Statistical physics of human cooperation. (English) Zbl 1366.80006

Summary: Extensive cooperation among unrelated individuals is unique to humans, who often sacrifice personal benefits for the common good and work together to achieve what they are unable to execute alone. The evolutionary success of our species is indeed due, to a large degree, to our unparalleled other-regarding abilities. Yet, a comprehensive understanding of human cooperation remains a formidable challenge. Recent research in the social sciences indicates that it is important to focus on the collective behavior that emerges as the result of the interactions among individuals, groups, and even societies. Non-equilibrium statistical physics, in particular Monte Carlo methods and the theory of collective behavior of interacting particles near phase transition points, has proven to be very valuable for understanding counterintuitive evolutionary outcomes. By treating models of human cooperation as classical spin models, a physicist can draw on familiar settings from statistical physics. However, unlike pairwise interactions among particles that typically govern solid-state physics systems, interactions among humans often involve group interactions, and they also involve a larger number of possible states even for the most simplified description of reality. The complexity of solutions therefore often surpasses that observed in physical systems. Here we review experimental and theoretical research that advances our understanding of human cooperation, focusing on spatial pattern formation, on the spatiotemporal dynamics of observed solutions, and on self-organization that may either promote or hinder socially favorable states.


80M31 Monte Carlo methods applied to problems in thermodynamics and heat transfer
65C05 Monte Carlo methods
82C22 Interacting particle systems in time-dependent statistical mechanics
91A12 Cooperative games
91D10 Models of societies, social and urban evolution
97M70 Behavioral and social sciences (aspects of mathematics education)
Full Text: DOI arXiv


[1] Peters, R. H., The Ecological Implications of Body Size, (1983), Cambridge University Press Cambridge
[2] Calder, W. A., Size, Function, and Life History, (1984), Cambridge University Press Cambridge, MA
[3] Hrdy, S. B., Mothers and Others: The Evolutionary Origins of Mutual Understanding, (2011), Harvard University Press Cambridge, MA
[4] Bowles, S.; Gintis, H., A Cooperative Species: Human Reciprocity and Its Evolution, (2011), Princeton University Press Princeton, NJ
[5] Axelrod, R., The Evolution of Cooperation, (1984), Basic Books New York
[6] Nowak, M. A.; Highfield, R., SuperCooperators: Altruism, Evolution, and Why We Need Each Other to Succeed, (2011), Free Press New York
[7] Perc, M., Self-organization of progress across the century of physics, Sci. Rep., 3, 1720, (2013)
[8] Sinatra, R.; Deville, P.; Szell, M.; Wang, D.; Barabási, A.-L., A century of physics, Nat. Phys., 11, 791-796, (2015)
[9] Arthus-Bertrand, Y., Human (Movie), (2014), Bettencourt Schueller Foundation Neuilly-sur-Seine, France
[10] Pinker, S., The Better Angels of Our Nature: Why Wiolence has Declined, (2011), Viking New york
[11] Pennisi, E., How did cooperative behavior evolve, Science, 309, 93, (2005)
[12] Kennedy, D.; Norman, C., What don’t we know?, Science, 309, 75, (2005)
[13] Castellano, C.; Fortunato, S.; Loreto, V., Statistical physics of social dynamics, Rev. Modern Phys., 81, 591-646, (2009)
[14] Szabó, G.; Fáth, G., Evolutionary games on graphs, Phys. Rep., 446, 97-216, (2007)
[15] Perc, M.; Szolnoki, A., Coevolutionary games -a mini review, Biosystems, 99, 109-125, (2010)
[16] Wang, Z.; Wang, L.; Szolnoki, A.; Perc, M., Evolutionary games on multilayer networks: a colloquium, Eur. Phys. J. B, 88, 124, (2015)
[17] Szabó, G.; Borsos, I., Evolutionary potential games on lattices, Phys. Rep., 624, 1-60, (2016) · Zbl 1357.91008
[18] D’Orsogna, M. R.; Perc, M., Statistical physics of crime: A review, Phys. Life Rev., 12, 1-21, (2015)
[19] Pastor-Satorras, R.; Castellano, C.; Van Mieghem, P.; Vespignani, A., Epidemic processes in complex networks, Rev. Modern Phys., 87, 925, (2015)
[20] Wang, Z.; Bauch, C. T.; Bhattacharyya, S.; d’Onofrio, A.; Manfredi, P.; Perc, M.; Perra, N.; Salathé, M.; Zhao, D., Statistical physics of vaccination, Phys. Rep., 664, 1-113, (2016) · Zbl 1359.92111
[21] Barabási, A.-L., Network Science, (2015), Cambridge University Press Cambridge
[22] Albert, R.; Barabási, A.-L., Statistical mechanics of complex networks, Rev. Modern Phys., 74, 47-97, (2002) · Zbl 1205.82086
[23] Newman, M. E.J., The structure and function of complex networks, SIAM Rev., 45, 167-256, (2003) · Zbl 1029.68010
[24] Boccaletti, S.; Latora, V.; Moreno, Y.; Chavez, M.; Hwang, D., Complex networks: structure and dynamics, Phys. Rep., 424, 175-308, (2006) · Zbl 1371.82002
[25] Fortunato, S., Community detection in graphs, Phys. Rep., 486, 75-174, (2010)
[26] Holme, P.; Saramäki, J., Temporal networks, Phys. Rep., 519, 97-125, (2012)
[27] Kivelä, M.; Arenas, A.; Barthelemy, M.; Gleeson, J. P.; Moreno, Y.; Porter, M. A., Multilayer networks, J. Complex Netw., 2, 203-271, (2014)
[28] Boccaletti, S.; Bianconi, G.; Criado, R.; del Genio, C.; Gómez-Gardeñes, J.; Romance, M.; Sendiña-Nadal, I.; Wang, Z.; Zanin, M., The structure and dynamics of multilayer networks, Phys. Rep., 544, 1-122, (2014)
[29] Hamilton, W. D., Genetical evolution of social behavior I & II, J. Theoret. Biol., 7, 1-51, (1964)
[30] Nowak, M. A., Five rules for the evolution of cooperation, Science, 314, 1560-1563, (2006)
[31] Nowak, M. A.; May, R. M., Evolutionary games and spatial chaos, Nature, 359, 826-829, (1992)
[32] Santos, F. C.; Pacheco, J. M., Scale-free networks provide a unifying framework for the emergence of cooperation, Phys. Rev. Lett., 95, 098104, (2005)
[33] Pacheco, J. M.; Traulsen, A.; Nowak, M. A., Coevolution of strategy and structure in complex networks with dynamical linking, Phys. Rev. Lett., 97, 258103, (2006)
[34] Gómez-Gardeñes, J.; Campillo, M.; Floría, L. M.; Moreno, Y., Dynamical organization of cooperation in complex networks, Phys. Rev. Lett., 98, 108103, (2007)
[35] Ohtsuki, H.; Nowak, M. A.; Pacheco, J. M., Breaking the symmetry between interaction and replacement in evolutionary dynamics on graphs, Phys. Rev. Lett., 98, 108106, (2007)
[36] Roca, C. P.; Cuesta, J. A.; Sánchez, A., Evolutionary game theory: temporal and spatial effects beyond replicator dynamics, Phys. Life Rev., 6, 208-249, (2009)
[37] Lee, S.; Holme, P.; Wu, Z.-X., Emergent hierarchical structures in multiadaptive games, Phys. Rev. Lett., 106, 028702, (2011)
[38] Mathiesen, J.; Mitarai, N.; Sneppen, K.; Trusina, A., Ecosystems with mutually exclusive interactions self-organize to a state of high diversity, Phys. Rev. Lett., 107, 188101, (2011)
[39] Szolnoki, A.; Perc, M.; Szabó, G., Defense mechanisms of empathetic players in the spatial ultimatum game, Phys. Rev. Lett., 109, 078701, (2012)
[40] Assaf, M.; Mobilia, M., Metastability and anomalous fixation in evolutionary games on scale-free networks, Phys. Rev. Lett., 109, 188701, (2012)
[41] Gómez, S.; Díaz-Guilera, A.; Gómez-Gardeñes, J.; Pérez-Vicente, C.; Moreno, Y.; Arenas, A., Diffusion dynamics on multiplex networks, Phys. Rev. Lett., 110, 028701, (2013)
[42] Knebel, J.; Krüger, T.; Weber, M.; Frey, E., Coexistence and survival in conservative Lotka-Volterra networks, Phys. Rev. Lett., 110, 168106, (2013)
[43] Pinheiro, F.; Santos, M. D.; Santos, F.; Pacheco, J., Origin of peer influence in social networks, Phys. Rev. Lett., 112, 098702, (2014)
[44] Szolnoki, A.; Szabó, G., Cooperation enhanced by inhomogeneous activity of teaching for evolutionary prisoner’s dilemma games, Europhys. Lett., 77, 30004, (2007)
[45] Perc, M.; Szolnoki, A., Social diversity and promotion of cooperation in the spatial prisoner’s dilemma game, Phys. Rev. E, 77, 011904, (2008)
[46] Poncela, J.; Gómez-Gardeñes, J.; Traulsen, A.; Moreno, Y., Evolutionary game dynamics in a growing structured population, New J. Phys., 11, 083031, (2009)
[47] Szolnoki, A.; Perc, M., Coevolution of teaching activity promotes cooperation, New J. Phys., 10, 043036, (2008)
[48] Szolnoki, A.; Perc, M., Leaders should not be conformists in evolutionary social dilemmas, Sci. Rep., 6, 23633, (2016)
[49] Gómez-Gardeñes, J.; Poncela, J.; Floría, L. M.; Moreno, Y., Natural selection of cooperation and degree hierarchy in heterogeneous populations, J. Theoret. Biol., 253, 296-301, (2008) · Zbl 1398.92172
[50] Szolnoki, A.; Perc, M., Correlation of positive and negative reciprocity fails to confer an evolutionary advantage: phase transitions to elementary strategies, Phys. Rev. X, 3, 041021, (2013)
[51] Andreoni, J.; Harbaugh, W.; Vesterlund, L., The carrot or the stick: rewards, punishments, and cooperation, Am. Econ. Rev., 93, 893-902, (2003)
[52] Rand, D. G.; Nowak, M. A., Human cooperation, Trends Cogn. Sci., 17, 413-425, (2013)
[53] Okada, I.; Yamamoto, H.; Toriumi, F.; Sasaki, T., The effect of incentives and meta-incentives on the evolution of cooperation, PLoS Comput. Biol., 11, e1004232, (2015)
[54] Rand, D. G.; Kraft-Todd, G.; Gruber, J., The collective benefits of feeling good and letting go: positive emotion and (dis) inhibition interact to predict cooperative behavior, PLoS One, 10, e0117426, (2015)
[55] Kraft-Todd, G.; Yoeli, E.; Bhanot, S.; Rand, D., Promoting cooperation in the field, Curr. Opin. Behav. Sci., 3, 96-101, (2015)
[56] Dreber, A.; Rand, D. G.; Fudenberg, D.; Nowa, M. A., Winners don’t punish, Nature, 452, 348-351, (2008)
[57] Rand, D. G.; Dreber, A.; Ellingsen, T.; Fudenberg, D.; Nowak, M. A., Positive interactions promote public cooperation, Science, 325, 1272-1275, (2009) · Zbl 1226.91018
[58] Hilbe, C.; Sigmund, K., Incentives and opportunism: from the carrot to the stick, Proc. R. Soc. B, 277, 2427-2433, (2010)
[59] Hauert, C., Replicator dynamics of reward & reputation in public goods games, J. Theoret. Biol., 267, 22-28, (2010) · Zbl 1410.91073
[60] Szolnoki, A.; Perc, M., Reward and cooperation in the spatial public goods game, Europhys. Lett., 92, 38003, (2010)
[61] Szolnoki, A.; Perc, M., Evolutionary advantages of adaptive rewarding, New J. Phys., 14, 093016, (2012)
[62] Szolnoki, A.; Perc, M., Antisocial pool rewarding does not deter public cooperation, Proc. R. Soc. B, 282, 20151975, (2015)
[63] Fehr, E.; Gächter, S., Cooperation and punishment in public goods experiments, Amer. Econ. Rev., 90, 980-994, (2000)
[64] Boyd, R.; Gintis, H.; Bowles, S.; Richerson, P., The evolution of altruistic punishment, Proc. Natl. Acad. Sci. USA, 100, 3531-3535, (2003)
[65] Gardner, A.; West, S. A., Cooperation, and punishment, especially in humans, Amer. Nat., 164, 753-764, (2004)
[66] Henrich, J.; McElreath, R.; Barr, A.; Ensminger, J.; Barrett, C.; Bolyanatz, A.; Cardenas, J.; Gurven, M.; Gwako, E.; Henrich, N.; Lesorogol, C.; Marlowe, F.; Tracer, D.; Ziker, J., Costly punishment across human societies, Science, 312, 1767-1770, (2006)
[67] Sigmund, K., Punish or perish? retailation and collaboration among humans, Trends Ecol. Evol., 22, 593-600, (2007)
[68] Raihani, A. T.N. J.; Bshary, R., Punishment and cooperation in nature, Trends Ecol. Evol., 27, 288-295, (2012)
[69] Szolnoki, A.; Perc, M., Effectiveness of conditional punishment for the evolution of public cooperation, J. Theoret. Biol., 325, 34-41, (2013) · Zbl 1314.91183
[70] Hauser, O. P.; Traulsen, A.; Nowak, M. A., Heterogeneity in background fitness acts as a suppressor of selection, J. Theoret. Biol., 343, 178-185, (2014) · Zbl 1411.92210
[71] Jordan, J. J.; Hoffman, M.; Bloom, P.; Rand, D. G., Third-party punishment as a costly signal of trustworthiness, Nature, 530, 473-476, (2016)
[72] Fehr, E., Don’t lose your reputation, Nature, 432, 449-450, (2004)
[73] Panchanathan, K.; Boyd, R., Indirect reciprocity can stabilize cooperation without the second-order free rider problem, Nature, 432, 499-502, (2004)
[74] Hauert, C.; Traulsen, A.; Brandt, H.; Nowak, M. A.; Sigmund, K., Via freedom to coercion: the emergence of costly punishment, Science, 316, 1905-1907, (2007) · Zbl 1226.91010
[75] Helbing, D.; Szolnoki, A.; Perc, M.; Szabó, G., Evolutionary establishment of moral and double moral standards through spatial interactions, PLoS Comput. Biol., 6, e1000758, (2010)
[76] Hilbe, C.; Traulsen, A., Emergence of responsible sanctions without second order free riders, antisocial punishment or spite, Sci. Rep., 2, 458, (2012)
[77] Chen, X.; Szolnoki, A.; Perc, M., Probabilistic sharing solves the problem of costly punishment, New J. Phys., 16, 083016, (2014)
[78] Henrich, J.; Henrich, N., Culture evolution and the puzzle of human cooperation, Cogn. Syst. Res., 7, 220-245, (2006)
[79] Boyd, R.; Richerson, P. J., Culture and the evolution of human cooperation, Philos. Trans. R. Soc. B, 364, 3281-3288, (2009)
[80] Szolnoki, A.; Perc, M., Conformity enhances network reciprocity in evolutionary social dilemmas, J. R. Soc. Interface, 12, 20141299, (2015)
[81] Chen, X.; Fu, F.; Wang, L., Social tolerance allows cooperation to prevail in an adaptive environment, Phys. Rev. E, 80, 051104, (2009)
[82] Szolnoki, A.; Chen, X., Benefits of tolerance in public goods games, Phys. Rev. E, 92, 042813, (2015)
[83] Chen, X.-J.; Wang, L., Cooperation enhanced by moderate tolerance ranges in myopically selective interactions, Phys. Rev. E, 80, 046109, (2009)
[84] Capraro, V.; Cococcioni, G., Social setting, intuition and experience in laboratory experiments interact to shape cooperative decision-making, Proc. R. Soc. B, 282, 20150237, (2015)
[85] Szolnoki, A.; Perc, M., Competition of tolerant strategies in the spatial public goods game, New J. Phys., 18, 083021, (2016)
[86] Rand, D. G., The promise of mechanical turk: how online labor markets can help theorists run behavioral experiments, J. Theoret. Biol., 299, 172-179, (2012)
[87] Herrmann, B.; Thoni, C.; Gächter, S., Antisocial punishment across societies, Science, 319, 1362-1367, (2008)
[88] Pillutla, M. M.; Malhotra, D.; Murnighan, J. K., Attributions of trust and the calculus of reciprocity, J. Exp. Soc. Psychol., 39, 448-455, (2003)
[89] Barclay, P., Reputational benefits for altruistic punishment, Evol. Hum. Behav., 27, 325-344, (2006)
[90] Fehrler, S.; Przepiorka, W., Charitable giving as a signal of trustworthiness: disentangling the signaling benefits of altruistic acts, Evol. Hum. Behav., 34, 139-145, (2013)
[91] Güth, W.; Schmittberger, R.; Schwarze, B., An experimental analysis of ultimatum bargaining, J. Econ. Behav. Organ., 3, 367-388, (1982)
[92] Falkinger, J.; Fehr, E.; Gächter, S.; Winter-Ebmer, R., A simple mechanism for the efficient provision of public goods: experimental evidence, Amer. Econ. Rev., 90, 247-264, (2000)
[93] Fehr, E.; Gächter, S., Altruistic punishment in humans, Nature, 415, 137-140, (2002)
[94] Balafoutas, L.; Grechenig, L.; Nikiforakis, N., Third-party punishment and counter-punishment in one-shot interactions, Econom. Lett., 122, 308-310, (2014)
[95] Charness, G.; Cobo-Reyes, R.; Jimenez, N., An investment game with third-party intervention, J. Econ. Behav. Organ., 68, 18-28, (2008)
[96] Sefton, M.; Schupp, O.; Walker, J., The effect of rewards and sanctions in provision of public goods, Econ. Inq., 45, 671-690, (2007)
[97] Hauser, O. P.; Hendriks, A.; Rand, D. G.; Nowak, M. A., Think global act local: preserving the global commons, Sci. Rep., 6, 36079, (2016)
[98] Pedersen, E. J.; Kurzban, R.; McCullough, M. E., Do humans really punish altruistically? A closer look, Proc. R. Soc. B, 280, 20122723, (2013)
[99] Almenberg, J.; Dreber, A.; Apicella, C.; Rand, D. G., Third party reward and punishment: group size, efficiency and public goods, Psychol. Punishment, (2017), forthcoming
[100] Gracia-Lázaro, C.; Ferrer, A.; Ruiz, G.; Tarancón, A.; Cuesta, J.; Sánchez, A.; Moreno, Y., Heterogeneous networks do not promote cooperation when humans play a prisoner’s dilemma, Proc. Natl. Acad. Sci. USA, 109, 12922-12926, (2012)
[101] Grujić, J.; Fosco, C.; Araujo, L.; Cuesta, J. A.; Sánchez, A., Social experiments in the mesoscale: humans playing a spatial prisoner’s dilemma, PLoS One, 5, e13749, (2010)
[102] Grujić, J.; Eke, B.; Cabrales, A.; Cuesta, J. A.; Sánchez, A., Three is a crowd in iterated prisoner’s dilemmas: experimental evidence on reciprocal behavior, Sci. Rep., 2, 638, (2012)
[103] Grujić, J.; Röhl, T.; Semmann, D.; Milinksi, M.; Traulsen, A., Consistent strategy updating in spatial and non-spatial behavioral experiments does not promote cooperation in social networks, PLoS One, 7, e47718, (2012)
[104] Traulsen, A.; Semmann, D.; Sommerfeld, R. D.; Krambeck, H.-J.; Milinski, M., Human strategy updating in evolutionary games, Proc. Natl. Acad. Sci. USA, 107, 2962-2966, (2010)
[105] Rand, D. G.; Arbesman, S.; Christakis, N. A., Dynamic social networks promote cooperation in experiments with humans, Proc. Natl. Acad. Sci. USA, 108, 19193-19198, (2011)
[106] Wang, J.; Suri, S.; Watts, D., Cooperation and assortativity with dynamic partner updating, Proc. Natl. Acad. Sci. USA, 109, 14363-14368, (2012)
[107] Shirado, H.; Fu, F.; Fowler, J. H.; Christakis, N. A., Quality versus quantity of social ties in experimental cooperative networks, Nature Commun., 4, 2814, (2013)
[108] Jordan, J. J.; Rand, D. G.; Arbesman, S.; Fowler, J. H.; Christakis, N. A., Contagion of cooperation in static and fluid social networks, PLoS One, 8, e66199, (2013)
[109] Perc, M.; Gómez-Gardeñes, J.; Szolnoki, A.; Floría, L. M.; Moreno, Y., Evolutionary dynamics of group interactions on structured populations: a review, J. R. Soc. Interface, 10, 20120997, (2013)
[110] Helbing, D.; Szolnoki, A.; Perc, M.; Szabó, G., Punish but not too hard: how costly punishment spreads in the spatial public goods game, New J. Phys., 12, 083005, (2010)
[111] Szolnoki, A.; Szabó, G.; Perc, M., Phase diagrams for the spatial public goods game with pool punishment, Phys. Rev. E, 83, 036101, (2011)
[112] Perc, M.; Szolnoki, A., Self-organization of punishment in structured populations, New J. Phys., 14, 043013, (2012)
[113] Binder, K.; Hermann, D. K., Monte Carlo Simulations in Statistical Physics, (1988), Springer Heidelberg
[114] Newman, M. E.J.; Barkema, G. T., Monte Carlo Methods in Statistical Physics, (1999), Oxford University Press Oxford · Zbl 1012.82019
[115] Stanley, H. E., Introduction to Phase Transitions and Critical Phenomena, (1971), Clarendon Press Oxford
[116] Liggett, T. M., Interacting Particle Systems, (1985), Springer New York · Zbl 0832.60094
[117] Marro, J.; Dickman, R., Nonequilibrium Phase Transitions in Lattice Models, (1999), Cambridge University Press Cambridge, UK
[118] Hinrichsen, H., Non-equilibrium critical phenomena and phase transitions into absorbing states, Adv. Phys., 49, 815-958, (2000)
[119] Helbing, D.; Szolnoki, A.; Perc, M.; Szabó, G., Defector-accelerated cooperativeness and punishment in public goods games with mutations, Phys. Rev. E, 81, 057104, (2010)
[120] Szolnoki, A.; Szabó, G.; Czakó, L., Competition of individual and institutional punishments in spatial public goods games, Phys. Rev. E, 84, 046106, (2011)
[121] Chen, X.; Perc, M., Optimal distribution of incentives for public cooperation in heterogeneous interaction environments, Front. Behav. Neurosci., 8, 248, (2014)
[122] Rand, D. G.; Armao, J. J.; Nakamaru, M.; Ohtsuki, H., Anti-social punishment can prevent the co-evolution of punishment and cooperation, J. Theoret. Biol., 265, 624-632, (2010)
[123] Rand, D. G.; Nowak, M. A., The evolution of antisocial punishment in optional public goods games, Nature Commun., 2, 434, (2011)
[124] Camerer, C. F., Behavioral Game Theory: Experiments in Strategic Interaction, (2003), Princeton University Press Princeton · Zbl 1019.91001
[125] Camerer, C. F.; Fehr, E., Measuring social norms and preferences using experimental games: A guide for social scientists, (Henrich, J.; Boyd, R.; Bowles, S.; Camerer, C.; Fehr, E.; Gintis, H., Foundations of Human Sociality, (2004), Oxford University Press New York), 55-95
[126] Forsythe, R.; Horowitz, J. L.; Savin, N. E.; Sefton, M., Fairness in simple bargaining experiments, Games Econom. Behav., 6, 347-369, (1994) · Zbl 0804.90146
[127] Rapoport, A.; Guyer, M., A taxonomy of \(2 \times 2\) games, (Yearbook of the Society for General Systems, vol. 11, (1966)), 203-214
[128] Fudenberg, D.; Maskin, E., The folk theorem in repeated games with discounting and incomplete information, Econometrica, 54, 533-554, (1986) · Zbl 0615.90099
[129] Trivers, R. L., The evolution of reciprocal altruism, Q. Rev. Biol., 46, 35-57, (1971)
[130] Dal Bo, P.; Frechette, G. R., On the determinants of cooperation in infinitely repeated games: A survey, J. Econ. Lit., (2017), forthcoming
[131] Blake, P. R.; Rand, D. G.; Tingley, D.; Warneken, F., The shadow of the future promotes cooperation in a repeated prisoner’s dilemma for children, Sci. Rep., 5, 14559, (2015)
[132] Nowak, M. A.; Sigmund, K., Evolution of indirect reciprocity, Nature, 437, 1291-1298, (2005)
[133] Milinski, M.; Semmann, D.; Krambeck, H.-J., Reputation helps to solve the ‘tragedy of the commons’, Nature, 415, 424-426, (2002)
[134] Pfeiffer, T.; Tran, L.; Krumme, C.; Rand, D. G., The value of reputation, J. R. Soc. Interface, 9, 2791-2797, (2012)
[135] Wedekind, C.; Milinski, M., Cooperation through image scoring in humans, Science, 288, 850-852, (2000)
[136] Amir, O.; Rand, D.; Gal, Y., Economic games on the Internet: the effect of \(1 stakes, PLoS One, 7, e31461, (2012\)
[137] Horton, J. J.; Rand, D. G.; Zeckhauser, R. J., The online laboratory: conducting experiments in a real labor market, Exp. Econ., 14, 399-425, (2011)
[138] Henrich, J.; Heine, S. J.; Norenzayan, A., Most people are not weird, Nature, 466, 29, (2010)
[139] Engel, C., Dictator games: A meta study, Exp. Econ., 14, 583-610, (2011)
[140] Henrich, J.; Boyd, R.; Bowles, S.; Camerer, C.; Fehr, E.; Gintis, H.; McElreath, R., In search of homo economicus: behavioral experiments in 15 small-scale societies, Am. Econ. Rev., 91, 73-78, (2001)
[141] Berg, J.; Dickhaut, J.; McCabe, K., Trust reciprocity, and social history, Games Econom. Behav., 10, 122-142, (1995) · Zbl 0831.90008
[142] Gächter, S.; Herrmann, B.; Thöni, C., Culture and cooperation, Philos. Trans. R. Soc. B, 365, 2651-2661, (2010)
[143] Stagnaro, M. N.; Dunham, Y.; Rand, D. G., Profit versus prejudice: harnessing self-interest to reduce in-group bias, Soc. Psychol. Pers. Sci., (2017), forthcoming
[144] Fehr, E.; Fischbacher, U., Third-party punishment and social norms, Evol. Hum. Behav., 25, 63-87, (2004)
[145] Horita, Y., Punishers may be chosen as providers but not as recipients, Evol. Behav. Sci., 1, 6-9, (2010)
[146] Kurzban, R.; DeScioli, P.; O’Brien, E., Audience effects on moralistic punishment, Evol. Hum. Behav., 28, 75-84, (2007)
[147] Jordan, J. J.; Rand, D. G., Third-party punishment as a costly signal of high continuation probabilities in repeated games, J. Theoret. Biol., 421, 189-202, (2017) · Zbl 1371.91015
[148] FeldmanHall, O.; Sokol-Hessner, P.; Van Bavel, J. J.; Phelps, E. A., Fairness violations elicit greater punishment on behalf of another than for oneself, Nature Commun., 5, 5306, (2014)
[149] Nowak, M. A.; Tarnita, C. E.; Antal, T., Evolutionary dynamics in structured populations, Philos. Trans. R. Soc. B, 365, 19-30, (2010)
[150] Ohtsuki, H.; Hauert, C.; Lieberman, E.; Nowak, M., A simple rule for the evolution of cooperation on graphs and social networks, Nature, 441, 502-505, (2006)
[151] Lieberman, E.; Hauert, C.; Nowak, M. A., Evolutionary dynamics on graphs, Nature, 433, 312-316, (2005)
[152] Allen, B.; Lippner, G.; Chen, Y.-T.; Fotouhi, B.; Nowak, M. A.; Yau, S.-T., Evolutionary dynamics on any population structure, Nature, 544, 227-230, (2017)
[153] Rand, D. G.; Nowak, M. A.; Fowler, J. H.; Christakis, N. A., Static network structure can stabilize human cooperation, Proc. Natl. Acad. Sci. USA, 111, 17093-17098, (2014)
[154] Fischbacher, U.; Gächter, S.; Fehr, E., Are people condoitionally cooperative? evidence from a public goods experiment, Econ. Lett., 71, 397-404, (2001) · Zbl 0999.91001
[155] Rand, D. G.; Greene, J. D.; Nowak, M. A., Spontaneous giving and calculated greed, Nature, 489, 427-430, (2012)
[156] Rand, D. G., Cooperation fast and slow: meta-analytic evidence for a theory of social heuristics and self-interested deliberation, Psychol. Sci., 27, 1192-1206, (2016)
[157] Sigmund, K., Games of Life: Exploration in Ecology, Evolution and Behavior, (1993), Oxford University Press Oxford, UK
[158] Weibull, J. W., Evolutionary Game Theory, (1995), MIT Press Cambridge, MA · Zbl 0879.90206
[159] Hofbauer, J.; Sigmund, K., Evolutionary Games and Population Dynamics, (1998), Cambridge University Press Cambridge, UK · Zbl 0914.90287
[160] Nowak, M. A., Evolutionary Dynamics, (2006), Harvard University Press Cambridge, MA · Zbl 1098.92051
[161] Sigmund, K., The Calculus of Selfishness, (2010), Princeton University Press Princeton, NJ · Zbl 1189.91010
[162] Capraro, V.; Cococcioni, G., Social setting, intuition and experience in laboratory experiments interact to shape cooperative decision-making, Proc. R Soc. B, 282, 20150237, (2015)
[163] Wasserman, S.; Faust, K., Social Network Analysis, (1994), Cambridge University Press Cambridge, UK
[164] Christakis, N. A.; Fowler, J. H., Connected: The Surprising Power of Our Social Networks and how They Shape Our Lives, (2009), Little Brown New York
[165] Hardin, G., The tragedy of the commons, Science, 162, 1243-1248, (1968)
[166] Szolnoki, A.; Perc, M.; Szabó, G., Topology-independent impact of noise on cooperation in spatial public goods games, Phys. Rev. E, 80, 056109, (2009)
[167] Szolnoki, A.; Perc, M., Impact of critical mass on the evolution of cooperation in spatial public goods games, Phys. Rev. E, 81, 057101, (2010)
[168] Archetti, M.; Scheuring, I., Review: game theory of public goods in one-shot social dilemmas without assortment, J. Theoret. Biol., 299, 9-20, (2012) · Zbl 1337.91041
[169] Isaac, R.; Walker, J., Group size effects in public goods provision: the voluntary contributions mechanism, Quart. J. Econ., 103, 179-199, (1988)
[170] Janssen, M. A.; Goldstone, R. L., Dynamic-persistence of cooperation in public good games when group size dynamic, J. Theoret. Biol., 243, 134-142, (2006)
[171] Szolnoki, A.; Perc, M., Group-size effects on the evolution of cooperation in the spatial public goods game, Phys. Rev. E, 84, 047102, (2011)
[172] Brandt, H.; Hauert, C.; Sigmund, K., Punishment and reputation in spatial public goods games, Proc. R. Soc. Lond. B, 270, 1099-1104, (2003)
[173] Sigmund, K.; De Silva, H.; Traulsen, A.; Hauert, C., Social learning promotes institutions for governing the commons, Nature, 466, 861-863, (2010)
[174] Sasaki, T.; Uchida, S.; Chen, X., Voluntary rewards mediate the evolution of pool punishment for maintaining public goods in large populations, Sci. Rep., 5, 8917, (2015)
[175] Sigmund, K.; Hauert, C.; Nowak, M. A., Reward and punishment, Proc. Natl. Acad. Sci. USA, 98, 10757-10762, (2001)
[176] dos Santos, M., The evolution of anti-social rewarding and its countermeasures in public goods games, Proc. R. Soc. B, 282, 20141994, (2015)
[177] Brandt, H.; Hauert, C.; Sigmund, K., Punishing and abstaining for public goods, Proc. Natl. Acad. Sci. USA, 103, 495-497, (2006)
[178] Sasaki, T.; Unemi, T., Replicator dynamics in public goods games with reward funds, J. Theoret. Biol., 287, 109-114, (2011) · Zbl 1397.91078
[179] Gintis, H., Strong reciprocity and human sociality, J. Theoret. Biol., 206, 169-179, (2000)
[180] Fehr, E.; Fischbacher, U.; Gächter, S., Strong reciprocity human cooperation and the enforcement of social norms, Hum. Nature, 13, 1-25, (2002)
[181] Bowles, S.; Gintis, H., The evolution of strong reciprocity: cooperation in heterogeneous populations, Theor. Popul. Biol., 65, 17-28, (2004) · Zbl 1105.92021
[182] Yamagishi, T.; Horita, Y.; Mifune, N.; Hashimoto, H.; Li, Y.; Shinada, M.; Miura, A.; Inukai, K.; Takagishi, H.; Simunovic, D., Rejection of unfair offers in the ultimatum game is no evidence of strong reciprocity, Proc. Natl. Acad. Sci. USA, 109, 20364-20368, (2012)
[183] Egloff, B.; Richter, D.; Schmukle, S., Need for conclusive evidence that positive and negative reciprocity are unrelated, Proc. Natl. Acad. Sci. USA, 110, E786, (2013)
[184] Gächter, S., Carrot or stick?, Nature, 483, 39-40, (2012)
[185] Chen, X.; Sasaki, T.; Brännström, Å.; Dieckmann, U., First carrot hen stick: how the adaptive hybridization of incentives promotes cooperation, J. R. Soc. Interface, 12, 20140935, (2014)
[186] Hauert, C.; De Monte, S.; Hofbauer, J.; Sigmund, K., Volunteering as red queen mechanism for cooperation in public goods game, Science, 296, 1129-1132, (2002)
[187] Kerr, B.; Riley, M. A.; Feldman, M. W.; Bohannan, B. J.M., Local dispersal promotes biodiversity in a real-life game of rock-paper-scissors, Nature, 418, 171-174, (2002)
[188] Kirkup, B. C.; Riley, M. A., Antibiotic-mediated antaginism leads to a bacterial game of rock-paper-scissors in vivo, Nature, 428, 412-414, (2004)
[189] Reichenbach, T.; Mobilia, M.; Frey, E., Coexistence versus extinction in the stochastic cyclic Lotka-Volterra model, Phys. Rev. E, 74, 051907, (2006)
[190] Arenas, A.; Camacho, J.; Cuesta, J. A.; Requejo, R., The joker effect: cooperation driven by destructive agents, J. Theoret. Biol., 279, 113-119, (2011) · Zbl 1397.91060
[191] Wang, W.-X.; Ni, X.; Lai, Y.-C.; Grebogi, C., Pattern formation synchronization, and outbreak of biodiversity in cyclically competing games, Phys. Rev. E, 83, 011917, (2011)
[192] Szolnoki, A.; Mobilia, M.; Jiang, L.-L.; Szczesny, B.; Rucklidge, A. M.; Perc, M., Cyclic dominance in evolutionary games: a review, J. R. Soc. Interface, 11, 20140735, (2014)
[193] Grošelj, D.; Jenko, F.; Frey, E., How turbulence regulates biodiversity in systems with cyclic competition, Phys. Rev. E, 91, 03309, (2015)
[194] Hauert, C.; De Monte, S.; Hofbauer, J.; Sigmund, K., Replicator dynamics in optional public goods games, J. Theoret. Biol., 218, 187-194, (2002)
[195] Semmann, D.; Krambeck, H.-J.; Milinski, M., Volunteering leads to rock-paper-scissors dynamics in a public goods game, Nature, 425, 390-393, (2003)
[196] Atomic Heritage Foundation, Computing and the Manhattan Project, 2016. http://www.atomicheritage.org/history
[197] Dickman, R., First- and second-order phase transitions in a driven lattice gas with nearest-neighbor exclusion, Phys. Rev. E, 64, 016124, (2001)
[198] Szolnoki, A., Dynamical mean-field approximation for a pair contact process with a particle source, Phys. Rev. E, 66, 057102, (2002)
[199] Dickman, R., N-site approximations and coherent-anomaly-method analysis for a stochastic sandpile, Phys. Rev. E, 66, 036122, (2002)
[200] Szolnoki, A.; Szabó, G.; Ravasz, M., Three-state Potts model in combination with the rock-scissors-paper game, Phys. Rev. E, 71, 027102, (2005)
[201] Szabó, G.; Tőke, C., Evolutionary prisoner’s dilemma game on a square lattice, Phys. Rev. E, 58, 69-73, (1998)
[202] Glauber, R. J., Time-dependent statistics of the Ising model, J. Math. Phys., 4, 294-307, (1963) · Zbl 0145.24003
[203] Binder, K.; Landau, D. P., Phase diagrams and critical behavior in Ising square lattices with nearest- and next-nearest-neighbor interactions, Phys. Rev. B, 21, 1941-1962, (1980)
[204] Szabó, G.; Szolnoki, A., Selfishness fraternity, and other-regarding preference in spatial evolutionary games, J. Theoret. Biol., 299, 81-87, (2012) · Zbl 1337.91024
[205] Amaral, M. A.; Perc, M.; Wardil, L.; Szolnoki, A.; da Silva Júnior, E. J.; da Silva, J. K., Role-separating ordering in social dilemmas controlled by topological frustration, Phys. Rev. E, 95, 032307, (2017)
[206] Traulsen, A.; Hauert, C.; De Silva, H.; Nowak, M. A.; Sigmund, K., Exploration dynamics in evolutionary games, Proc. Natl. Acad. Sci. USA, 106, 709-712, (2009) · Zbl 1202.91029
[207] Sysi-Aho, M.; Saramäki, J.; Kertész, J.; Kaski, K., Spatial snowdrift game with myopic agents, Eur. Phys. J. B, 44, 129-135, (2005)
[208] Roca, C. P.; Cuesta, J. A.; Sánchez, A., Effect of spatial structure on the evolution of cooperation, Phys. Rev. E, 80, 046106, (2009)
[209] Szabó, G.; Szolnoki, A.; Varga, M.; Hanusovszky, L., Ordering in spatial evolutionary games for pairwise collective strategy updates, Phys. Rev. E, 80, 026110, (2010)
[210] Szabó, G.; Szolnoki, A.; Czakó, L., Coexistence of fraternity and egoism for spatial social dilemmas, J. Theoret. Biol., 317, 126-132, (2013) · Zbl 1368.91033
[211] Wang, Z.; Szolnoki, A.; Perc, M., If players are sparse social dilemmas are too: importance of percolation for evolution of cooperation, Sci. Rep., 2, 369, (2012)
[212] Vilone, D.; Ramasco, J. J.; Sánchez, A.; San Miguel, M., Social imitation versus strategic choice or consensus versus cooperation, in the networked prisoner’s dilemma, Phys. Rev. E, 90, 022810, (2014)
[213] Szolnoki, A.; Perc, M., Evolution of extortion in structured populations, Phys. Rev. E, 89, 022804, (2014)
[214] Szolnoki, A.; Perc, M., Defection and extortion as unexpected catalysts of unconditional cooperation in structured populations, Sci. Rep., 4, 5496, (2014)
[215] Amaral, M.; Wardil, L.; Perc, M.; da Silva, J., Stochastic win-stay-lose-shift strategy with dynamic aspirations in evolutionary social dilemmas, Phys. Rev. E, 94, 032317, (2016)
[216] Kadanoff, L. P., Scaling laws for Ising models near tc, Physics, 2, 263-272, (1966)
[217] Kadanoff, L. P.; Götze, W.; Hamblen, D.; Hecht, R.; Lewis, E.; Palciauskas, V. V.; Rayl, M.; Swift, J.; Aspnes, D.; Kane, J., Static phenomena near critical points: theory and experiment, Rev. Modern Phys., 39, 395, (1967)
[218] Wilson, K. G., The renormalization group: critical phenomena and the Kondo problem, Rev. Modern Phys., 47, 773, (1975)
[219] Hohenberg, P. C.; Halperin, B. I., Theory of dynamic critical phenomena, Rev. Modern Phys., 49, 435, (1977)
[220] Ódor, G., Universality classes in nonequilibrium lattice systems, Rev. Modern Phys., 76, 663-724, (2004) · Zbl 1205.82102
[221] Perc, M., Does strong heterogeneity promote cooperation by group interactions?, New J. Phys., 13, 123027, (2011)
[222] Griffiths, R. B., Phys. Rev. Lett., 23, 17-19, (1969)
[223] Muñoz, M. A.; Juhász, R.; Castellano, C.; Ódor, G., Phys. Rev. Lett., 105, 128701, (2010)
[224] Vazquez, F.; Bonachela, J. A.; López, C.; Muñoz, M. A., Phys. Rev. Lett., 106, 235702, (2011)
[225] Droz, M.; Szwabinski, J.; Szabó, G., Motion of influential players can support cooperation in prisoner’s dilemma, Eur. Phys. J. B, 71, 579-585, (2009) · Zbl 1188.91144
[226] Noest, A. J., Phys. Rev. Lett., 57, 90-93, (1986)
[227] Noest, A. J., Phys. Rev. B, 38, 2715-2720, (1988)
[228] Helbing, D.; Johansson, A., Evolutionary dynamics of populations with conflicting interactions: classification and analytical treatment considering asymmetry and power, Phys. Rev. E, 81, 016112, (2010)
[229] Ohtsuki, H.; Iwasa, Y.; Nowak, M. A., Indirect reciprocity provides only a narrow margin of efficiency for costly punishment, Nature, 457, 79-82, (2009)
[230] Dornic, I.; Chaté, H.; Chave, J.; Hinrichsen, H., Critical coarsening without surface tension: the universality class of the voter model, Phys. Rev. Lett., 87, 045-701, (2001)
[231] Janssen, H. K., On the non-equilibrium phase-transition in reaction-diffusion systems with an absorbing state, Z. Phys. B, 42, 151-154, (1981)
[232] Grassberger, P., On phase-transitions in Schlögl 2nd model, Z. Phys. B, 47, 365-374, (1982)
[233] Hintze, A.; Adami, C., Punishment in public goods games leads to meta-stable phase transitions and hysteresis, Phys. Biol., 12, 046005, (2015)
[234] Nakamaru, M.; Iwasa, Y., The evolution of altruism and punishment: role of selfish punisher, J. Theoret. Biol., 240, 475-488, (2006)
[235] Short, M. B.; Brantingham, P. J.; D’Orsogna, M. R., Cooperation and punishment in an adversarial game: how defectors pave the way to a peaceful society, Phys. Rev. E, 82, 066114, (2010)
[236] Amor, D. R.; Fort, J., Effects of punishment in a mobile population playing the prisoner’s dilemma game, Phys. Rev. E, 84, 066115, (2011)
[237] Xu, C.; Ji, M.; Yap, Y.; Zheng, D.-F.; Hui, P. M., Costly punishment and cooperation in evolutionary snowdrift game, Physica A, 390, 1607-1614, (2011)
[238] Gao, J.; Li, Z.; Cong, R.; Wang, L., Tolerance-based punishment in continuous public goods game, Physica A, 391, 4111-4120, (2012)
[239] Chan, N. W.; Xu, C.; Tey, S. K.; Yap, Y. J.; Hui, P. M., Evolutionary snowdrift game incorporating costly punishment in structured populations, Physica A, 392, 168-176, (2013)
[240] Vukov, J.; Pinheiro, F.; Santos, F.; Pacheco, J., Reward from punishment does not emerge at all costs, PLoS Comput. Biol., 9, e1002868, (2013)
[241] Luo, J.-S.; Zhao, M., Proportional cost for punishment enhances spatial reciprocity in evolutionary games, Chaos Solitons Fractals, 56, 139-144, (2013) · Zbl 1348.91039
[242] Wang, Z.; Xia, C.-Y.; Meloni, S.; Zhou, C.-S.; Moreno, Y., Impact of social punishment on cooperative behavior in complex networks, Sci. Rep., 3, 3055, (2013)
[243] Chen, X.; Sasaki, T.; Perc, M., Evolution of public cooperation in a monitored society with implicated punishment and within-group enforcement, Sci. Rep., 5, 17050, (2015)
[244] Chen, X.; Szolnoki, A.; Perc, M., Competition and cooperation among different punishing strategies in the spatial public goods game, Phys. Rev. E, 92, 012819, (2015)
[245] Milinski, M.; Rockenbach, B., On the interaction of the stick and the carrot in social dilemmas, J. Theoret. Biol., 299, 139-143, (2012)
[246] Reichenbach, T.; Mobilia, M.; Frey, E., Mobility promotes and jeopardizes biodiversity in rock-paper-scissors games, Nature, 448, 1046-1049, (2007)
[247] Reichenbach, T.; Mobilia, M.; Frey, E., Noise and correlations in a spatial population model with cyclic competititon, Phys. Rev. Lett., 99, 238105, (2007)
[248] Mobilia, M., Oscillatory dynamics in rock-paper-scissors games with mutations, J. Theoret. Biol., 264, 1-10, (2010) · Zbl 1406.91043
[249] Mobilia, M., Fixation and polarization in a three-species opinion dynamics model, Europhys. Lett., 95, 50002, (2011)
[250] Wu, Z.-X.; Xu, X.-J.; Chen, Y.; Wang, Y.-H., Spatial prisoner’s dilemma game with volunteering in Newman-Watts small-world networks, Phys. Rev. E, 71, 037103, (2005)
[251] Traulsen, A.; Röhl, T.; Milinski, M., An economic experiment reveals that humans prefer pool punishment to maintain the commons, Proc. R. Soc. B, 279, 3716-3721, (2012)
[252] Gurerk, O.; Irlenbusch, B.; Rockenbach, B., The competitive advantage of sanctioning institutions, Science, 312, 108-111, (2006)
[253] Axelrod, R.; Keohane, R. O., Achieving cooperation under anarchy: strategies and institutions, World Polit., 38, 226-254, (1985)
[254] Ostrom, E., Governing the Commons: The Evolution of Institutions for Collective Action, (1990), Cambridge University Press Cambridge, UK
[255] Bowles, S.; Choi, J.-K.; Hopfensitz, A., The co-evolution of individual behaviors and social institutions, J. Theoret. Biol., 223, 135-147, (2003)
[256] Henrich, J., Cooperation, punishment, and the evolution of human institutions, Science, 312, 60-61, (2006)
[257] Isakov, A.; Rand, D., The evolution of coercive institutional punishment, Dyn. Games Appl., 2, 97-109, (2012) · Zbl 1273.91057
[258] Cressman, R.; Song, J.-W.; Zhang, B.-Y.; Tao, Y., Cooperation and evolutionary dynamics in the public goods game with institutional incentives, J. Theoret. Biol., 299, 144-151, (2012) · Zbl 1337.91042
[259] Vasconcelos, V. V.; Santos, F. C.; Pacheco, J. M., A bottom-up institutional approach to cooperative governance of riskly commons, Nature Clim. Change, 3, 797-801, (2013)
[260] Zhang, B.; Li, C.; De Silva, H.; Bednarik, P.; Sigmund, K., The evolution of sanctioning institutions: an experimental approach to the social contract, Exp. Econ., 17, 285-303, (2014)
[261] Sasaki, T., The evolution of cooperation through institutional incentives and optional participation, Dyn. Games Appl., 4, 345-362, (2014) · Zbl 1302.91025
[262] Gao, L.; Wang, Z.; Pansini, R.; an Rui-Wu Wang, Y.-T. L., Collective punishment is more effective than collective reward for promoting cooperation, Sci. Rep., 5, 17752, (2015)
[263] Perc, M., Sustainable institutionalized punishment requires elimination of second-order free-riders, Sci. Rep., 2, 344, (2012)
[264] Tainaka, K., Paradoxial effect in a three-candidate voter model, Phys. Lett. A, 176, 303-306, (1993)
[265] Frean, M.; Abraham, E. D., Rock-scissors-paper and the survival of the weakest, Proc. R. Soc. B, 268, 1323-1327, (2001)
[266] Kendall, B. E.; Briggs, C. J.; Murdoch, W. W.; Turchin, P.; Ellner, S. P.; McCauley, E.; Nisbet, R. M.; Wood, S. N., Why do populations cycle? A synthesis of statistical and mechanistic modeling approaches, Ecology, 80, 1789-1805, (1999)
[267] Laird, R. A.; Schamp, B. S., Does local competition increase the coexistence of species in intransitive networks?, Ecology, 89, 237-247, (2008)
[268] Laird, R. A.; Schamp, B. S., Competitive intransitivity population interaction structure, and strategy coexistence, J. Theoret. Biol., 365, 149-158, (2015) · Zbl 1314.92132
[269] Masuda, N., Participation costs dismiss the advantage of heterogeneous networks in evolution of cooperation, Proc. R. Soc. B, 274, 1815-1821, (2007)
[270] Szolnoki, A.; Perc, M.; Danku, Z., Towards effective payoffs in the prisoner’s dilemma game on scale-free networks, Physica A, 387, 2075-2082, (2008)
[271] Santos, F. C.; Santos, M. D.; Pacheco, J. M., Social diversity promotes the emergence of cooperation in public goods games, Nature, 454, 213-216, (2008)
[272] Barabási, A.-L.; Albert, R., Emergence of scaling in random networks, Science, 286, 509-512, (1999) · Zbl 1226.05223
[273] Boyd, R.; Gintis, H.; Bowles, S., Coordinated punishment of defectors sustains cooperation and can proliferate when rare, Science, 328, 617-620, (2010) · Zbl 1226.91014
[274] Harmer, G. P.; Abbott, D., Losing strategies can win by parrondo’s paradox, Nature, 402, 864, (1999) · Zbl 1059.60503
[275] Parrondo, J. M.R.; Harmer, G. P.; Abbott, D., New paradoxical games based on Brownian ratchets, Phys. Rev. Lett., 85, 5226-5229, (2000)
[276] Raihani, N.; McAuliffe, K., Human punishment is motivated by inequity aversion not a desire for reciprocity, Biol. Lett., 8, 802-804, (2012)
[277] Nakamaru, M.; Iwasa, Y., Evolution of altruism by costly punishment in lattice-structured population: score-dependent viability versus score-dependent fertility, Evol. Ecol. Res., 7, 853-870, (2005)
[278] dos Santos, M.; Rankin, D. J.; Wedekind, C., The evolution of punishment through reputation, Proc. R. Soc. B, 278, 371-377, (2011)
[279] Perc, M.; Szolnoki, A.; Szabó, G., Cyclical interactions with alliance specific heterogeneous invasion rates, Phys. Rev. E, 75, 052102, (2007)
[280] Szolnoki, A.; Perc, M., Reentrant phase transitions and defensive alliances in social dilemmas with informed strategies, Europhys. Lett., 110, 38003, (2015)
[281] Boyd, R.; Richerson, P.; Henrich, J., The cultural niche: why social learning is essential for human adaptation, Proc. Natl. Acad. Sci. USA, 108, 10918-10925, (2011)
[282] Poncela-Casasnovas, J.; Gutiérrez-Roig, M.; Gracia-Lázaro, C.; Vicens, J.; Gómez-Gardeñes, J.; Perelló, J.; Moreno, Y.; Duch, J.; Sánchez, A., Humans display a reduced set of consistent behavioral phenotypes in dyadic games, Sci. Adv., 2, e1600451, (2016)
[283] Wang, Z.; Jusup, M.; Wang, R.-W.; Shi, L.; Iwasa, Y.; Moreno, Y.; Kurths, J., Onymity promotes cooperation in social dilemma experiments, Sci. Adv., 3, e1601444, (2017)
[284] Bear, A.; Rand, D. G., Intuition deliberation, and the evolution of cooperation, Proc. Natl. Acad. Sci. USA, 113, 936-941, (2016)
[285] Wang, Z.; Szolnoki, A.; Perc, M., Different perceptions of social dilemmas: evolutionary multigames in structured populations, Phys. Rev. E, 90, 032813, (2014)
[286] Szolnoki, A.; Perc, M., Coevolutionary success-driven multigames, Europhys. Lett., 108, 28004, (2014)
[287] Amaral, M. A.; Wardil, L.; Perc, M.; da Silva, J. K., Evolutionary mixed games in structured populations: cooperation and the benefits of heterogeneity, Phys. Rev. E, 93, 042304, (2016)
[288] Mantegna, R. N.; Stanley, H. E., Introduction to Econophysics: Correlations and Complexity in Finance, (1999), Cambridge University Press Cambridge
[289] Plerou, V.; Gopikrishnan, P.; Rosenow, B.; Amaral, L. A.N.; Stanley, H. E., Universal and nonuniversal properties of cross correlations in financial time series, Phys. Rev. Lett., 83, 1471, (1999)
[290] Plerou, V.; Gopikrishnan, P.; Rosenow, B.; Amaral, L. A.N.; Guhr, T.; Stanley, H. E., Random matrix approach to cross correlations in financial data, Phys. Rev. E, 65, 066126, (2002)
[291] Onnela, J.-P.; Chakraborti, A.; Kaski, K.; Kertesz, J.; Kanto, A., Dynamics of market correlations: taxonomy and portfolio analysis, Phys. Rev. E, 68, 056110, (2003)
[292] Matteo, T. D.; Aste, T.; Dacorogna, M. M., Long-term memories of developed and emerging markets: using the scaling analysis to characterize their stage of development, J. Bank. Finance, 29, 827-851, (2005)
[293] Aste, T.; Shaw, W.; Di Matteo, T., Correlation structure and dynamics in volatile markets, New J. Phys., 12, 085009, (2010)
[294] Battiston, S.; Caldarelli, G.; May, R. M.; Roukny, T.; Stiglitz, J. E., The price of complexity in financial networks, Proc. Natl. Acad. Sci. USA, 113, 10031-10036, (2016) · Zbl 1355.91086
[295] Helbing, D.; Brockmann, D.; Chadefaux, T.; Donnay, K.; Blanke, U.; Woolley-Meza, O.; Moussaid, M.; Johansson, A.; Krause, J.; Perc, M., Saving human lives: what complexity science and information systems can contribute, J. Stat. Phys., 158, 735-781, (2015) · Zbl 1332.91092
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.