Promotion of cooperation in evolutionary game dynamics with local information. (English) Zbl 1394.91044
Summary: In this paper, we propose a strategy-updating rule driven by local information, which is called Local process. Unlike the standard Moran process, the Local process does not require global information about the strategic environment. By analyzing the dynamical behavior of the system, we explore how the local information influences the fixation of cooperation in two-player evolutionary games. Under weak selection, the decreasing local information leads to an increase of the fixation probability when natural selection does not favor cooperation replacing defection. In the limit of sufficiently large selection, the analytical results indicate that the fixation probability increases with the decrease of the local information, irrespective of the evolutionary games. Furthermore, for the dominance of defection games under weak selection and for coexistence games, the decreasing of local information will lead to a speedup of a single cooperator taking over the population. Overall, to some extent, the local information is conducive to promoting the cooperation.
Keywords:
evolutionary game dynamics; evolution of cooperation; stochastic process; local informationReferences:
| [1] | Altrock, P. M.; Gokhale, C. S.; Traulsen, A., Stochastic slowdown in evolutionary processes, Phys. Rev. E, 82, Article 011925 pp. (2010) |
| [2] | Altrock, P. M.; Traulsen, A., Fixation times in evolutionary games under weak selection, New J. Phys., 11, Article 013012 pp. (2009) |
| [3] | Altrock, P. M.; Traulsen, A.; Galla, T., The mechanics of stochastic slowdown in evolutionary games, J. Theor. Biol., 311, 94-106 (2012) · Zbl 1337.91017 |
| [4] | Antal, T.; Scheuring, I., Fixation of strategies for an evolutionary game in finite populations, Bull . Math. Biol., 68, 1923-1944 (2006) · Zbl 1296.92238 |
| [5] | Axelrod, R.; Hamilton, W. D., The evolution of cooperation, Science, 211, 1390-1396 (1981) · Zbl 1225.92037 |
| [6] | Boyd, R.; Gintis, H.; Bowles, S.; Richerson, P. J., The evolution of altruistic punishment, Proc. Natl. Acad. Sci., 100, 3531-3535 (2003) |
| [7] | Brauchli, K.; Killingback, T.; Doebeli, M., Evolution of cooperation in spatially structured populations, J. Theor. Biol., 200, 405-417 (1999) |
| [8] | Cabrales, A., Stochastic replicator dynamics, Intl. Econ. Rev., 41, 451-481 (2000) |
| [9] | Carroll, C. R.; Janzen, D. H., Ecology of foraging by ants, Annu. Rev. Ecol. Syst., 4, 231-257 (1973) |
| [10] | Chen, X.; Wang, L., Promotion of cooperation induced by appropriate payoff aspirations in a small-world networked game, Phys. Rev. E, 77, Article 017103 pp. (2008) |
| [11] | Claussen, J. C.; Traulsen, A., Non-Gaussian fluctuations arising from finite populations: Exact results for the evolutionary Moran process.Phys, Rev. E, 71, Article 025101 pp. (2005) |
| [12] | Deneubourg, J. L.; Pasteels, J. M.; Verhaeghe, J. C., Probabilistic behaviour in ants: a strategy of errors?, J. Theor. Biol., 105, 259-271 (1983) |
| [13] | Detrain, C.; Deneubourg, J. L., Collective decision-making and foraging patterns in ants and honeybees, Adv. Insect. Physiol., 35, 123-173 (2008) |
| [14] | Doebeli, M.; Hauert, C., Models of cooperation based on the Prisoner’s Dilemma and the Snowdrift game, Ecol. Lett., 8, 748-766 (2005) |
| [15] | Du, J.; Wu, B.; Wang, L., Aspiration dynamics in structured population acts as if in a well-mixed one, Sci. Rep., 5, 8014 (2015) |
| [16] | Grüter, C.; Czaczkes, T. J.; Ratnieks, F. L.W., Decision making in ant foragers (Lasius niger) facing conflicting private and social information, Behav. ecol. sociobiol., 65, 141-148 (2011) |
| [17] | Hauert, C.; Holmes, M.; Doebeli, M., Evolutionary games and population dynamics: maintenance of cooperation in public goods games, Proc. R. Soc. B, 273, 2565-2570 (2006) |
| [18] | Hofbauer, J.; Schuster, P.; Sigmund, K., Evolutionary stable strategies and game dynamics, J. Theor. Biol., 81, 609-612 (1979) |
| [19] | Hofbauer, J.; Sigmund, K., Evolutionary Game and Population Dynamics (1998), Cambridge University Press · Zbl 0914.90287 |
| [20] | Imhof, L. A.; Nowak, M. A., Evolutionary game dynamics in a Wright-Fisher process, J. Math. Biol., 52, 667-681 (2006) · Zbl 1110.92028 |
| [21] | Karlin, S.; Taylor, H., A First Course in Stochastic Processes (1975), Academic Press · Zbl 0315.60016 |
| [22] | Kurokawa, S.; Ihara, Y., Emergence of cooperation in public goods games, Pro. R. Soc. B, 276, 1379-1384 (2009) |
| [23] | Liu, X.; Pan, Q.; Kang, Y.; He, M., Fixation times in evolutionary games with the Moran and Fermi processes, J. Theor. Biol., 387, 214-220 (2015) · Zbl 1343.91007 |
| [24] | Liu, X.; Pan, Q.; Kang, Y.; He, M., Fixation probabilities in evolutionary games with the Moran and Fermi processes, J. Theor. Biol., 364, 242-248 (2015) · Zbl 1405.91038 |
| [25] | Nowak, M. A., Evolutionary dynamics: Exploring the Equations of Life (2006), Harward University Press · Zbl 1115.92047 |
| [26] | Nowak, M. A., Five rules for the evolution of cooperation, Science, 314, 1560-1563 (2006) |
| [27] | Nowak, M. A., Evolving cooperation, J. Theor. Biol., 299, 1-8 (2012) · Zbl 1337.92152 |
| [28] | Nowak, M. A.; Sasaki, A.; Taylor, C.; Fudenberg, D., Emergence of cooperation and evolutionary stability in finite populations, Nature, 428, 646-650 (2004) |
| [29] | Oechssler, J., Cooperation as a result of learning with aspiration levels, J. Econ. Behav. Organ., 49, 405-409 (2002) |
| [30] | Ohtsuki, H.; Nowak, M. A., Evolutionary games on cycles, Proc. Biol. Sci., 273, 2249-2256 (2006) |
| [31] | Ohtsuki, H.; Nowak, M. A., Evolutionary stability on graphs, J. Theor. Biol., 251, 698-707 (2008) · Zbl 1398.91079 |
| [32] | Perc, M.; Wang, Z., Heterogeneous Aspirations Promote Cooperation in the Prisoner’s Dilemma Game, Plos One, 5, e15117 (2010) |
| [33] | Platkowski, T., Enhanced cooperation in prisoner’s dilemma with aspiration, Appl. Math. Lett., 22, 1161-1165 (2009) · Zbl 1173.91329 |
| [34] | Platkowski, T., Aspiration-based full cooperation in finite systems of players, Appl. Math. Comput., 251, 46-54 (2015) · Zbl 1328.91030 |
| [35] | Platkowski, T.; Bujnowski, P., Cooperation in aspiration-based N-person prisoner’s dilemmas, Phys. Rev. E, 79, Article 036103 pp. (2009) |
| [36] | Smith, J. M., Theory of games and evolution of animal conflicts, J. Theor. Biol., 47, 209-221 (1974) |
| [37] | Smith, J. M., Evolution and the Theory of Games (1982), Cambridge University Press · Zbl 0526.90102 |
| [38] | Smith, J. M.; Price, G. R., Logic of animal conflict, Nature, 246, 15-18 (1973) · Zbl 1369.92134 |
| [39] | Stahl, D. O.; Haruvy, E., Aspiration-based and reciprocity-based rules in learning dynamics for symmetric normal-form games, J. Math. Psychol., 46, 531-553 (2002) · Zbl 1027.91012 |
| [40] | Szabo, G.; Szolnoki, A., Cooperation in spatial prisoner’s dilemma with two types of players for increasing number of neighbors, Phys. Rev. E, 79, Article 016106 pp. (2009) |
| [41] | Szolnoki, A.; Perc, M.; Szabo, G., Topology-independent impact of noise on cooperation in spatial public goods games, Phys. Rev. E, 80, Article 056109 pp. (2009) |
| [42] | Szolnoki, A.; Perc, M.; Szabo, G.; Stark, H.-U., Impact of aging on the evolution of cooperation in the spatial prisoner’s dilemma game, Phys. Rev. E, 80, Article 021901 pp. (2009) |
| [43] | Taylor, C.; Chen, J.; Iwasa, Y., Cooperation maintained by fitness adjustment, Evo. Ecol.Res., 9, 1023-1041 (2007) |
| [44] | Taylor, C.; Fudenberg, D.; Sasaki, A.; Nowak, M. A., Evolutionary game dynamics in finite populations, Bull. Math. Biol., 66, 1621-1644 (2004) · Zbl 1334.92372 |
| [45] | Taylor, C.; Iwasa, Y.; Nowak, M. A., A symmetry of fixation times in evoultionary dynamics, J. Theor. Biol., 243, 245-251 (2006) · Zbl 1447.92296 |
| [46] | Taylor, P. D.; Jonker, L. B., Evolutionarily stable strategies and game dynamics, Math. Bios., 40, 145-156 (1978) · Zbl 0395.90118 |
| [47] | Traniello, J. F.A., Recruitment behavior, orientation, and the organization of foraging in the carpenter ant Camponotus pennsylvanicus DeGeer (Hymenoptera: Formicidae), Behav. Ecol. Sociobiol., 2, 61-79 (1977) |
| [48] | Traulsen, A.; Claussen, J.; Hauert, C., Coevolutionary Dynamics: From Finite to Infinite Populations, Phys. Rev. Lett., 95, Article 238701 pp. (2005) |
| [49] | Traulsen, A.; Nowak, M. A.; Pacheco, J. M., Stochastic dynamics of invasion and fixation, Phys. Rev. E, 74, Article 011909 pp. (2006) |
| [50] | Traulsen, A.; Pacheco, J.; Imhof, L., Stochasticity and evolutionary stability, Phys. Rev. E, 74, Article 021905 pp. (2006) |
| [51] | Weibull, J. M., Evolutionary Game Theory (1997), MIT press |
| [52] | Wu, B.; Altrock, P. M.; Wang, L.; Traulsen, A., Universality of weak selection, Phys. Rev. E, 82, Article 046106 pp. (2010) |
| [53] | Wu, B.; Traulsen, A.; Gokhale, C. S., Dynamic properties of evolutionary multi-player games in finite populations, Games, 4, 182-199 (2013) · Zbl 1314.91039 |
| [54] | Yang, H. X.; Wu, Z. X.; Wang, B. H., Role of aspiration-induced migration in cooperation, Phys. Rev. E, 81, Article 065101 pp. (2010) |
| [55] | Zhou, D.; Wu, B.; Ge, H., Evolutionary stability and quasi-stationary strategy in stochastic evolutionary game dynamics, J. Theor. Biol, 264, 874-881 (2010) · Zbl 1406.91061 |
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