On the extreme points of the core of neighbour games and assignment games
AbstractNeighbour games arise from certain matching or sequencing situations in which only some specific pairs of players can obtain a positive gain. As a consequence, neighbour games are as well assignment games as line graph restricted games. We will show that the intersection of the class of assignment games and the class of line graph restricted games yields the class of neighbour games. Further, we give a necessary and sufficient condition for the convexity of neighbour games. In spite of the possible non-convexity of neighbour games, it turns out that for any neighbour game the extreme points of the core are marginal vectors. Moreover, we prove this for assignment games in general. Hence, for any assignment game the core is the convex hull of some marginal vectors.
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Bibliographic InfoPaper provided by Tilburg University, Center for Economic Research in its series Discussion Paper with number 1999-43.
Date of creation: 1999
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Find related papers by JEL classification:
- C71 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Cooperative Games
- C78 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Bargaining Theory; Matching Theory
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- Solymosi, Tamas & Raghavan, Tirukkannamangai E S, 1994. "An Algorithm for Finding the Nucleolus of Asignment Games," International Journal of Game Theory, Springer, vol. 23(2), pages 119-43.
- 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.
- Borm, P.E.M. & Hamers, H.J.M. & Hendrickx, R.L.P., 2001.
"Operations research games: A survey,"
Open Access publications from Tilburg University
urn:nbn:nl:ui:12-305110, Tilburg University.
- Peter Borm & Herbert Hamers & Ruud Hendrickx, 2001. "Operations research games: A survey," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer, vol. 9(2), pages 139-199, December.
- Marina Nunez Oliva & Carlos Rafels Pallarola, 2001. "The extreme core allocations of the assignment game," Working Papers in Economics 65, Universitat de Barcelona. Espai de Recerca en Economia.
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