Abstract
We consider in this paper the Hawk-Dove game in which each of infinitely many individuals, involved with pairwise encounters with other individuals, can decide whether to act aggressively (Hawk) or peacefully (Dove). Each individual is characterized by its strength. The strength distribution among the population is assumed to be fixed and not to vary in time. If both individuals involved in an interaction are Hawks, there will be a fight, the result of which will be determined by the strength of each of the individuals involved. The larger the difference between the strength of the individuals is, the larger is the cost for the weaker player involved in the fight. Our goal is to study the influence of the parameters (such as the strength level distribution) on the equilibrium of the game. We show that for some parameters there exists a threshold equilibrium policy while for other parameters there is no equilibrium policy at all.
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References
Altman, E., El-Azouzi, R., Hayel, Y., Tembine, H.: The evolution of transport protocols: an evolutionary game perspective. Comput. Netw. 53(10), 1751–1759 (2009)
Altman, E., Fiems, D., Haddad, M., Gaillard, J.: Semi-dynamic hawk and dove game, applied to power control. In: Proceedings IEEE INFOCOM, pp. 2771–2775, March 2012
Altman, E., Gaillard, J., Haddad, M., Wiecek, P.: Dynamic hawk and dove games within flocks of birds. In: Hart, E., Timmis, J., Mitchell, P., Nakamo, T., Dabiri, F. (eds.) BIONETICS 2011. LNICST, vol. 103, pp. 115–124. Springer, Heidelberg (2012). doi:10.1007/978-3-642-32711-7_9
Altman, E., Brunetti, I.: Revisiting evolutionary game theory. In: IEEE Conference on Decision and Control (CDC) 2013, pp. 1842–1847 (2013)
Auger, P., Pontier, D.: Fast game dynamics coupled to slow population dynamics: a single population with hawk-dove strategies. Math. Comput. Modell. 27(4), 81–88 (1998)
Ben Khalifa, N., ElAzouzi, R., Hayel, Y.: Evolutionary games in interacting communities. Dyn. Games Appl. J. 7, 131–156 (2017)
Cressman, R.: The Stability Concept of Evolutionary Game Theory. Springer, Heidelberg (1992)
Friedman, E., Henderson, S.: Fairness and efficiency in processor sharing protocols to minimize sojourn times. In: Proceedings of ACM SIGMETRICS, pp. 229–337 (2003)
Haddad, M., Altman, E., Fiems, D., Gaillard, J.: Paradoxes in semi-dynamic evolutionary power control game: when intuition fools you!. IEEE Trans. Wirel. Commun. 12(11), 5728–5739 (2013)
Hayel, Y., Belmega, E.V., Altman, E.: Hawks and doves in a dynamic framework. Dyn. Games Appl. 3(1), 24–37 (2012)
Houston, A.I., McNamara, J.M.: Fighting for food: a dynamic version of the hawk-dove game. Evol. Ecol. 2(1), 51–64 (1988)
McNamara, J.M., Houston, A.I.: If animals know their own fighting ability, the evolutionarily stable level of fighting is reduced. J. Theor. Biol. 232(1), 1–6 (2005)
McNamara, J.M., Merad, S., Collins, E.J.: The hawk-dove game as an average-cost problem. Adv. Appl. Probab. 23(4), 667–682 (1991)
Shakkottai, S., Altman, E., Kumar, A.: The case for non-cooperative multihoming of users to access points in IEEE 802.11 WLANs. In: IEEE Infocom, Barcelona, Spain (2006)
Smith, M.: Game theory and the evolution of fighting. In: Maynard Smith, J. (ed.) On Evolution, pp. 8–28. Edinburgh University Press (1972)
Kumar, A., Shakkottai, S., Altman, E.: Evolutionary power control games in wireless networks. J. Sel. Areas Commun. 25(6), 1207–1215 (2007)
Tembine, H., Altman, E., El-Azouzi, R.: Delayed evolutionary game dynamics applied to medium access control. In: Proceedings of the IEEE 4th International Conference on Mobile Adhoc and Sensor Systems, Pisa, Italy, pp. 1–6, October 2007
Wright, C.C.: An explanation for some aspects of the behaviour of congested road traffic in terms of a simple model. Transp. Res. 9(5), 267–273 (1975)
Yearsley, J.: Hawks and doves in heterogeneous environments. Math. Comput. Modell. 27(4), 99–108 (1998)
Zheng, Y., Feng, Z.: Evolutionary game and resources competition in the internet. In: Modern Communication Technologies 2001. SIBCOM-2001. The IEEE-Siberian Workshop of Students and Young Researchers, pp. 51–54 (2001)
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Aradhye, A., Altman, E., El-Azouzi, R. (2017). A Multitype Hawk and Dove Game. In: Duan, L., Sanjab, A., Li, H., Chen, X., Materassi, D., Elazouzi, R. (eds) Game Theory for Networks. GameNets 2017. Lecture Notes of the Institute for Computer Sciences, Social Informatics and Telecommunications Engineering, vol 212. Springer, Cham. https://doi.org/10.1007/978-3-319-67540-4_2
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DOI: https://doi.org/10.1007/978-3-319-67540-4_2
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