Abstract
We study safety level coalitions in competitive games. Given a normal form game, we define a corresponding cooperative game with transferable utility, where the value of each coalition is determined by the safety level payoff it derives in the original—non-cooperative—game. We thus capture several key features of agents’ behavior: (i) the possible monetary transfer among the coalition members; (ii) the solidarity of the outsiders against the collaborators; (iii) the need for the coalition to optimize its actions against the worst possible behavior of those outside the coalition. We examine the concept of safety level cooperation in congestion games, and focus on computing the value of coalitions, the core and the Shapley value in the resulting safety level cooperative games. We provide tractable algorithms for anonymous cooperative games and for safety level cooperative games that correspond to symmetric congestion games with singleton strategies. However, we show hardness of several problems such as computing values in games with multi-resource strategies or asymmetric strategy spaces.
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References
Ackermann, H., Röglin, H., Vöcking, B.: On the impact of combinatorial structure on congestion games. Journal of the ACM 55(6) (2008)
Aumann, R.: Acceptable points in general cooperative n-person games. In: Cont. to the Theory of Games, Princeton, NJ, vol. IV, pp. 287–324 (1959)
Bachrach, Y.: Honor among thieves - collusion in multi-unit auctions. In: AAMAS (2010)
Bachrach, Y., Elkind, E., Meir, R., Pasechnik, D., Zuckerman, M., Rothe, J., Rosenschein, J.: The cost of stability in coalitional games. In: Mavronicolas, M., Papadopoulou, V.G. (eds.) SAGT 2009. LNCS, vol. 5814, pp. 122–134. Springer, Heidelberg (2009)
Bachrach, Y., Rosenschein, J.S.: Power in threshold network flow games. In: Autonomous Agents and Multi-Agent Systems (2009)
Byde, A., Polukarov, M., Jennings, N.R.: Games with congestion-averse utilities. In: Mavronicolas, M., Papadopoulou, V.G. (eds.) SAGT 2009. LNCS, vol. 5814, pp. 220–232. Springer, Heidelberg (2009)
Conitzer, V., Sandholm, T.: Computing Shapley values, manipulating value division schemes, and checking core membership in multi-issue domains. In: AAAI (2004)
Elkind, E., Goldberg, L.A., Goldberg, P., Wooldridge, M.: Computational complexity of weighted threshold games. In: AAAI (2007)
Gillies, D.B.: Some theorems on n-person games. PhD thesis, Princeton University (1953)
Hayrapetyan, A., Tardos, E., Wexler, T.: The effect of collusion in congestion games. In: STOC 2006 (2006)
Holzman, R., Law-Yone, N.: Strong equilibrium in congestion games. Games and Economic Behavior 21, 85–101 (1997)
Ieong, S., McGrew, R., Nudelman, E., Shoham, Y., Sun, Q.: Fast and compact: A simple class of congestion games. In: AAAI 2005, pp. 489–494 (2005)
Milchtaich, I.: Congestion models of competition. American Naturalist (1996)
Resnick, E., Bachrach, Y., Meir, R., Rosenschein, J.S.: The cost of stability in network flow games. In: Královič, R., Niwiński, D. (eds.) MFCS 2009. LNCS, vol. 5734, pp. 636–650. Springer, Heidelberg (2009)
Rosenthal, R.W.: A class of games possessing pure-strategy Nash equilibria. International Journal of Game Theory 2, 65–67 (1973)
Roughgarden, T., Tardos, E.: How bad is selfish routing. J. ACM 49(2), 236–259 (2002)
Rozenfeld, O., Tennenholtz, M.: Strong and correlated strong equilibria in monotone congestion games. In: Spirakis, P.G., Mavronicolas, M., Kontogiannis, S.C. (eds.) WINE 2006. LNCS, vol. 4286, pp. 74–86. Springer, Heidelberg (2006)
Shapley, L.S.: A value for n-person games. Cont. to the Theory of Games (1953)
Voice, T., Polukarov, M., Byde, A., Jennings, N.R.: On the impact of strategy and utility structures on congestion-averse games. In: Leonardi, S. (ed.) WINE 2009. LNCS, vol. 5929, pp. 600–607. Springer, Heidelberg (2009)
Yokoo, M., Conitzer, V., Sandholm, T., Ohta, N., Iwasaki, A.: Coalitional games in open anonymous environments. In: AAAI 2005, pp. 509–514 (2005)
Zuckerman, M., Faliszewski, P., Bachrach, Y., Elkind, E.: Manipulating the quota in weighted voting games. In: AAAI (2008)
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Bachrach, Y., Polukarov, M., Jennings, N.R. (2010). The Good, The Bad and The Cautious: Safety Level Cooperative Games. In: Saberi, A. (eds) Internet and Network Economics. WINE 2010. Lecture Notes in Computer Science, vol 6484. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-17572-5_36
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DOI: https://doi.org/10.1007/978-3-642-17572-5_36
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