Abstract
We introduce an analytical model to study the evolution towards equilibrium in spatial games, with ‘memory-aware’ agents, i.e., agents that accumulate their payoff over time. In particular, we focus our attention on the spatial Prisoner’s Dilemma, as it constitutes an emblematic example of a game whose Nash equilibrium is defection. Previous investigations showed that, under opportune conditions, it is possible to reach, in the evolutionary Prisoner’s Dilemma, an equilibrium of cooperation. Notably, it seems that mechanisms like motion may lead a population to become cooperative. In the proposed model, we map agents to particles of a gas so that, on varying the system temperature, they randomly move. In doing so, we are able to identify a relation between the temperature and the final equilibrium of the population, explaining how it is possible to break the classical Nash equilibrium in the spatial Prisoner’s Dilemma when considering agents able to increase their payoff over time. Moreover, we introduce a formalism to study order-disorder phase transitions in these dynamics. As result, we highlight that the proposed model allows to explain analytically how a population, whose interactions are based on the Prisoner’s Dilemma, can reach an equilibrium far from the expected one; opening also the way to define a direct link between evolutionary game theory and statistical physics.
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References
M. Perc, P. Grigolini, Chaos Solitons Fractals 56, 1 (2013)
M.A. Nowak, Evolutionary Dynamics: Exploring the Equations of Life (Harvard University Press, 2006)
M. Tomassini, Introduction to evolutionary game theory, in Proc. Conf. on Genetic and evolutionary computation companion (2014)
P.C. Julia, J. Gomez-Gardenes, A. Traulsen, Y. Moreno, New J. Phys. 11, 083031 (2009)
L.M. Floria, C. Gracia-Lazaro, J. Gomez-Gardenes, Y. Moreno, Phys. Rev. E 79, 026106 (2009)
J. Hofbauer, K. Sigmund, The Theory of Evolution and Dynamical Systems (Cambridge University Press, 1988)
A.M. Colman, Game Theory and Its Applications (Digital Printing, 2008)
M. Perc, A. Szolnoki, Phys. Rev. E 77, 011904 (2008)
A. Szolnoki, M. Perc, J. R. Soc. Interface 12, 20141299 (2015)
Z. Wang, A. Szolnoki, M. Perc, Sci. Rep. 3, 1183 (2013)
A. Szolnoki, N.-G. Xie, C. Wang, M. Perc, Europhys. Lett. 96, 38002 (2011)
M. Perc, A. Szolnoki, New J. Phys. 14, 043013 (2012)
D. Friedman, J. Evol. Econ. 8, 15 (1998)
S. Schuster, L. de Figueiredo, A. Schroeter, C. Kaleta, BioSystems 105, 147 (2011)
E. Frey, Physica A 389, 4265 (2010)
F. Fu, D.I. Rosenbloom, L. Wang, M.A. Nowak, Proc. R. Soc. B 278, 42 (2011)
E. Lieberman, C. Hauert, M.A. Nowak, Nature 433, 312 (2005)
S. Galam, B. Walliser, Physica A 389, 481 (2010)
S. Meloni, A. Buscarino, L. Fortuna, M. Frasca, J. Gomez-Gardenes, V. Latora, Y. Moreno, Phys. Rev. E 79, 067101 (2009)
A. Antonioni, M. Tomassini, P. Buesser, J. Theor. Biol. 344, 40 (2014)
M. Tomassini, A. Antonioni, J. Theor. Biol. 364, 154 (2015)
A. Antonioni, M. Tomassini, A. Sanchez, Sci. Rep. 5, 10282 (2015)
M. Perc, J. Gomez-Gardenes, A. Szolnoki, L.M. Floria, Y. Moreno, J. R. Soc. Interface 10, 20120997 (2013)
M.A. Javarone, A.E. Atzeni, Comput. Soc. Netw. 2, 15 (2015)
M.A. Javarone, A.E. Atzeni, S. Galam, Lect. Notes Comput. Sci. 9028, 155 (2015)
M.A. Nowak, Science 314, 1560 (2006)
G. Szabo, G. Fath, Phys. Rep. 446, 97 (2007)
M.A. Nowak, R.M. May, Nature 359, 826 (1992)
C. Hauert, G. Szabo, Am. J. Phys. 73, 405 (2005)
K. Huang, Statistical Mechanics, 2nd edn. (Wiley, 1987)
A. Szolnoki, G. Szabo, M. Perc, Phys. Rev. E 83, 0361101 (2011)
A. Szolnoki, M. Perc, Europhys. Lett. 92, 38003 (2010)
M.A. Javarone, Europhys. Lett. 110, 58003 (2015)
M. Mobilia, S. Redner, Phys. Rev. E 68, 046106 (2003)
A. Barra, J. Stat. Phys. 132, 787 (2008)
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Javarone, M. Statistical physics of the spatial Prisoner’s Dilemma with memory-aware agents. Eur. Phys. J. B 89, 42 (2016). https://doi.org/10.1140/epjb/e2016-60901-5
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DOI: https://doi.org/10.1140/epjb/e2016-60901-5