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Chen F, Zhou L, Wang L. Cooperation among unequal players with aspiration-driven learning. J R Soc Interface 2024; 21:20230723. [PMID: 38471536 PMCID: PMC10932695 DOI: 10.1098/rsif.2023.0723] [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: 12/07/2023] [Accepted: 02/14/2024] [Indexed: 03/14/2024] Open
Abstract
Direct reciprocity promotes the evolution of cooperation when players are sufficiently equal, such that they have similar influence on each other. In the light of ubiquitous inequality, this raises the question of how reciprocity evolves among unequal players. Existing studies on inequality mainly focus on payoff-driven learning rules, which rely on the knowledge of others' strategies. However, inferring one's strategy is a difficult task even if the whole interaction history is known. Here, we consider aspiration-driven learning rules, where players seek strategies that satisfy their aspirations based on their own information. Under aspiration-driven learning rules, we explore the evolutionary dynamics among players with inequality in endowments and productivity. We model the interactions among unequal players with asymmetric games and characterize the condition where cooperation is feasible. Remarkably, we find that aspiration-driven learning rules lead to a higher level of cooperation than payoff-driven ones over a wide range of inequality. Moreover, our results show that high aspiration levels are conducive to the evolution of cooperation when more productive players are equipped with higher endowments. Our work highlights the advantages of aspiration-driven learning for promoting cooperation among unequal players and suggests that aspiration-based decision-making may be more beneficial for the collective.
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Affiliation(s)
- Fang Chen
- Center for Systems and Control, College of Engineering, Peking University, Beijing 100871, People’s Republic of China
| | - Lei Zhou
- School of Automation, Beijing Institute of Technology, Beijing 100081, People’s Republic of China
| | - Long Wang
- Center for Systems and Control, College of Engineering, Peking University, Beijing 100871, People’s Republic of China
- Center for Multi-Agent Research, Institute for Artificial Intelligence, Peking University, Beijing 100871, People’s Republic of China
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Khan MMUR, Arefin MR, Tanimoto J. Investigating the trade-off between self-quarantine and forced quarantine provisions to control an epidemic: An evolutionary approach. APPLIED MATHEMATICS AND COMPUTATION 2022; 432:127365. [PMID: 35812766 PMCID: PMC9257552 DOI: 10.1016/j.amc.2022.127365] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 04/18/2022] [Revised: 06/19/2022] [Accepted: 06/26/2022] [Indexed: 06/15/2023]
Abstract
During a pandemic event like the present COVID-19, self-quarantine, mask-wearing, hygiene maintenance, isolation, forced quarantine, and social distancing are the most effective nonpharmaceutical measures to control the epidemic when the vaccination and proper treatments are absent. In this study, we proposed an epidemiological model based on the SEIR dynamics along with the two interventions defined as self-quarantine and forced quarantine by human behavior dynamics. We consider a disease spreading through a population where some people can choose the self-quarantine option of paying some costs and be safer than the remaining ones. The remaining ones act normally and send to forced quarantine by the government if they get infected and symptomatic. The government pays the forced quarantine costs for individuals, and the government has a budget limit to treat the infected ones. Each intervention derived from the so-called behavior model has a dynamical equation that accounts for a proper balance between the costs for each case, the total budget, and the risk of infection. We show that the infection peak cannot be reduced if the authority does not enforce a proactive (quantified by a higher sensitivity parameter) intervention. While comparing the impact of both self- and forced quarantine provisions, our results demonstrate that the latter is more influential to reduce the disease prevalence and the social efficiency deficit (a gap between social optimum payoff and equilibrium payoff).
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Affiliation(s)
- Md Mamun-Ur-Rashid Khan
- Interdisciplinary Graduate School of Engineering Sciences, Kyushu University, Kasuga-koen, Kasuga-shi, Fukuoka 816-8580, Japan
- Department of Mathematics, University of Dhaka, Dhaka 1000, Bangladesh
| | - Md Rajib Arefin
- Interdisciplinary Graduate School of Engineering Sciences, Kyushu University, Kasuga-koen, Kasuga-shi, Fukuoka 816-8580, Japan
- Department of Mathematics, University of Dhaka, Dhaka 1000, Bangladesh
| | - Jun Tanimoto
- Interdisciplinary Graduate School of Engineering Sciences, Kyushu University, Kasuga-koen, Kasuga-shi, Fukuoka 816-8580, Japan
- Faculty of Engineering Sciences, Kyushu University, Kasuga-koen, Kasuga-shi, Fukuoka 816-8580, Japan
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3
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The Effect of Bounded Rationality on Human Cooperation with Voluntary Participation. MATHEMATICS 2022. [DOI: 10.3390/math10091550] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 01/27/2023]
Abstract
The evolution of human cooperation is an important issue concerning social science. A deep understanding of human bounded rationality is a prerequisite for promoting collective cooperation and solving social dilemmas. Here we construct an asymmetric micro-dynamic based on bounded rationality from a micro perspective by combining behavioral economics and cognitive psychology with evolutionary game theory. Asynchronously updated Monte Carlo simulations were conducted where individuals were located on a square lattice to play a voluntary public goods game. The results showed that “free riding” behaviors can be effectively suppressed in most situations. The cooperation level can be obviously enhanced in a population comprising easily satisfied cooperators and greedy defectors. Moreover, essential conditions for the stability of the system are further discussed at the microscopic level, and altruistic behavior can be explained that an individual with lower expectations for or underestimation of a single game is more likely to cooperate. We argue that, compared to traditional approaches, the integration of interdisciplinary ideas should be taken more seriously.
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Arefin MR, Tanimoto J. Impact of the baseline payoff on evolutionary outcomes. Phys Rev E 2021; 104:044314. [PMID: 34781447 DOI: 10.1103/physreve.104.044314] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/29/2021] [Accepted: 10/06/2021] [Indexed: 11/07/2022]
Abstract
Do individuals enjoying a higher baseline payoff behave similarly in competitive scenarios compared to their counterparts? The classical replicator equation does not answer such a question since it is invariant to the background or baseline payoff of individuals. In reality, however, if one's baseline payoff is higher than the possible payoffs of an interaction (or game), the individual may respond generously or indifferently if s(he) is satisfied with the prevailing benchmark payoff. This work intends to explore such a phenomenon within the realm of pairwise interactions-taking the prisoner's dilemma as a metaphor-in well-mixed finite and infinite populations. In this framework, a player uses the payoff (comprising baseline and game payoffs) -expectation difference to estimate a degree of eagerness and, with that degree of eagerness, revises his or her strategy with a certain probability. We adopt two approaches to explore such a context, naming them as the Fermi and imitation processes, in which the former uses a pairwise Femi function and the latter considers the relative fitness to estimate probabilities for strategy revision. In a finite population, we examine the effect of intensities to payoff-expectation and strategic payoff differences (denoted by k_{1} and k_{2}, respectively) as well as the level of contentment (ω) on the fixation probability and fixation time (for a single defector). We observe that the fixation probability surges with the increase of intensity parameters. Nevertheless, the maximum fixation probability may require a substantially larger time to fixate, especially when the expectation is lower than the baseline payoff. This means that cooperators can persist for a longer period of time. A higher expectation or greed, however, considerably reduces the fixation time. Interestingly, our numerical simulation reveals that both approaches are equivalent under weak k_{2}(≪1) in the Fermi process. We further derive mean-field equations for both approaches in the context of an infinite population, where we observe two possible evolutionary consequences: either full-scale defection or the persistence of the initial frequency of cooperators. The latter scenario indicates players' uninterested or neutral behavior in relation to the interaction due to their satisfaction on the baseline payoff.
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Affiliation(s)
- Md Rajib Arefin
- Interdisciplinary Graduate School of Engineering Sciences, Kyushu University, Kasuga-koen, Kasuga-shi, Fukuoka 816-8580, Japan.,Department of Mathematics, University of Dhaka, Dhaka-1000, Bangladesh
| | - Jun Tanimoto
- Interdisciplinary Graduate School of Engineering Sciences, Kyushu University, Kasuga-koen, Kasuga-shi, Fukuoka 816-8580, Japan.,Faculty of Engineering Sciences, Kyushu University, Kasuga-koen, Kasuga-shi, Fukuoka 816-8580, Japan
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5
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Wu Z. Social distancing is a social dilemma game played by every individual against his/her population. PLoS One 2021; 16:e0255543. [PMID: 34339481 PMCID: PMC8328347 DOI: 10.1371/journal.pone.0255543] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/21/2021] [Accepted: 07/16/2021] [Indexed: 11/18/2022] Open
Abstract
Since the outbreak of the global COVID-19 pandemic, social distancing has been known to everyone and recommended almost everywhere everyday. Social distancing has been and will be one of the most effective measures and sometimes, the only available one for fighting epidemics and saving lives. However, it has not been so clear how social distancing should be practiced or managed, especially when it comes to regulating everyone's otherwise normal social activities. The debate on how to implement social distancing often leads to a heated political argument, while research on the subject is lacking. This paper is to provide a theoretical basis for the understanding of the scientific nature of social distancing by considering it as a social dilemma game played by every individual against his/her population. From this perspective, every individual needs to make a decision on how to engage in social distancing, or risk being trapped into a dilemma either exposing to deadly diseases or getting no access to necessary social activities. As the players of the game, the individual's decisions depend on the population's actions and vice versa, and an optimal strategy can be found when the game reaches an equilibrium. The paper shows how an optimal strategy can be determined for a population with either closely related or completely separated social activities and with either single or multiple social groups, and how the collective behaviors of social distancing can be simulated by following every individual's actions as the distancing game progresses. The simulation results for populations of varying sizes and complexities are presented, which not only justify the choices of the strategies based on the theoretical analysis, but also demonstrate the convergence of the individual actions to an optimal distancing strategy in silico and possibly in natura as well, if every individual makes rational distancing decisions.
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Affiliation(s)
- Zhijun Wu
- Graduate Program on Bioinformatics and Computational Biology, Iowa State University, Ames, Iowa, United States of America
- Department of Mathematics, Iowa State University, Ames, Iowa, United States of America
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Arefin MR, Tanimoto J. Imitation and aspiration dynamics bring different evolutionary outcomes in feedback-evolving games. Proc Math Phys Eng Sci 2021. [DOI: 10.1098/rspa.2021.0240] [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
Feedback-evolving games characterize the interplay between the evolution of strategies and environments. Rich dynamics have been derived for such games under the premise of the replicator equation, which unveils persistent oscillations between cooperation and defection. Besides replicator dynamics, here we have employed aspiration dynamics, in which individuals, instead of comparing payoffs with opposite strategies, assess their payoffs by self-evaluation to update strategies. We start with a brief review of feedback-evolving games with replicator dynamics and then comprehensively discuss such games with aspiration dynamics. Interestingly, the tenacious cycles, as perceived in replicator dynamics, cannot be observed in aspiration dynamics. Our analysis reveals that a parameter
θ
—which depicts the strength of cooperation in enhancing the environment—plays a pivotal role in comprehending the dynamics. In particular, with the symmetric aspiration level, if replete and depleted states, respectively, experience Prisoner's Dilemma and Trivial games, the rich environment is achievable only when
θ
> 1. The case
θ
< 1 never allows us to reach the replete state, even with a higher cooperation level. Furthermore, if cooperators aspire less than defectors, then the enhanced state can be achieved with a relatively lower
θ
value compared with the opposite scenario because too much expectation from cooperation can be less beneficial.
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Affiliation(s)
- Md. Rajib Arefin
- Interdisciplinary Graduate School of Engineering Sciences, Kyushu University, Kasuga-koen, Kasuga-shi, Fukuoka 816-8580, Japan
- Department of Mathematics, University of Dhaka, Dhaka 1000, Bangladesh
| | - Jun Tanimoto
- Interdisciplinary Graduate School of Engineering Sciences, Kyushu University, Kasuga-koen, Kasuga-shi, Fukuoka 816-8580, Japan
- Faculty of Engineering Sciences, Kyushu University, Kasuga-koen, Kasuga-shi, Fukuoka 816-8580, Japan
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Shi Z, Wei W, Feng X, Li X, Zheng Z. Dynamic aspiration based on Win-Stay-Lose-Learn rule in spatial prisoner's dilemma game. PLoS One 2021; 16:e0244814. [PMID: 33395443 PMCID: PMC7781394 DOI: 10.1371/journal.pone.0244814] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/10/2020] [Accepted: 12/16/2020] [Indexed: 11/18/2022] Open
Abstract
Prisoner’s dilemma game is the most commonly used model of spatial evolutionary game which is considered as a paradigm to portray competition among selfish individuals. In recent years, Win-Stay-Lose-Learn, a strategy updating rule base on aspiration, has been proved to be an effective model to promote cooperation in spatial prisoner’s dilemma game, which leads aspiration to receive lots of attention. In this paper, according to Expected Value Theory and Achievement Motivation Theory, we propose a dynamic aspiration model based on Win-Stay-Lose-Learn rule in which individual’s aspiration is inspired by its payoff. It is found that dynamic aspiration has a significant impact on the evolution process, and different initial aspirations lead to different results, which are called Stable Coexistence under Low Aspiration, Dependent Coexistence under Moderate aspiration and Defection Explosion under High Aspiration respectively. Furthermore, a deep analysis is performed on the local structures which cause defectors’ re-expansion, the concept of END- and EXP-periods are used to justify the mechanism of network reciprocity in view of time-evolution, typical feature nodes for defectors’ re-expansion called Infectors, Infected nodes and High-risk cooperators respectively are found. Compared to fixed aspiration model, dynamic aspiration introduces a more satisfactory explanation on population evolution laws and can promote deeper comprehension for the principle of prisoner’s dilemma.
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Affiliation(s)
- Zhenyu Shi
- School of Mathematical Sciences, Beihang University, Beijing, China
- Key Laboratory of Mathematics, Informatics and Behavioral Semantics, Ministry of Education, Beijing, China
- Peng Cheng Laboratory, Shenzhen, Guangdong, China
- Beijing Advanced Innovation Center for Big Data and Brain Computing, Beihang University, Beijing, China
| | - Wei Wei
- School of Mathematical Sciences, Beihang University, Beijing, China
- Key Laboratory of Mathematics, Informatics and Behavioral Semantics, Ministry of Education, Beijing, China
- Peng Cheng Laboratory, Shenzhen, Guangdong, China
- Beijing Advanced Innovation Center for Big Data and Brain Computing, Beihang University, Beijing, China
- * E-mail:
| | - Xiangnan Feng
- School of Mathematical Sciences, Beihang University, Beijing, China
- Key Laboratory of Mathematics, Informatics and Behavioral Semantics, Ministry of Education, Beijing, China
- Peng Cheng Laboratory, Shenzhen, Guangdong, China
- Beijing Advanced Innovation Center for Big Data and Brain Computing, Beihang University, Beijing, China
| | - Xing Li
- School of Mathematical Sciences, Beihang University, Beijing, China
- Key Laboratory of Mathematics, Informatics and Behavioral Semantics, Ministry of Education, Beijing, China
- Peng Cheng Laboratory, Shenzhen, Guangdong, China
- Beijing Advanced Innovation Center for Big Data and Brain Computing, Beihang University, Beijing, China
| | - Zhiming Zheng
- School of Mathematical Sciences, Beihang University, Beijing, China
- Key Laboratory of Mathematics, Informatics and Behavioral Semantics, Ministry of Education, Beijing, China
- Peng Cheng Laboratory, Shenzhen, Guangdong, China
- Beijing Advanced Innovation Center for Big Data and Brain Computing, Beihang University, Beijing, China
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