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Gry Koalicyjne miedzy Agentami Tomasz Michalak, Uniwersytet Warszawski

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Representation: CFG Benchmark: DP of [Yen 86] Approach: Improve upon DP a 1 5 a 2 7 a 3 4 a 1 a 2 1 a 1 a 3 2 Modelowanie Gier Koalicyjnych 1.Optimization of coalitions’ values 2.Division of coalitions’ values (core, SV) 3.Coalition Structure Generation CFG Game theory I. Gry bez efektow zewnetrznychII. Gry z efektami zewnetrznymi N = { a 1, a 2, a 3 } a1a1 a2a2 a3a3 a 1 a 2 a 1 a 3 a 2 a 3 a 1 a 2 a 3 5 7 4 13 12 16 11 a1a1 a2a2 a3a3 a3a3 Sandholm et al. (1999) 1.Optimization of coalitions’ values 2.Division of coalitions’ values (core, SV) 3.Coalition Structure Generation a 1 a 2 a2a2 a 1 a 3 a1a1 a 2 a 3 a 1 a 2 a 3 5+7+4 = 16 13 + 4 = 17 11 + 7 = 18 12 + 5 = 17 16 1.Optimization of coalitions’ values 2.Division of coalitions’ values (core, SV) 3.Coalition Structure Generation O(n n ) O(2 n ) 1.Optimization of coalitions’ values 2.Division of coalitions’ values (core, SV) 3.Coalition Structure Generation DP 1 IDP 3 IP 50 IP+IDP 200 Ohta et al., AMEC 2009 a1a1 a 1 a 2 a 1 a 2 a 3 Externalities – value of a coalition depends on the existence/performance of other coalitions in the sys. a2a2 a3a3 a3a3 5 74 13 a1a1 a2a2 +2 6 a 1 a 3 a1a1 a3a3 a2a2 4 -3 11 a1a1 a2a2 a3a3 a 2 a 3 +4 12 9 a3a3 a 1 a 2 16 a 1 a 3 a2a2 a 2 a 3 a1a1 16 19 15 21 16 PFG EXAMPLES 1.R&D cooperation on an oligopolistic market (negative externalities); 2.Production cartels, OPEC (positive externalities); 3.CO 2 emission reductions, Kyoto protocol (positive externalities); 4.Fiscal and monetary policy coordination (no simple pattern, mixed); 5.Supply chain (negative, mixed). Still a discussion about an exact definition of SV and the core in games with externalities (McQuillin/DeC&S) Michalak et al., ECAI 2008 1)Super-additivity + only positive externalities (↑↑); 2)Super-additivity + only negative externalities (↑↓); 3)Sub-additivity + only positive externalities (↓↑); 4)Sub-additivity + only negative externalities (↓↓); Michalak et al., ECAI 2008 1)Grand Coalition 2)Super-additivity + only negative externalities (↑↓); 3)Sub-additivity + only positive externalities (↓↑); 4)Non-cooperation Rahwan et al, IJCAI 2009 1)Positive externalities 2)Negative externalities IP +/- Michalak et al.ECAI’08 Rahwan et al, IJCAI’09 all PFG ? IP approach Michalak et al. (2009b)4 PFG = CFG + EXTERNALITIES IP approach a1a1 a 1 a 2 a 1 a 2 a 3 a2a2 a3a3 a3a3 5 74 13 a1a1 a2a2 6 a 1 a 3 a1a1 a3a3 a2a2 4 11 a1a1 a2a2 a3a3 a 2 a 3 12 9 a3a3 a 1 a 2 16 a 1 a 3 a2a2 a 2 a 3 a1a1 a3a3 a1a1 a2a2 PFG New Concise Representations (i)Induced Subgraph Rep. (ii)MC-nets (iii)Synergies, C&S2003 a)Concise; b)Fully Expressive; c)Simple; d)Effective (computing SV linear w.r.t number of rules)

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Coalition Structure Graph (Sandholm et al. 1999)

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Struktura Koalicyjna a1a1 a4a4 a2 a3a2 a3 a5 a6 a7a5 a6 a7 2 3 14 10 5 12 3 19

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a1a1 a4a4 a2 a3a2 a3 a5 a6 a7a5 a6 a7 2 5 12 3 19 14 3 10 -2 Struktura Koalicyjna

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