1
|
Lee HW, Malik N, Mucha PJ. Evolutionary prisoner's dilemma games coevolving on adaptive networks. JOURNAL OF COMPLEX NETWORKS 2018; 6:1-23. [PMID: 29732158 PMCID: PMC5931405 DOI: 10.1093/comnet/cnx018] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/08/2023]
Abstract
We study a model for switching strategies in the Prisoner's Dilemma game on adaptive networks of player pairings that coevolve as players attempt to maximize their return. We use a node-based strategy model wherein each player follows one strategy at a time (cooperate or defect) across all of its neighbors, changing that strategy and possibly changing partners in response to local changes in the network of player pairing and in the strategies used by connected partners. We compare and contrast numerical simulations with existing pair approximation differential equations for describing this system, as well as more accurate equations developed here using the framework of approximate master equations. We explore the parameter space of the model, demonstrating the relatively high accuracy of the approximate master equations for describing the system observations made from simulations. We study two variations of this partner-switching model to investigate the system evolution, predict stationary states, and compare the total utilities and other qualitative differences between these two model variants.
Collapse
Affiliation(s)
- Hsuan-Wei Lee
- Department of Sociology, University of Nebraska-Lincoln
| | | | - Peter J Mucha
- Department of Mathematics, University of North Carolina at Chapel Hill
| |
Collapse
|
2
|
Szabó G, Bodó KS, Samani KA. Separation of cyclic and starlike hierarchical dominance in evolutionary matrix games. Phys Rev E 2017; 95:012320. [PMID: 28208502 DOI: 10.1103/physreve.95.012320] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/10/2016] [Indexed: 06/06/2023]
Abstract
We study antisymmetric components of matrices characterizing pair interactions in multistrategy evolutionary games. Based on the dyadic decomposition of matrices we distinguish cyclic and starlike hierarchical dominance in the appropriate components. In the symmetric matrix games the strengths of these elementary components are determined. The general features and intrinsic symmetries of these interactions are represented by directed graphs. It is found that the variation of a single matrix component modifies simultaneously the strengths of two starlike hierarchical basis games and many other independent rock-paper-scissors type cyclic basis games. The application of the related concepts is illustrated by discussing the three-strategy voluntary prisoner's dilemma.
Collapse
Affiliation(s)
- György Szabó
- Institute of Technical Physics and Materials Science, Centre for Energy Research, Hungarian Academy of Sciences, P.O. Box 49, H-1525 Budapest, Hungary
| | - Kinga S Bodó
- Budapest University of Technology and Economics, Budafoki út 8, H-1111 Budapest, Hungary
| | | |
Collapse
|
3
|
Antoci A, Delfino A, Paglieri F, Panebianco F, Sabatini F. Civility vs. Incivility in Online Social Interactions: An Evolutionary Approach. PLoS One 2016; 11:e0164286. [PMID: 27802271 PMCID: PMC5089744 DOI: 10.1371/journal.pone.0164286] [Citation(s) in RCA: 26] [Impact Index Per Article: 3.3] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/12/2016] [Accepted: 09/22/2016] [Indexed: 11/22/2022] Open
Abstract
Evidence is growing that forms of incivility–e.g. aggressive and disrespectful behaviors, harassment, hate speech and outrageous claims–are spreading in the population of social networking sites’ (SNS) users. Online social networks such as Facebook allow users to regularly interact with known and unknown others, who can behave either politely or rudely. This leads individuals not only to learn and adopt successful strategies for using the site, but also to condition their own behavior on that of others. Using a mean field approach, we define anevolutionary game framework to analyse the dynamics of civil and uncivil ways of interaction in online social networks and their consequences for collective welfare. Agents can choose to interact with others–politely or rudely–in SNS, or to opt out from online social networks to protect themselves from incivility. We find that, when the initial share of the population of polite users reaches a critical level, civility becomes generalized if its payoff increases more than that of incivility with the spreading of politeness in online interactions. Otherwise, the spreading of self-protective behaviors to cope with online incivility can lead the economyto non-socially optimal stationary states. JEL Codes: C61, C73, D85, O33, Z13. PsycINFO Codes: 2240, 2750.
Collapse
Affiliation(s)
- Angelo Antoci
- Department of Economics and Management, University of Sassari, Sassari, Italy
- * E-mail:
| | - Alexia Delfino
- Department of Economics, London School of Economics and Political Science, London, United Kingdom
| | - Fabio Paglieri
- National Research Council, Institute of Cognitive Sciences and Technologies, Rome, Italy
| | | | - Fabio Sabatini
- Department of Economics and Law, Sapienza University of Rome, Rome, Italy
| |
Collapse
|
4
|
Deng X, Zhang Q, Deng Y, Wang Z. A novel framework of classical and quantum prisoner's dilemma games on coupled networks. Sci Rep 2016; 6:23024. [PMID: 26975447 PMCID: PMC4792163 DOI: 10.1038/srep23024] [Citation(s) in RCA: 22] [Impact Index Per Article: 2.8] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/30/2015] [Accepted: 02/22/2016] [Indexed: 11/16/2022] Open
Abstract
Evolutionary games on multilayer networks are attracting growing interest. While among previous studies, the role of quantum games in such a infrastructure is still virgin and may become a fascinating issue across a myriad of research realms. To mimick two kinds of different interactive environments and mechanisms, in this paper a new framework of classical and quantum prisoner's dilemma games on two-layer coupled networks is considered. Within the proposed model, the impact of coupling factor of networks and entanglement degree in quantum games on the evolutionary process has been studied. Simulation results show that the entanglement has no impact on the evolution of the classical prisoner's dilemma, while the rise of the coupling factor obviously impedes cooperation in this game, and the evolution of quantum prisoner's dilemma is greatly impacted by the combined effect of entanglement and coupling.
Collapse
Affiliation(s)
- Xinyang Deng
- School of Computer and Information Science, Southwest University, Chongqing, 400715, China
- Center for Quantitative Sciences, Vanderbilt University School of Medicine, Nashville, TN, 37232, USA
| | - Qi Zhang
- School of Computer and Information Science, Southwest University, Chongqing, 400715, China
| | - Yong Deng
- School of Computer and Information Science, Southwest University, Chongqing, 400715, China
- Big Data Decision Institute, Jinan University, Tianhe, Guangzhou, 510632, China
| | - Zhen Wang
- School of Automation, Northwestern Polytechnical University, Xi’an, 710072, China
| |
Collapse
|
5
|
Universal scaling for the dilemma strength in evolutionary games. Phys Life Rev 2015; 14:1-30. [PMID: 25979121 DOI: 10.1016/j.plrev.2015.04.033] [Citation(s) in RCA: 345] [Impact Index Per Article: 38.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/11/2015] [Revised: 04/20/2015] [Accepted: 04/20/2015] [Indexed: 11/24/2022]
Abstract
Why would natural selection favor the prevalence of cooperation within the groups of selfish individuals? A fruitful framework to address this question is evolutionary game theory, the essence of which is captured in the so-called social dilemmas. Such dilemmas have sparked the development of a variety of mathematical approaches to assess the conditions under which cooperation evolves. Furthermore, borrowing from statistical physics and network science, the research of the evolutionary game dynamics has been enriched with phenomena such as pattern formation, equilibrium selection, and self-organization. Numerous advances in understanding the evolution of cooperative behavior over the last few decades have recently been distilled into five reciprocity mechanisms: direct reciprocity, indirect reciprocity, kin selection, group selection, and network reciprocity. However, when social viscosity is introduced into a population via any of the reciprocity mechanisms, the existing scaling parameters for the dilemma strength do not yield a unique answer as to how the evolutionary dynamics should unfold. Motivated by this problem, we review the developments that led to the present state of affairs, highlight the accompanying pitfalls, and propose new universal scaling parameters for the dilemma strength. We prove universality by showing that the conditions for an ESS and the expressions for the internal equilibriums in an infinite, well-mixed population subjected to any of the five reciprocity mechanisms depend only on the new scaling parameters. A similar result is shown to hold for the fixation probability of the different strategies in a finite, well-mixed population. Furthermore, by means of numerical simulations, the same scaling parameters are shown to be effective even if the evolution of cooperation is considered on the spatial networks (with the exception of highly heterogeneous setups). We close the discussion by suggesting promising directions for future research including (i) how to handle the dilemma strength in the context of co-evolution and (ii) where to seek opportunities for applying the game theoretical approach with meaningful impact.
Collapse
|
6
|
Szolnoki A, Mobilia M, Jiang LL, Szczesny B, Rucklidge AM, Perc M. Cyclic dominance in evolutionary games: a review. J R Soc Interface 2014; 11:20140735. [PMID: 25232048 PMCID: PMC4191105 DOI: 10.1098/rsif.2014.0735] [Citation(s) in RCA: 143] [Impact Index Per Article: 14.3] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/07/2014] [Accepted: 08/22/2014] [Indexed: 11/12/2022] Open
Abstract
Rock is wrapped by paper, paper is cut by scissors and scissors are crushed by rock. This simple game is popular among children and adults to decide on trivial disputes that have no obvious winner, but cyclic dominance is also at the heart of predator-prey interactions, the mating strategy of side-blotched lizards, the overgrowth of marine sessile organisms and competition in microbial populations. Cyclical interactions also emerge spontaneously in evolutionary games entailing volunteering, reward, punishment, and in fact are common when the competing strategies are three or more, regardless of the particularities of the game. Here, we review recent advances on the rock-paper-scissors (RPS) and related evolutionary games, focusing, in particular, on pattern formation, the impact of mobility and the spontaneous emergence of cyclic dominance. We also review mean-field and zero-dimensional RPS models and the application of the complex Ginzburg-Landau equation, and we highlight the importance and usefulness of statistical physics for the successful study of large-scale ecological systems. Directions for future research, related, for example, to dynamical effects of coevolutionary rules and invasion reversals owing to multi-point interactions, are also outlined.
Collapse
Affiliation(s)
- Attila Szolnoki
- Institute of Technical Physics and Materials Science, Research Centre for Natural Sciences, Hungarian Academy of Sciences, PO Box 49, 1525 Budapest, Hungary
| | - Mauro Mobilia
- Department of Applied Mathematics, School of Mathematics, University of Leeds, Leeds LS2 9JT, UK
| | - Luo-Luo Jiang
- College of Physics and Electronic Information Engineering, Wenzhou University, 325035 Wenzhou, People's Republic of China
| | - Bartosz Szczesny
- Department of Applied Mathematics, School of Mathematics, University of Leeds, Leeds LS2 9JT, UK
| | - Alastair M Rucklidge
- Department of Applied Mathematics, School of Mathematics, University of Leeds, Leeds LS2 9JT, UK
| | - Matjaž Perc
- Faculty of Natural Sciences and Mathematics, University of Maribor, Koroška cesta 160, 2000 Maribor, Slovenia
| |
Collapse
|
7
|
Szabó G, Bodó KS, Allen B, Nowak MA. Fourier decomposition of payoff matrix for symmetric three-strategy games. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2014; 90:042811. [PMID: 25375553 DOI: 10.1103/physreve.90.042811] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/30/2014] [Indexed: 06/04/2023]
Abstract
In spatial evolutionary games the payoff matrices are used to describe pair interactions among neighboring players located on a lattice. Now we introduce a way how the payoff matrices can be built up as a sum of payoff components reflecting basic symmetries. For the two-strategy games this decomposition reproduces interactions characteristic to the Ising model. For the three-strategy symmetric games the Fourier components can be classified into four types representing games with self-dependent and cross-dependent payoffs, variants of three-strategy coordinations, and the rock-scissors-paper (RSP) game. In the absence of the RSP component the game is a potential game. The resultant potential matrix has been evaluated. The general features of these systems are analyzed when the game is expressed by the linear combinations of these components.
Collapse
Affiliation(s)
- György Szabó
- Institute of Technical Physics and Materials Science, Research Centre for Natural Sciences, Hungarian Academy of Sciences, P.O. Box 49, H-1525 Budapest, Hungary and Regional Knowledge Centre, Eötvös University, Irányi Dániel u. 4, H-8000 Székesfehérvár, Hungary
| | - Kinga S Bodó
- Roland Eötvös University, Institute of Physics, Pázmány P. sétány 1/A, H-1117 Budapest, Hungary
| | - Benjamin Allen
- Program for Evolutionary Dynamics, Harvard University, One Brattle Square, Cambridge, Massachusetts 02138, USA
| | - Martin A Nowak
- Program for Evolutionary Dynamics, Harvard University, One Brattle Square, Cambridge, Massachusetts 02138, USA and Department of Mathematics, Department of Organismic and Evolutionary Biology, Harvard University, Cambridge, Massachusetts 02138, USA
| |
Collapse
|
8
|
Cameron SM, Cintron-Arias A. Prisoner's dilemma on real social networks: revisited. MATHEMATICAL BIOSCIENCES AND ENGINEERING : MBE 2013; 10:1381-1398. [PMID: 24245621 DOI: 10.3934/mbe.2013.10.1381] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/02/2023]
Abstract
Prisoner's Dilemma is a game theory model used to describe altruistic behavior seen in various populations. This theoretical game is important in understanding why a seemingly selfish strategy does persist and spread throughout a population that is mixing homogeneously at random. For a population with structure determined by social interactions, Prisoner's Dilemma brings to light certain requirements for the altruistic strategy to become established. Monte Carlo simulations of Prisoner's Dilemma are carried out using both simulated social networks and a dataset of a real social network. In both scenarios we confirm the requirements for the persistence of altruism in a population.
Collapse
Affiliation(s)
- Sharon M Cameron
- East Tennessee State University, Department of Mathematics and Statistics, Box 70663, Johnson City, TN 37614-1701, United States.
| | | |
Collapse
|
9
|
Spatial prisoner’s dilemma games with increasing size of the interaction neighborhood on regular lattices. ACTA ACUST UNITED AC 2012. [DOI: 10.1007/s11434-011-4890-4] [Citation(s) in RCA: 27] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/28/2022]
|
10
|
Coevolutionary games--a mini review. Biosystems 2009; 99:109-25. [PMID: 19837129 DOI: 10.1016/j.biosystems.2009.10.003] [Citation(s) in RCA: 583] [Impact Index Per Article: 38.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/04/2009] [Revised: 10/02/2009] [Accepted: 10/05/2009] [Indexed: 01/10/2023]
Abstract
Prevalence of cooperation within groups of selfish individuals is puzzling in that it contradicts with the basic premise of natural selection. Favoring players with higher fitness, the latter is key for understanding the challenges faced by cooperators when competing with defectors. Evolutionary game theory provides a competent theoretical framework for addressing the subtleties of cooperation in such situations, which are known as social dilemmas. Recent advances point towards the fact that the evolution of strategies alone may be insufficient to fully exploit the benefits offered by cooperative behavior. Indeed, while spatial structure and heterogeneity, for example, have been recognized as potent promoters of cooperation, coevolutionary rules can extend the potentials of such entities further, and even more importantly, lead to the understanding of their emergence. The introduction of coevolutionary rules to evolutionary games implies, that besides the evolution of strategies, another property may simultaneously be subject to evolution as well. Coevolutionary rules may affect the interaction network, the reproduction capability of players, their reputation, mobility or age. Here we review recent works on evolutionary games incorporating coevolutionary rules, as well as give a didactic description of potential pitfalls and misconceptions associated with the subject. In addition, we briefly outline directions for future research that we feel are promising, thereby particularly focusing on dynamical effects of coevolutionary rules on the evolution of cooperation, which are still widely open to research and thus hold promise of exciting new discoveries.
Collapse
|