Clique games: a family of games with coincidence between the nucleolus and the Shapley value
We introduce a new family of cooperative games for which there is coincidence between the nucleolus and the Shapley value. These so-called clique games are such that players are divided into cliques, with the value created by a coalition linearly increasing with the number of agents belonging to the same clique. Agents can belong to multiple cliques, but for a pair of cliques, at most a single agent belong to their intersection. Finally, if two players do not belong to the same clique, there is at most one way to link the two players through a chain of players, with any two adjacent players in the chain belonging to a common clique. We provide multiple examples for clique games, chief among them minimum cost spanning tree problems. This allows us to obtain new correspondence results between the nucleolus and the Shapley value, as well as other cost sharing methods for the minimum cost spanning tree problem.
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- Dutta, Bhaskar & Kar, Anirban, 2004.
"Cost monotonicity, consistency and minimum cost spanning tree games,"
Games and Economic Behavior,
Elsevier, vol. 48(2), pages 223-248, August.
- Dutta, Bhaskar & Kar, Anirban, 2002. "Cost Monotonicity, Consistency And Minimum Cost Spanning Tree Games," The Warwick Economics Research Paper Series (TWERPS) 629, University of Warwick, Department of Economics.
- Bhaskar Dutta & Anirban Kar, 2002. "Cost monotonicity, consistency and minimum cost spanning tree games," Indian Statistical Institute, Planning Unit, New Delhi Discussion Papers 02-04, Indian Statistical Institute, New Delhi, India.
- A. van den Nouweland & P. Borm & W. van Golstein Brouwers & R. Groot Bruinderink & S. Tijs, 1996. "A Game Theoretic Approach to Problems in Telecommunication," Management Science, INFORMS, vol. 42(2), pages 294-303, February.
- van den Nouweland, A. & Borm, P. & van Golstein, W. & Bruinderink, R.G. & Tijs, S., 1994. "A Game Theoretic Approach to Problems in Telecommunication," Papers 9407, Tilburg - Center for Economic Research.
- van den Nouweland, C.G.A.M. & Borm, P.E.M. & van Golstein Brouwers, W. & Groot Bruinderink, R. & Tijs, S.H., 1996. "A game theoretic approach to problems in telecommunication," Other publications TiSEM a3b30529-fe17-484c-8eab-7, Tilburg University, School of Economics and Management.
- Juan J. Vidal-Puga, 2004. "Bargaining with commitments," International Journal of Game Theory, Springer;Game Theory Society, vol. 33(1), pages 129-144, January.
- Tijs, S.H., 2005. "The First Steps with Alexia, the Average Lexicographic Value," Discussion Paper 2005-123, Tilburg University, Center for Economic Research.
- Bergantinos, Gustavo & Vidal-Puga, Juan J., 2007. "A fair rule in minimum cost spanning tree problems," Journal of Economic Theory, Elsevier, vol. 137(1), pages 326-352, November.
- Gustavo Bergantiños & Juan Vidal-Puga, 2005. "A fair rule in minimum cost spanning tree problems," Game Theory and Information 0504001, EconWPA.
- Trudeau, Christian, 2012. "A new stable and more responsive cost sharing solution for minimum cost spanning tree problems," Games and Economic Behavior, Elsevier, vol. 75(1), pages 402-412.
- Trudeau, Christian & Vidal-Puga, Juan, 2017. "On the set of extreme core allocations for minimal cost spanning tree problems," Journal of Economic Theory, Elsevier, vol. 169(C), pages 425-452.
- Christian Trudeau & Juan Vidal-Puga, 2015. "On the set of extreme core allocations for minimal cost spanning tree problems," Working Papers 1505, University of Windsor, Department of Economics.
- Graham, Daniel A & Marshall, Robert C & Richard, Jean-Francois, 1990. "Differential Payments within a Bidder Coalition and the Shapley Value," American Economic Review, American Economic Association, vol. 80(3), pages 493-510, June.
- S. C. Littlechild & G. Owen, 1973. "A Simple Expression for the Shapley Value in a Special Case," Management Science, INFORMS, vol. 20(3), pages 370-372, November.
- Gustavo Bergantiños & Juan Vidal-Puga, 2007. "The optimistic TU game in minimum cost spanning tree problems," International Journal of Game Theory, Springer;Game Theory Society, vol. 36(2), pages 223-239, October.
- Ichiishi, Tatsuro, 1981. "Super-modularity: Applications to convex games and to the greedy algorithm for LP," Journal of Economic Theory, Elsevier, vol. 25(2), pages 283-286, October.
- Xiaotie Deng & Christos H. Papadimitriou, 1994. "On the Complexity of Cooperative Solution Concepts," Mathematics of Operations Research, INFORMS, vol. 19(2), pages 257-266, May. Full references (including those not matched with items on IDEAS)
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