer probabilistically selects cooperators after the first game round to participate in the following possible game interactions. We then investigate the evolutionary dynamics of cooperation both in infinite and finite well-mixed populations. Through theoretical analysis and numerical calculations, we find that the introduction of indirect exclusion can induce the stable coexistence of cooperators and defectors or the dominance of cooperators, which thus effectively promotes the evolution of cooperation. Besides, we show that the identifying probability of the organizer has a nonlinear effect on public cooperation when its value is lower than an intermediate value, while the higher identifying probability can maintain a high level of cooperation. Furthermore, our results show that increasing the average rounds of game interactions can effectively promote the evolution of cooperation.
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Affiliation(s)
- Linjie Liu
- College of Science, Northwest A & F University, Yangling 712100, People’s Republic of China
- School of Mathematical Sciences, University of Electronic Science and Technology of China, Chengdu 611731, People’s Republic of China
| | - Xiaojie Chen
- School of Mathematical Sciences, University of Electronic Science and Technology of China, Chengdu 611731, People’s Republic of China
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6
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Chowdhury SN, Kundu S, Perc M, Ghosh D. Complex evolutionary dynamics due to punishment and free space in ecological multigames. Proc Math Phys Eng Sci 2021. [DOI: 10.1098/rspa.2021.0397] [Citation(s) in RCA: 16] [Impact Index Per Article: 5.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/13/2022] Open
Abstract
The concurrence of ecological and evolutionary processes often arises as an integral part of various biological and social systems. We here study eco-evolutionary dynamics by adopting two paradigmatic metaphors of social dilemmas with contrasting outcomes. We use the Prisoner’s Dilemma and Snowdrift games as the backbone of the proposed mathematical model. Since cooperation is a costly proposition in the face of the Darwinian theory of evolution, we go beyond the traditional framework by introducing punishment as an additional strategy. Punishers bare an additional cost from their own resources to try and discourage or prohibit free-riding from selfish defectors. Our model also incorporates the ecological signature of free space, which has an altruistic-like impact because it allows others to replicate and potentially thrive. We show that the consideration of these factors has broad implications for better understanding the emergent complex evolutionary dynamics. In particular, we report the simultaneous presence of different subpopulations through the spontaneous emergence of cyclic dominance, and we determine various stationary points using traditional game-theoretic concepts and stability analysis.
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Affiliation(s)
- Sayantan Nag Chowdhury
- Physics and Applied Mathematics Unit, Indian Statistical Institute, 203 B. T. Road, Kolkata 700108, India
| | - Srilena Kundu
- Physics and Applied Mathematics Unit, Indian Statistical Institute, 203 B. T. Road, Kolkata 700108, India
| | - Matjaž Perc
- Faculty of Natural Sciences and Mathematics, University of Maribor, Koroška cesta 160, 2000 Maribor, Slovenia
- Alma Mater Europaea, Slovenska ulica, 17, 2000 Maribor, Slovenia
- Department of Medical Research, China Medical University Hospital, China Medical University, Taichung, Taiwan
- Complexity Science Hub Vienna, Josefstädterstraße 39, 1080 Vienna, Austria
| | - Dibakar Ghosh
- Physics and Applied Mathematics Unit, Indian Statistical Institute, 203 B. T. Road, Kolkata 700108, India
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7
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Flores LS, Fernandes HCM, Amaral MA, Vainstein MH. Symbiotic behaviour in the public goods game with altruistic punishment. J Theor Biol 2021; 524:110737. [PMID: 33930439 DOI: 10.1016/j.jtbi.2021.110737] [Citation(s) in RCA: 6] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/17/2020] [Revised: 04/12/2021] [Accepted: 04/23/2021] [Indexed: 11/29/2022]
Abstract
Finding ways to overcome the temptation to exploit one another is still a challenge in behavioural sciences. In the framework of evolutionary game theory, punishing strategies are frequently used to promote cooperation in competitive environments. Here, we introduce altruistic punishers in the spatial public goods game. This strategy acts as a cooperator in the absence of defectors, otherwise it will punish all defectors in their vicinity while bearing a cost to do so. We observe three distinct behaviours in our model: i) in the absence of punishers, cooperators (who don't punish defectors) are driven to extinction by defectors for most parameter values; ii) clusters of punishers thrive by sharing the punishment costs when these are low; iii) for higher punishment costs, punishers, when alone, are subject to exploitation but in the presence of cooperators can form a symbiotic spatial structure that benefits both. This last observation is our main finding since neither cooperation nor punishment alone can survive the defector strategy in this parameter region and the specificity of the symbiotic spatial configuration shows that lattice topology plays a central role in sustaining cooperation. Results were obtained by means of Monte Carlo simulations on a square lattice and subsequently confirmed by a pairwise comparison of different strategies' payoffs in diverse group compositions, leading to a phase diagram of the possible states.
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Affiliation(s)
- Lucas S Flores
- Instituto de Física, Universidade Federal do Rio Grande do Sul, CP 15051, CEP 91501-970 Porto Alegre - RS, Brazil
| | - Heitor C M Fernandes
- Instituto de Física, Universidade Federal do Rio Grande do Sul, CP 15051, CEP 91501-970 Porto Alegre - RS, Brazil.
| | - Marco A Amaral
- Instituto de Humanidades, Artes e Ciências, Universidade Federal do Sul da Bahia, CEP, 45638-000 Teixeira de Freitas - BA, Brazil
| | - Mendeli H Vainstein
- Instituto de Física, Universidade Federal do Rio Grande do Sul, CP 15051, CEP 91501-970 Porto Alegre - RS, Brazil.
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8
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Abstract
The combination of complex networks and game theory is one of the most suitable ways to describe the evolutionary laws of various complex systems. In order to explore the evolution of group cooperation in multiple social dilemmas, a model of a group game with a double-layer network is proposed here. Firstly, to simulate a multiplayer game under multiple identities, we combine a double-layer network and public goods game. Secondly, in order to make an individual’s strategy selection process more in line with a practical context, a new strategy learning method that incorporates individual attributes is designed here, referred to as a “public goods game with selection preferences” (PGG-SP), which makes strategic choices that are more humane and diversified. Finally, a co-evolution mechanism for strategies and topologies is introduced based on the double-layer network, which effectively explains the dynamic game process in real life. To verify the role of multiple double-layer networks with a PGG-SP, four types of double-layer networks are applied in this paper. In addition, the corresponding game results are compared between single-layer, double-layer, static, and dynamic networks. Accordingly, the results show that double-layer networks can facilitate cooperation in group games.
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9
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Abstract
Trust and trustworthiness form the basis for continued social and economic interactions, and they are also fundamental for cooperation, fairness, honesty, and indeed for many other forms of prosocial and moral behaviour. However, trust entails risks, and building a trustworthy reputation requires effort. So how did trust and trustworthiness evolve, and under which conditions do they thrive? To find answers, we operationalize trust and trustworthiness using the trust game with the trustor's investment and the trustee's return of the investment as the two key parameters. We study this game on different networks, including the complete network, random and scale-free networks, and in the well-mixed limit. We show that in all but one case, the network structure has little effect on the evolution of trust and trustworthiness. Specifically, for well-mixed populations, lattices, random and scale-free networks, we find that trust never evolves, while trustworthiness evolves with some probability depending on the game parameters and the updating dynamics. Only for the scale-free network with degree non-normalized dynamics, we find parameter values for which trust evolves but trustworthiness does not, as well as values for which both trust and trustworthiness evolve. We conclude with a discussion about mechanisms that could lead to the evolution of trust and outline directions for future work.
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Affiliation(s)
- Aanjaneya Kumar
- Department of Physics, Indian Institute of Science Education and Research, Dr. Homi Bhabha Road, Pune 411008, India
| | - Valerio Capraro
- Department of Economics, Middlesex University, The Burroughs, London NW4 4BT, UK
| | - 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 404, Taiwan.,Complexity Science Hub Vienna, Josefstädterstraße 39, 1080 Vienna, Austria
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10
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Capraro V, Perc M, Vilone D. Lying on networks: The role of structure and topology in promoting honesty. Phys Rev E 2020; 101:032305. [PMID: 32289998 DOI: 10.1103/physreve.101.032305] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/05/2019] [Accepted: 02/24/2020] [Indexed: 06/11/2023]
Abstract
Lies can have a negating impact on governments, companies, and the society as a whole. Understanding the dynamics of lying is therefore of crucial importance across different fields of research. While lying has been studied before in well-mixed populations, it is a fact that real interactions are rarely well-mixed. Indeed, they are usually structured and thus best described by networks. Here we therefore use the Monte Carlo method to study the evolution of lying in the sender-receiver game in a one-parameter family of networks, systematically covering complete networks, small-world networks, and one-dimensional rings. We show that lies that benefit the sender at a cost to the receiver, the so-called black lies, are less likely to proliferate on networks than they do in well-mixed populations. Honesty is thus more likely to evolve, but only when the benefit for the sender is smaller than the cost for the receiver. Moreover, this effect is particularly strong in small-world networks, but less so in the one-dimensional ring. For lies that favor the receiver at a cost to the sender, the so-called altruistic white lies, we show that honesty is also more likely to evolve than it is in well-mixed populations. But contrary to black lies, this effect is more expressed in the one-dimensional ring, whereas in small-world networks it is present only when the cost to the sender is greater than the benefit for the receiver. Last, for lies that benefit both the sender and the receiver, the so-called Pareto white lies, we show that the network structure actually favors the evolution of lying, but this only occurs when the benefit for the sender is slightly greater than the benefit for the receiver. In this case again the small-world topology acts as an amplifier of the effect, while other network topologies fail to do the same. In addition to these main results we discuss several other findings, which together show clearly that the structure of interactions and the overall topology of the network critically determine the dynamics of lying.
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Affiliation(s)
- Valerio Capraro
- Department of Economics, Middlesex University, The Burroughs, London NW4 4BT, United Kingdom
| | - 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 404, Taiwan
- Complexity Science Hub Vienna, Josefstädterstraße 39, 1080 Vienna, Austria
| | - Daniele Vilone
- Laboratory of Agent Based Social Simulation, Institute of Cognitive Science and Technology, National Research Council, Via Palestro 32, 00185 Rome, Italy
- Grupo Interdisciplinar de Sistemas Complejos, Departamento de Matemáticas, Universidad Carlos III de Madrid, 28911 Leganés, Spain
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11
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Góis AR, Santos FP, Pacheco JM, Santos FC. Reward and punishment in climate change dilemmas. Sci Rep 2019; 9:16193. [PMID: 31700020 PMCID: PMC6838173 DOI: 10.1038/s41598-019-52524-8] [Citation(s) in RCA: 25] [Impact Index Per Article: 5.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/20/2019] [Accepted: 09/15/2019] [Indexed: 11/09/2022] Open
Abstract
Mitigating climate change effects involves strategic decisions by individuals that may choose to limit their emissions at a cost. Everyone shares the ensuing benefits and thereby individuals can free ride on the effort of others, which may lead to the tragedy of the commons. For this reason, climate action can be conveniently formulated in terms of Public Goods Dilemmas often assuming that a minimum collective effort is required to ensure any benefit, and that decision-making may be contingent on the risk associated with future losses. Here we investigate the impact of reward and punishment in this type of collective endeavors - coined as collective-risk dilemmas - by means of a dynamic, evolutionary approach. We show that rewards (positive incentives) are essential to initiate cooperation, mostly when the perception of risk is low. On the other hand, we find that sanctions (negative incentives) are instrumental to maintain cooperation. Altogether, our results are gratifying, given the a-priori limitations of effectively implementing sanctions in international agreements. Finally, we show that whenever collective action is most challenging to succeed, the best results are obtained when both rewards and sanctions are synergistically combined into a single policy.
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Affiliation(s)
- António R Góis
- INESC-ID and Instituto Superior Técnico, Universidade de Lisboa, IST-Taguspark, 2744-016, Porto, Salvo, Portugal.,ATP-group, P-2744-016, Porto, Salvo, Portugal.,Unbabel, R. Visc. de Santarém 67B, 1000-286, Lisboa, Portugal
| | - Fernando P Santos
- INESC-ID and Instituto Superior Técnico, Universidade de Lisboa, IST-Taguspark, 2744-016, Porto, Salvo, Portugal.,ATP-group, P-2744-016, Porto, Salvo, Portugal.,Department of Ecology and Evolutionary Biology, Princeton University, Princeton, USA
| | - Jorge M Pacheco
- ATP-group, P-2744-016, Porto, Salvo, Portugal.,Centro de Biologia Molecular e Ambiental, Universidade do Minho, 4710 - 057, Braga, Portugal.,Departamento de Matemática e Aplicações, Universidade do Minho, 4710 - 057, Braga, Portugal
| | - Francisco C Santos
- INESC-ID and Instituto Superior Técnico, Universidade de Lisboa, IST-Taguspark, 2744-016, Porto, Salvo, Portugal. .,ATP-group, P-2744-016, Porto, Salvo, Portugal. .,Machine Learning Group, Université Libre de Bruxelles, Boulevard du Triomphe CP212, 1050, Bruxelles, Belgium.
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