Abstract
How to form effective coalitions is an important issue in multi-agent systems. Coalition Structure Generation (\(\mathsf {CSG}\)) involves partitioning a set of agents into coalitions so that the social surplus (i.e. the sum of the rewards obtained by each coalition) is maximized. In many cases, one is interested in computing a partition of the set of agents which maximizes the social surplus, but is robust as well, which means that it is not required to recompute new coalitions if some agents break down. In this paper, the focus is laid on the Robust Coalition Structure Generation (\(\mathsf {RCSG}\)) problem. A formal framework is defined and some decision and optimization problems for \(\mathsf {RCSG}\) are pointed out. The computational complexity of \(\mathsf {RCSG}\) is then identified. An algorithm for \(\mathsf {RCSG}\) (called \(\mathsf {AmorCSG}\)) is presented and evaluated on a number of benchmarks.
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Note that the property of monotonicity differs from the super-additivity which requires that for all coalitions C, \(C'\), it holds \(v(C) + v(C') \le v(C \cup C')\) and is stronger than monotonicity.
References
Björklund, A., Husfeldt, T., Koivisto, M.: Set partitioning via inclusion-exclusion. SIAM J. Comput. 39(2), 546–563 (2009)
Conitzer, V., Sandholm, T.: Complexity of constructing solutions in the core based on synergies among coalitions. Artif. Intell. 170(6–7), 607–619 (2006)
Dang, V., Dash, R., Rogers, A., Jennings, N.: Overlapping coalition formation for efficient data fusion in multi-sensor networks. In: AAAI, pp. 635–640 (2006)
Dasgupta, P., Cheng, K.: Robust multi-robot team formations using weighted voting games. In: Martinoli, A. (ed.) Distributed Autonomous Robotic Systems. STAR, vol. 83, pp. 373–387. Springer, Heidelberg (2013). https://doi.org/10.1007/978-3-642-32723-0_27
Dinar, A., Moretti, S., Patrone, F., Zara, S.: Application of stochastic cooperative games in water resources. In: Goetz, R.U., Berga, D. (eds.) Frontiers in Water Resource Economics. NRMP, vol. 29, pp. 1–20. Springer, Boston (2006). https://doi.org/10.1007/0-387-30056-2_1
Ieong, S., Shoham, Y.: Marginal contribution nets: a compact representation scheme for coalitional games. In: ACM EC, pp. 193–202 (2005)
Karp, R.M.: Reducibility among combinatorial problems. In: Miller, R.E., Thatcher, J.W., Bohlinger, J.D. (eds.) Complexity of Computer Computations. IRSS, pp. 85–103. Springer, Boston (1972). https://doi.org/10.1007/978-1-4684-2001-2_9
Larson, K., Sandholm, T.: Anytime coalition structure generation: an average case study. J. Exp. Theor. Artif. Intell. 12(1), 23–42 (2000)
Lesser, V., Tambe, M., Ortiz, C. (eds.): Distributed Sensor Networks: A Multiagent Perspective. Kluwer Academic Publishers, Dordrecht (2003)
Michalak, T., Rahwan, T., Elkind, E., Wooldridge, M., Jennings, N.: A hybrid exact algorithm for complete set partitioning. J. Artif. Intell. 230, 14–50 (2016)
Nair, R., Tambe, M.: Hybrid BDI-POMDP framework for multiagent teaming. J. Artif. Intell. Res. 23, 367–420 (2005)
Ohta, N., Conitzer, V., Ichimura, R., Sakurai, Y., Iwasaki, A., Yokoo, M.: Coalition structure generation utilizing compact characteristic function representations. In: Gent, I.P. (ed.) CP 2009. LNCS, vol. 5732, pp. 623–638. Springer, Heidelberg (2009). https://doi.org/10.1007/978-3-642-04244-7_49
Okimoto, T., Schwind, N., Clement, M., Ribeiro, T., Inoue, K., Marquis, P.: How to form a task-oriented robust team. In: AAMAS, pp. 395–403 (2015)
Rahwan, T., Jennings, N.: Coalition structure generation: dynamic programming meets anytime optimization. In: AAAI, pp. 156–161 (2008)
Rahwan, T., Michalak, T., Jennings, N.: A hybrid algorithm for coalition structure generation. In: AAAI, pp. 1443–1449 (2012)
Rahwan, T., Ramchurn, S., Dang, V., Giovannucci, A., Jennings, N.: Anytime optimal coalition structure generation. In: AAAI, pp. 1184–1190 (2007)
Rahwan, T., Ramchurn, S., Jennings, N., Giovannucci, A.: An anytime algorithm for optimal coalition structure generation. J. Artif. Intell. Res. (JAIR) 34, 521–567 (2009)
Sandholm, T.: An implementation of the contract net protocol based on marginal cost calculations. In: 11th National Conference on Artificial Intelligence, pp. 295–308 (1993)
Sandholm, T., Larson, K., Andersson, M., Shehory, O., Tohmé, F.: Coalition structure generation with worst case guarantees. Artif. Intell. 111(1–2), 209–238 (1999)
Sandholm, T., Lesser, V.R.: Coalitions among computationally bounded agents. Artif. Intell. 94(1–2), 99–137 (1997)
Service, T., Adams, J.: Approximate coalition structure generation. In: AAAI, pp. 854–859 (2010)
Vidal, J.: The effects of co-operation on multiagent search in task-oriented domains. J. Exp. Theor. Artif. Intell. 16(1), 5–18 (2004)
Yeh, D.: A dynamic programming approach to the complete set partitioning problem. BIT Comput. Sci. Numer. Math. 26(4), 467–474 (1986)
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Okimoto, T., Schwind, N., Demirović, E., Inoue, K., Marquis, P. (2018). Robust Coalition Structure Generation. In: Miller, T., Oren, N., Sakurai, Y., Noda, I., Savarimuthu, B.T.R., Cao Son, T. (eds) PRIMA 2018: Principles and Practice of Multi-Agent Systems. PRIMA 2018. Lecture Notes in Computer Science(), vol 11224. Springer, Cham. https://doi.org/10.1007/978-3-030-03098-8_9
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