On 1-convexity and nucleolus of co-insurance games
The insurance situation in which an enormous risk is insured by a number of insurance companies is modeled through a cooperative TU game, the so-called co-insurance game, first introduced in Fragnelli and Marina (2004). In this paper we present certain conditions on the parameters of the model that guarantee the 1-convexity property of co-insurance games which in turn ensures the nonemptiness of the core and the linearity of the nucleolus as a function of the variable premium. Further we reveal conditions when a co-insurance game is representable in the form of a veto-removed game and present an efficient final algorithm for computing the nucleolus of a veto-removed game.
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- Marieke Quant & Peter Borm & Hans Reijnierse & Bas van Velzen, 2005.
"The core cover in relation to the nucleolus and the Weber set,"
International Journal of Game Theory,
Springer, vol. 33(4), pages 491-503, November.
- Quant, M. & Borm, P.E.M. & Reijnierse, J.H. & van Velzen, S., 2005. "The core cover in relation to the nucleolus and the Weber set," Other publications TiSEM 9723cee6-92c9-49a2-90d3-9, Tilburg University, School of Economics and Management.
- Deprez, Olivier & Gerber, Hans U., 1985. "On convex principles of premium calculation," Insurance: Mathematics and Economics, Elsevier, vol. 4(3), pages 179-189, July.
- Aumann, Robert J. & Maschler, Michael, 1985. "Game theoretic analysis of a bankruptcy problem from the Talmud," Journal of Economic Theory, Elsevier, vol. 36(2), pages 195-213, August.
- Arin, J. & Feltkamp, V., 1994.
"The nucleolus and kernel of veto-rich transferable utility games,"
1994-40, Tilburg University, Center for Economic Research.
- Vincent Feltkamp & Javier Arin, 1997. "The Nucleolus and Kernel of Veto-Rich Transferable Utility Games," International Journal of Game Theory, Springer, vol. 26(1), pages 61-73.
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