Abstract
MC-nets is a concise representation of the characteristic functions that exploits a set of rules to compute payoffs. Given a MC-nets instance, the problem of computing a payoff division in the least core, which is a generalization of the core-non-emptiness problem that is known to be coNP-complete, is definitely a hard computational problem. In fact, to the best of our knowledge, no algorithm can actually compute such a payoff division for MC-nets instances with dozens of agents. We propose a new algorithm for this problem, that exploits the constraint generation technique to solve the linear programming problem that potentially has a huge number of constraints. Our experimental results are striking since, using 8 GB memory, our proposed algorithm can successfully compute a payoff division in the least core for the instances with up to 100 agents, but the naive algorithm fails due to a lack of memory for instances with 30 or more agents.
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References
Chalkiadakis, G., Elkind, E., Wooldridge, M.: Computational Aspects of Cooperative Game Theory. Morgan & Claypool Publishers (2011)
Conitzer, V., Sandholm, T.: Complexity of constructing solutions in the core based on synergies among coalitions. Artificial Intelligence 170, 607–619 (2006)
Gillies, D.: Some Theorems on n-Person Games. Ph.D. thesis, Princeton University (1953)
Greco, G., Malizia, E., Palopoli, L., Scarcello, F.: On the complexity of core, kernel, and bargaining set. Artificial Intelligence 175(12–13), 1877–1910 (2011)
Hillier, F.S., Lieberman, G.J.: Introduction to Operations Research, 9th edn. McGraw-Hill (2010)
Ieong, S., Shoham, Y.: Marginal contribution nets: A compact representation scheme for coalitional games. In: Proceedings of the 6th ACM Conference on Electronic Commerce (EC 2005), pp. 193–202 (2005)
Liao, X., Koshimura, M., Fujita, H., Hasegawa, R.: Solving the coalition structure generation problem with MaxSAT. In: Proceedings of the 2012 IEEE 24th International Conference on Tools with Artificial Intelligence (ICTAI 2012), pp. 910–915 (2012)
Malizia, E., Palopoli, L., Scarcello, F.: Infeasibility certificates and the complexity of the core in coalitional games. In: Proceedings of the 20th International Joint Conference on Artificial Intelligence (IJCAI 2007), pp. 1402–1407 (2007)
Sandholm, T.: Algorithm for optimal winner determination in combinatorial auctions. Artificial Intelligence 135(1–2), 1–54 (2002)
Shapley, L.S.: A value for n-person games. In: Contributions to the Theory of Games, vol. 2. Princeton University Press (1953)
Tombuş, Ö., Bilgiç, T.: A column generation approach to the coalition formation problem in multi-agent systems. Computers & Operations Research 31, 1635–1653 (2004)
Tran-Thanh, L., Nguyen, T.D., Rahwan, T., Rogers, A., Jennings, N.R.: An efficient vector-based representation for coalitional games. In: Proceedings of the 23rd International Joint Conference on Artificial Intelligence (IJCAI 2013), pp. 383–389 (2013)
Ueda, S., Hasegawa, T., Hashimoto, N., Ohta, N., Iwasaki, A., Yokoo, M.: Handling negative value rules in MC-net-based coalition structure generation. In: Proceedings of the 11th International Conference on Autonomous Agents and Multiagent Systems (AAMAS 2012), pp. 795–802 (2012)
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Hirayama, K., Hanada, K., Ueda, S., Yokoo, M., Iwasaki, A. (2014). Computing a Payoff Division in the Least Core for MC-nets Coalitional Games. In: Dam, H.K., Pitt, J., Xu, Y., Governatori, G., Ito, T. (eds) PRIMA 2014: Principles and Practice of Multi-Agent Systems. PRIMA 2014. Lecture Notes in Computer Science(), vol 8861. Springer, Cham. https://doi.org/10.1007/978-3-319-13191-7_26
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DOI: https://doi.org/10.1007/978-3-319-13191-7_26
Publisher Name: Springer, Cham
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