Abstract

PLATA-PEREZ, Leobardo  and  SANCHEZ-PEREZ, Joss. Convexity and marginal contributions in bankruptcy games. EconoQuantum [online]. 2011, vol.8, n.1-2, pp.61-72. ISSN 2007-9869.

In this paper we analyze two natural convexity definitions for cooperative bankruptcy games, one of them was introduced by Aumann and Maschler (1985). In particular, we show that convexity in the sense of increasing marginal contributions is not satisfied by the game introduced by these authors. Furthermore, we propose an alternative game that captures the situation of bankruptcy problems and characterize the anticore of such game; and using duality theory of cooperative games, we show that the core, anticore and its Shapley value coincide with the one studied by Aumann and Maschler (1985).

Keywords : Bankruptcy problems; cooperative games; convexity; marginal contributions.

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