Theory and Decision

, Volume 56, Issue 1–2, pp 229–238 | Cite as

The Lovász Extension of Market Games

  • E. Algaba
  • J.M. Bilbao
  • J.R. Fernández
  • A. Jiménez
Article

Abstract

The multilinear extension of a cooperative game was introduced by Owen in 1972. In this contribution we study the Lovász extension for cooperative games by using the marginal worth vectors and the dividends. First, we prove a formula for the marginal worth vectors with respect to compatible orderings. Next, we consider the direct market generated by a game. This model of utility function, proposed by Shapley and Shubik in 1969, is the concave biconjugate extension of the game. Then we obtain the following characterization: The utility function of a market game is the Lovász extension of the game if and only if the market game is supermodular. Finally, we present some preliminary problems about the relationship between cooperative games and combinatorial optimization.

Owen extension Lovász extension Market games 

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Copyright information

© Kluwer Academic Publishers 2004

Authors and Affiliations

  • E. Algaba
    • 1
  • J.M. Bilbao
    • 1
  • J.R. Fernández
    • 1
  • A. Jiménez
    • 1
  1. 1.Department of Applied Mathematics IIEscuela Superior de Ingenieros, Camino de los DescubrimientosSpain

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