Abstract
We explore the impact of mutual altruism among the players belonging to the same set – their tribe – in a partition of all players in arbitrary strategic games upon the quality of equilibria attained. To this end, we introduce the notion of a \(\tau \)-tribal extension of an arbitrary strategic game, in which players’ subjective cost functions are updated to reflect this, and the associated Price of Tribalism, which is the ratio of the social welfare of the worst Nash equilibrium of the tribal extension to that of the optimum of social welfare. We show that in a well-known game of friendship cliques, network contribution games as well as atomic linear congestion games, the Price of Tribalism is higher than the Price of Anarchy of either the purely selfish players or fully altruistic players (i.e. ones who seek to maximise the social welfare). This phenomenon is observed under a variety of equilibrium concepts. In each instance, we present upper bounds on the Price of Tribalism that match the lower bounds established by our example.
We would like to thank Jerry Anunrojwong, Ioannis Caragiannis, Artur Gorokh, Bart de Keijzer, Bobby Kleinberg, Guido Schaefer and Éva Tardos, as well as the anonymous reviewers, for helpful feedback and discussions regarding the paper. M.S. was supported by NSF grants IIS-1703846 and IIS-1718108, ARO grant W911NF-17-1-0592, and a grant from the Open Philanthropy project. Y.W.’s research was partially supported by NSF grant DMS-1645643. For a full version of this paper, please see https://arxiv.org/abs/1907.06862.
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Han, S., Soloviev, M., Wang, Y. (2019). The Impact of Tribalism on Social Welfare. In: Fotakis, D., Markakis, E. (eds) Algorithmic Game Theory. SAGT 2019. Lecture Notes in Computer Science(), vol 11801. Springer, Cham. https://doi.org/10.1007/978-3-030-30473-7_13
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