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Heterogeneous aspirations promote cooperation in the prisoner's dilemma game
Matjaž Perc, Zhen Wang, 2010, original scientific article

Abstract: To be the fittest is central to proliferation in evolutionary games. Individuals thus adopt the strategies of better performing players in the hopeof successful reproduction. In structured populations the array of those that are eligible to act as strategy sources is bounded to the immediate neighbors of each individual. But which one of these strategy sources should potentially be copied? Previous research dealt with this question either by selecting the fittest or by selecting one player uniformly at random. Here we introduce a parameter that interpolates between these two extreme options. Setting equal to zero returns the random selection of the opponent, while positive favor the fitter players. In addition, we divide the population intotwo groups. Players from group select their opponents as dictated by the parameter , while players from group do so randomly irrespective of . We denote the fraction of players contained in groups and by and , respectively. The two parameters and allow us to analyze in detail how aspirations in the context of the prisoner's dilemma game influence the evolution of cooperation. We find that for sufficiently positive values of there exist a robust intermediate for which cooperation thrives best. The robustness of this observation is tested against different levels of uncertainty in the strategy adoption process and for different interaction networks. We also provide complete phase diagrams depicting the dependence of the impact of and for different values of , and contrast the validity of ourconclusions by means of an alternative model where individual aspiration levels are subject to evolution as well. Our study indicates that heterogeneity in aspirations may be key for the sustainability of cooperation in structured populations.
Keywords: evolutionary game theory, prisoner's dilemma, spatial games, aspirations, social systems, physics and society
Published: 19.06.2017; Views: 320; Downloads: 103
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Uncertainties facilitate aggressive behavior in a spatial hawk-dove game
Matjaž Perc, 2007, original scientific article

Abstract: We study effects of additive spatiotemporal random variations, introduced to the payoffs of a spatial hawk-dove game, on the evolution of the reconciliatory and the aggressive strategy. We show that uncertainties facilitate aggressive behavior for a broad range of resource values. In particular, aggressors thrive best if stochastic influences are of the order of magnitude of deterministic payoff values. We argue that random payoff variations are potent and plausible promoters of aggressive behavior in human as well as animal societies if only the hawk-dove game payoff ranking applies.
Keywords: evolutionary game theory, hawk-dove game, noise, spatial games
Published: 31.05.2012; Views: 801; Downloads: 9
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Encyclopedia of complexity and systems science
dictionary, encyclopaedia, lexicon, manual, atlas, map

Abstract: Encyclopedia of Complexity and Systems Science provides an authoritative single source for understanding and applying the concepts of complexity theory together with the tools and measures for analyzing complex systems in all fields of science and engineering. The science and tools of complexity and systems science include theories of self-organization, complex systems, synergetics, dynamical systems, turbulence, catastrophes, instabilities, nonlinearity, stochastic processes, chaos, neural networks, cellular automata, adaptive systems, and genetic algorithms. Examples of near-term problems and major unknowns that can be approached through complexity and systems science include: The structure, history and future of the universe; the biological basis of consciousness; the integration of genomics, proteomics and bioinformatics as systems biology; human longevity limits; the limits of computing; sustainability of life on earth; predictability, dynamics and extent of earthquakes, hurricanes, tsunamis, and other natural disasters; the dynamics of turbulent flows; lasers or fluids in physics, microprocessor design; macromolecular assembly in chemistry and biophysics; brain functions in cognitive neuroscience; climate change; ecosystem management; traffic management; and business cycles. All these seemingly quite different kinds of structure formation have a number of important features and underlying structures in common. These deep structural similarities can be exploited to transfer analytical methods and understanding from one field to another. This unique work will extend the influence of complexity and system science to a much wider audience than has been possible to date.
Keywords: cellular automata, complex networks, computational nanoscience, ecological complexity, ergodic theory, fractals, game theory, granular computing, graph theory, intelligent systems, perturbation theory, quantum information science, system dynamics, traffic management, chaos, climate modelling, complex systems, dynamical sistems, fuzzy theory systems, nonlinear systems, soft computing, stochastic processes, synergetics, self-organization, systems biology, systems science
Published: 01.06.2012; Views: 1405; Downloads: 34
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Flights towards defection in economic transactions
Matjaž Perc, 2007, original scientific article

Abstract: We show that Lévy distributed variations of payoffs in the prisoner's dilemma game impede cooperation as the frequency of rare events increases. Lévy flights thus facilitate defection, but also uphold the evolutionary process, arguably maintaining a healthy level of competitiveness amongst the agents.
Keywords: chaotic systems, game theory, Lévy process, cooperation, social welfare
Published: 07.06.2012; Views: 963; Downloads: 26
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Microeconomic uncertainties facilitate cooperative alliances and social welfare
Matjaž Perc, 2007, original scientific article

Abstract: We show that microeconomic chaotic variations of payoffs in the prisoner's dilemma game maintain cooperation over a broad range of defection temptation values where otherwise economic stalemate reigns. Thus, unpredictability at micro scales impedes mutual defection that inflicts social poverty.
Keywords: chaotic systems, game theory, microeconomic chaos, cooperation, social welfare
Published: 07.06.2012; Views: 949; Downloads: 23
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Domination game played on trees and spanning subgraphs
Boštjan Brešar, Sandi Klavžar, Douglas F. Rall, 2011

Abstract: Igra dominacije na grafu ▫$G$▫ je bila vpeljana v [B. Brešar, S. Klavžar, D. F. Rall, Domination game and an imagination strategy, SIAM J. Discrete Math. 24 (2010) 979-991]. Dva igralca, Dominator in Zavlačevalec, drug za drugim izbirata po eno vozlišče grafa. Vsako izbrano vozlišče mora povečati množico vozlišč, ki so bila dominirana do tega trenutka igre. Oba igralca izbirata optimalno strategijo, pri čemer Dominator želi igro končati v najmanjšem možnem številu korakov, Zavlačevalec pa v največjem možnem številu korakov. Igralno dominacijsko število ▫$gamma_g(G)$▫ je število izbranih vozlišč v igri, kjer je Dominator prvi izbral vozlišče. Ustrezno invarianto, ko igro začne Zavlačevalec, označimo z ▫$gamma_g'(G)$▫. V članku sta obe igri proučevani na drevesih in vpetih podgrafih. Dokazana je spodnja meja za igralno dominacijsko število drevesa, ki je funkcija njegovega reda in maksimalne stopnje. Pokazano je, da je meja asimptotično optimalna. Dokazano je, da za vsak ▫$k$▫ obstaja drevo ▫$T$▫ z ▫$(gamma_g(T),gamma_g'(T)) = (k,k+1)$▫ in postavljena je domneva, da ne obstaja drevo z ▫$(gamma_g(T),gamma_g'(T)) = (k,k-1)$▫. Obravnavana je povezava med igralnim dominacijskim številom grafa in njegovimi vpetimi podgrafi. Dokazano je, da za vsako naravno število ▫$ell geq 1$▫ obstaja graf ▫$G$▫ z vpetim drevesom ▫$T$▫, tako da velja ▫$gamma_g(G)-gamma_g(T)ge ell$▫. Nadalje obstajajo 3-povezani grafi ▫$G$▫, ki imajo vpeta drevesa z igralnim dominacijskim številom poljubno manjšim od ▫$G$▫.
Keywords: igra dominacije, igralno dominacijsko število, drevo, vpeti podgraf, graph theory, domination game, game domination number, tree, spanning subgraph
Published: 10.07.2015; Views: 489; Downloads: 32
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Game chromatic number of Cartesian product graphs
T. Bartnicki, Boštjan Brešar, J. Grytczuk, Matjaž Kovše, Z. Miechowicz, Iztok Peterin, 2008, original scientific article

Abstract: Obravnavamo igralno kromatično število ▫$chi_g$▫ kartezičnega produkta ▫$G Box H$▫ dveh grafov ▫$G$▫ in ▫$H$▫. Določimo točne vrednosti za ▫$chi_g(K_2 Box H$▫, ko je ▫$H$▫ pot, cikel ali poln graf. S pomočjo novo vpeljane "igre kombinacij" pokažemo, da igralno kromatično število ni omejeno znotraj razreda kartezičnih produktov dveh polnih dvodelnih grafov. Iz tega rezultata sledi, da igralno kromatično število ▫$chi_g(G Box H$▫ ni navzgor omejeno s kako funkcijo igralnih kromatičnih števil grafov ▫$G$▫ in ▫$H$▫. Analogen rezultat je izpeljan za igralno barvno število kartezičnih produktov grafov.
Keywords: matematika, teorija grafov, kartezični produkt grafov, igralno kromatično število, mathematics, graph theory, Cartesian prodict, game chromatic number
Published: 10.07.2015; Views: 306; Downloads: 49
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Domination game
Boštjan Brešar, Sandi Klavžar, Douglas F. Rall, 2009

Abstract: The domination game played on a graph ▫$G$▫ consists of two players, Dominator and Staller who alternate taking turns choosing a vertex from ▫$G$▫ such that whenever a vertex is chosen the graph in as few steps as possible and Staller wishes to delay the process as much as possible. The game domination number ▫$gamma_g(G)$▫ is the number of vertices chosen when Dominator starts the game and the Staller-start game domination number ▫$gamma'_g(G)$▫ when Staller starts the game. It is proved that for any graph ▫$G$▫, ▫$gamma(G) le gamma_g(G) le 2gamma(G) - 1$▫, and that all possible values can be realized. It is also proved that for any graph ▫$G$▫, ▫$gamma_g(G) - 1 le gamma'_g(G) le gamma_g(G) + 2$▫, and that most of the possibilities for mutual values of ▫$gamma_g(G)$▫ and ▫$gamma'_g(G)$▫ can be realized. A connection with Vizing's conjecture is established and several problems and conjectures stated.
Keywords: teorija grafov, teorija iger, dominantnost, Vizingova domneva, graph theory, game theory, domination, domination game, game domination number, Vizing's conjecture
Published: 10.07.2015; Views: 345; Downloads: 5
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