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Meylahn BV, den Boer AV, Mandjes M. Interpersonal trust: Asymptotic analysis of a stochastic coordination game with multi-agent learning. CHAOS (WOODBURY, N.Y.) 2024; 34:063119. [PMID: 38848273 DOI: 10.1063/5.0205136] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/24/2024] [Accepted: 05/16/2024] [Indexed: 06/09/2024]
Abstract
We study the interpersonal trust of a population of agents, asking whether chance may decide if a population ends up with high trust or low trust. We model this by a discrete time, stochastic coordination game with pairwise interactions occurring at random in a finite population. Agents learn about the behavior of the population using a weighted average of what they have observed in past interactions. This learning rule, called an "exponential moving average," has one parameter that determines the weight of the most recent observation and may, thus, be interpreted as the agent's memory. We prove analytically that in the long run, the whole population always either trusts or doubts with the probability one. This remains true when the expectation of the dynamics would indicate otherwise. By simulation, we study the impact of the distribution of the payoff matrix and of the memory of the agents. We find that as the agent memory increases (i.e., the most recent observation weighs less), the actual dynamics increasingly resemble the expectation of the process. We conclude that it is possible that a population may converge upon high or low trust between its citizens simply by chance, though the game parameters (context of the society) may be quite telling.
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Affiliation(s)
- Benedikt V Meylahn
- Korteweg-de Vries Institute for Mathematics, University of Amsterdam, Science Park 904, 1098 XH Amsterdam, The Netherlands
| | - Arnoud V den Boer
- Korteweg-de Vries Institute for Mathematics, University of Amsterdam, Science Park 904, 1098 XH Amsterdam, The Netherlands
| | - Michel Mandjes
- Korteweg-de Vries Institute for Mathematics, University of Amsterdam, Science Park 904, 1098 XH Amsterdam, The Netherlands
- Mathematical Institute, Leiden University, Niels Bohrweg 1, 2333 CA Leiden, The Netherlands
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Capraro V, Di Paolo R, Perc M, Pizziol V. Language-based game theory in the age of artificial intelligence. J R Soc Interface 2024; 21:20230720. [PMID: 38471531 PMCID: PMC10932721 DOI: 10.1098/rsif.2023.0720] [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: 12/05/2023] [Accepted: 02/12/2024] [Indexed: 03/14/2024] Open
Abstract
Understanding human behaviour in decision problems and strategic interactions has wide-ranging applications in economics, psychology and artificial intelligence. Game theory offers a robust foundation for this understanding, based on the idea that individuals aim to maximize a utility function. However, the exact factors influencing strategy choices remain elusive. While traditional models try to explain human behaviour as a function of the outcomes of available actions, recent experimental research reveals that linguistic content significantly impacts decision-making, thus prompting a paradigm shift from outcome-based to language-based utility functions. This shift is more urgent than ever, given the advancement of generative AI, which has the potential to support humans in making critical decisions through language-based interactions. We propose sentiment analysis as a fundamental tool for this shift and take an initial step by analysing 61 experimental instructions from the dictator game, an economic game capturing the balance between self-interest and the interest of others, which is at the core of many social interactions. Our meta-analysis shows that sentiment analysis can explain human behaviour beyond economic outcomes. We discuss future research directions. We hope this work sets the stage for a novel game-theoretical approach that emphasizes the importance of language in human decisions.
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Affiliation(s)
- Valerio Capraro
- Department of Psychology, University of Milan Bicocca, Milano, Italy
| | - Roberto Di Paolo
- Department of Economics and Management, University of Parma, Parma, Italy
| | - Matjaž Perc
- Faculty of Natural Sciences and Mathematics, University of Maribor, Maribor, Slovenia
- Community Healthcare Center Dr. Adolf Drolc Maribor, Maribor, Slovenia
- Complexity Science Hub Vienna, Vienna, Austria
- Department of Physics, Kyung Hee University, Seoul, Republic of Korea
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Li W, Zhu Y, Xia C. Evolutionary dynamics of N-player sender-receiver game in networks with community structure. CHAOS (WOODBURY, N.Y.) 2023; 33:103117. [PMID: 37831798 DOI: 10.1063/5.0157761] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/10/2023] [Accepted: 09/18/2023] [Indexed: 10/15/2023]
Abstract
Network typology largely affects the evolutionary dynamics of collective behaviors in many real-world complex systems. As a conventional transmission model, the sender-receiver game paves the way to explore the evolution of honest signals between senders and receivers. In practice, the utilities of an agent often depend not only on pairwise interactions, but also on the group influence of players around them, and thus there is an urgent need for deeper theoretical modeling and investigations on individuals' non-pairwise interactions. Considering the underlying evolutionary game dynamics and multiple community network structures, we explore the evolution of honest behaviors by extending the sender-receiver game to multiple communities. With the new dynamical model of the multi-community system, we perform a stability analysis of the system equilibrium state. Our results reveal the condition to promote the evolution of honest behaviors and provide an effective method for enhancing collaboration behaviors in distributed complex systems. Current results help us to deeply understand how collective decision-making behaviors evolve, influenced by the spread of true information and misinformation in large dynamic systems.
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Affiliation(s)
- Wenbo Li
- Tianjin Key Laboratory of Intelligence Computing and Novel Software Technology, Tianjin University of Technology, Tianjin 300384, China
| | - Yuying Zhu
- School of Artificial Intelligence, Tiangong University, Tianjin 300387, China
| | - Chengyi Xia
- School of Artificial Intelligence, Tiangong University, Tianjin 300387, China
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Wang S, Chen X, Xiao Z, Szolnoki A, Vasconcelos VV. Optimization of institutional incentives for cooperation in structured populations. J R Soc Interface 2023; 20:20220653. [PMID: 36722070 PMCID: PMC9890111 DOI: 10.1098/rsif.2022.0653] [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: 09/05/2022] [Accepted: 01/03/2023] [Indexed: 02/02/2023] Open
Abstract
The application of incentives, such as reward and punishment, is a frequently applied way for promoting cooperation among interacting individuals in structured populations. However, how to properly use the incentives is still a challenging problem for incentive-providing institutions. In particular, since the implementation of incentive is costly, to explore the optimal incentive protocol, which ensures the desired collective goal at a minimal cost, is worthy of study. In this work, we consider the positive and negative incentives for a structured population of individuals whose conflicting interactions are characterized by a Prisoner's Dilemma game. We establish an index function for quantifying the cumulative cost during the process of incentive implementation, and theoretically derive the optimal positive and negative incentive protocols for cooperation on regular networks. We find that both types of optimal incentive protocols are identical and time-invariant. Moreover, we compare the optimal rewarding and punishing schemes concerning implementation cost and provide a rigorous basis for the usage of incentives in the game-theoretical framework. We further perform computer simulations to support our theoretical results and explore their robustness for different types of population structures, including regular, random, small-world and scale-free networks.
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Affiliation(s)
- Shengxian Wang
- School of Mathematical Sciences, University of Electronic Science and Technology of China, Chengdu 611731, People’s Republic of China
- Faculty of Science and Engineering, University of Groningen, Groningen 9747 AG, The Netherlands
| | - Xiaojie Chen
- School of Mathematical Sciences, University of Electronic Science and Technology of China, Chengdu 611731, People’s Republic of China
| | - Zhilong Xiao
- School of Mathematical Sciences, University of Electronic Science and Technology of China, Chengdu 611731, People’s Republic of China
- School of Computer Science and Engineering, Sun Yat-sen University, Guangzhou 510006, People’s Republic of China
| | - Attila Szolnoki
- Institute of Technical Physics and Materials Science, Centre for Energy Research, P.O. Box 49, Budapest 1525, Hungary
| | - Vítor V. Vasconcelos
- Computational Science Lab, Informatics Institute, University of Amsterdam, Amsterdam 1098XH, The Netherlands
- Institute for Advanced Study, University of Amsterdam, Amsterdam 1012 GC, The Netherlands
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Kumar A, Chowdhary S, Capraro V, Perc M. Evolution of honesty in higher-order social networks. Phys Rev E 2021; 104:054308. [PMID: 34942761 DOI: 10.1103/physreve.104.054308] [Citation(s) in RCA: 7] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/19/2021] [Accepted: 11/03/2021] [Indexed: 11/07/2022]
Abstract
Sender-receiver games are simple models of information transmission that provide a formalism to study the evolution of honest signaling and deception between a sender and a receiver. In many practical scenarios, lies often affect groups of receivers, which inevitably entangles the payoffs of individuals to the payoffs of other agents in their group, and this makes the formalism of pairwise sender-receiver games inapt for where it might be useful the most. We therefore introduce group interactions among receivers and study how their interconnectedness in higher-order social networks affects the evolution of lying. We observe a number of counterintuitive results that are rooted in the complexity of the underlying evolutionary dynamics, which has thus far remained hidden in the realm of pairwise interactions. We find conditions for honesty to persist even when there is a temptation to lie, and we observe the prevalence of moral strategy profiles even when lies favor the receiver at a cost to the sender. We confirm the robustness of our results by further performing simulations on hypergraphs created from real-world data using the SocioPatterns database. Altogether, our results provide persuasive evidence that moral behavior may evolve on higher-order social networks, at least as long as individuals interact in groups that are small compared to the size of the network.
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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
| | - Sandeep Chowdhary
- Department of Network and Data Science, Central European University, 1100 Vienna, Austria
| | - 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, Taiwan Alma Mater Europaea ECM, Slovenska Ulica 17, 2000 Maribor, Slovenia; and Complexity Science Hub Vienna, Josefstädterstraße 39, 1080 Vienna, Austria
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Kovalenko K, Dai X, Alfaro-Bittner K, Raigorodskii AM, Perc M, Boccaletti S. Contrarians Synchronize beyond the Limit of Pairwise Interactions. PHYSICAL REVIEW LETTERS 2021; 127:258301. [PMID: 35029445 DOI: 10.1103/physrevlett.127.258301] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/03/2021] [Revised: 10/12/2021] [Accepted: 11/05/2021] [Indexed: 06/14/2023]
Abstract
We give evidence that a population of pure contrarian globally coupled D-dimensional Kuramoto oscillators reaches a collective synchronous state when the interplay between the units goes beyond the limit of pairwise interactions. Namely, we will show that the presence of higher-order interactions may induce the appearance of a coherent state even when the oscillators are coupled negatively to the mean field. An exact solution for the description of the microscopic dynamics for forward and backward transitions is provided, which entails imperfect symmetry breaking of the population into a frequency-locked state featuring two clusters of different instantaneous phases. Our results contribute to a better understanding of the powerful potential of group interactions entailing multidimensional choices and novel dynamical states in many circumstances, such as in social systems.
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Affiliation(s)
- K Kovalenko
- Moscow Institute of Physics and Technology, Dolgoprudny, Moscow Region 141701, Russian Federation
| | - X Dai
- Northwestern Polytechnical University, Xi'an 710072, People's Republic of China
| | - K Alfaro-Bittner
- Departamento de Física, Universidad Técnica Federico Santa María, Avenida España 1680, Casilla 110V, Valparaíso, Chile
| | - A M Raigorodskii
- Moscow Institute of Physics and Technology, Dolgoprudny, Moscow Region 141701, Russian Federation
- Adyghe State University, ulica Pervomaiskaya, 208, Maykop 385000, Russia
- Moscow State University, Leninskie Gory, 1, Moscow 119991, Russia
- Buryat State University, ulica Ranzhurova, 5, Ulan-Ude 670000, Russia
| | - M 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
- Complexity Science Hub Vienna, Josefstädterstraße 39, 1080 Vienna, Austria
- Alma Mater Europaea, Slovenska ulica 17, 2000 Maribor, Slovenia
| | - S Boccaletti
- Moscow Institute of Physics and Technology, Dolgoprudny, Moscow Region 141701, Russian Federation
- Universidad Rey Juan Carlos, Calle Tulipán s/n, 28933 Móstoles, Madrid, Spain
- CNR - Institute of Complex Systems, Via Madonna del Piano 10, I-50019 Sesto Fiorentino, Italy
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When to (or not to) trust intelligent machines: Insights from an evolutionary game theory analysis of trust in repeated games. COGN SYST RES 2021. [DOI: 10.1016/j.cogsys.2021.02.003] [Citation(s) in RCA: 16] [Impact Index Per Article: 5.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/17/2022]
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Abstract
One-shot anonymous unselfishness in economic games is commonly explained by social preferences, which assume that people care about the monetary pay-offs of others. However, during the last 10 years, research has shown that different types of unselfish behaviour, including cooperation, altruism, truth-telling, altruistic punishment and trustworthiness are in fact better explained by preferences for following one's own personal norms-internal standards about what is right or wrong in a given situation. Beyond better organizing various forms of unselfish behaviour, this moral preference hypothesis has recently also been used to increase charitable donations, simply by means of interventions that make the morality of an action salient. Here we review experimental and theoretical work dedicated to this rapidly growing field of research, and in doing so we outline mathematical foundations for moral preferences that can be used in future models to better understand selfless human actions and to adjust policies accordingly. These foundations can also be used by artificial intelligence to better navigate the complex landscape of human morality.
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Affiliation(s)
- 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 404332, Taiwan.,Alma Mater Europaea ECM, Slovenska ulica, 17 2000, Maribor, Slovenia.,Complexity Science Hub Vienna, Josefstädterstraße 39, 1080 Vienna, Austria
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Cluster Structure of Optimal Solutions in Bipartitioning of Small Worlds. ENTROPY 2020; 22:e22111319. [PMID: 33287084 PMCID: PMC7712369 DOI: 10.3390/e22111319] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 11/07/2020] [Revised: 11/16/2020] [Accepted: 11/17/2020] [Indexed: 12/02/2022]
Abstract
Using simulated annealing, we examine a bipartitioning of small worlds obtained by adding a fraction of randomly chosen links to a one-dimensional chain or a square lattice. Models defined on small worlds typically exhibit a mean-field behavior, regardless of the underlying lattice. Our work demonstrates that the bipartitioning of small worlds does depend on the underlying lattice. Simulations show that for one-dimensional small worlds, optimal partitions are finite size clusters for any fraction of additional links. In the two-dimensional case, we observe two regimes: when the fraction of additional links is sufficiently small, the optimal partitions have a stripe-like shape, which is lost for a larger number of additional links as optimal partitions become disordered. Some arguments, which interpret additional links as thermal excitations and refer to the thermodynamics of Ising models, suggest a qualitative explanation of such a behavior. The histogram of overlaps suggests that a replica symmetry is broken in a one-dimensional small world. In the two-dimensional case, the replica symmetry seems to hold, but with some additional degeneracy of stripe-like partitions.
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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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