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On 1-convexity and nucleolus of co-insurance games

  • Driessen, Theo S.H.
  • Fragnelli, Vito
  • Katsev, Ilya V.
  • Khmelnitskaya, Anna B.

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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Article provided by Elsevier in its journal Insurance: Mathematics and Economics.

Volume (Year): 48 (2011)
Issue (Month): 2 (March)
Pages: 217-225

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Handle: RePEc:eee:insuma:v:48:y:2011:i:2:p:217-225
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  1. 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.
  2. Deprez, Olivier & Gerber, Hans U., 1985. "On convex principles of premium calculation," Insurance: Mathematics and Economics, Elsevier, vol. 4(3), pages 179-189, July.
  3. Arin, J. & Feltkamp, V., 1994. "The nucleolus and kernel of veto-rich transferable utility games," Discussion Paper 1994-40, Tilburg University, Center for Economic Research.
  4. 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.
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