Profit Sharing with Thresholds and Non-monotone Player Utilities
We study profit sharing games in which players select projects to participate in and share the reward resulting from that project equally. Unlike most existing work, in which it is assumed that the player utility is monotone in the number of participants working on their project, we consider non-monotone player utilities. Such utilities could result, for example, from “threshold” or “phase transition” effects, when the total benefit from a project improves slowly until the number of participants reaches some critical mass, then improves rapidly, and then slows again due to diminishing returns.
Non-monotone player utilities result in a lot of instability: strong Nash equilibrium may no longer exist, and the quality of Nash equilibria may be far away from the centralized optimum. We show, however, that by adding additional requirements such as players needing permission to leave a project from the players currently on this project, or instead players needing permission to a join a project from players on that project, we ensure that strong Nash equilibrium always exists. Moreover, just the addition of permission to leave already guarantees the existence of strong Nash equilibrium within a factor of 2 of the social optimum. In this paper, we provide results on the existence and quality of several different coalitional solution concepts, focusing especially on permission to leave and join projects, and show that such requirements result in the existence of good stable solutions even for the case when player utilities are non-monotone.
Unable to display preview. Download preview PDF.
- 1.Anshelevich, E., Postl, J.: Profit Sharing with Thresholds and Non-monotone Player Utilities, http://www.cs.rpi.edu/~eanshel
- 2.Augustine, J., Chen, N., Elkind, E., Fanelli, A., Gravin, N., Shiryaev, D.: Dynamics of profit-sharing games. In: IJCAI 2011, pp. 37–42 (2011)Google Scholar
- 3.Awerbuch, B., Azar, Y., Epstein, A., Mirrkoni, V.S., Skopalik, A.: Fast convergence to nearly optimal solutions in potential games. In: EC 2008, pp. 264–273 (2008)Google Scholar
- 4.Aziz, H.: Stable marriage and roommate problems with individual-based stability. arXiv: 1204.1628Google Scholar
- 5.Aziz, H., Brandl, F.: Existence of Stability in Hedonic Coalition Formation Games. In: AAMAS 2012, pp. 763–770 (2012)Google Scholar
- 10.Feldman, M., Lewin-Eytan, L., Naor, J.S.: Hedonic clustering games. In: SPAA 2012, pp. 267–276 (2012)Google Scholar
- 11.Goemans, M.X., Li, L., Mirrokni, V.S.: M. Thottan. Market sharing games applied to content distribution in ad-hoc networks. JSAC 2006 24(5), 1020–1033 (2006)Google Scholar
- 15.Kleinberg, J., Oren, S.: Mechanisms for (Mis)allocating Scientific Credit. In: STOC 2011, pp. 529–538 (2011)Google Scholar
- 16.Kutten, S., Lavi, R., Trehan, A.: Composition Games for Distributed Systems: the EU Grant Games. In: AAAI 2013, pp. 1–16 (2013)Google Scholar
- 18.Tardos, É., Wexler, T.: Network formation games. In: Nisan, N., Tardos, É., Roughgarden, T., Vazirani, V. (eds.) Algorithmic Game Theory, ch. 19, Cambridge University Press (2007)Google Scholar
- 19.Vetta, A.: Nash equilibria in competitive societies, with applications to facility location, traffic routing and auctions. In: FOCS 2002, pp. 416–425 (2002)Google Scholar