Jocs cooperatius i problemes de bancarrota

Abstract

[en] Cooperative game theory is the study of mathematical models of cooperation, in transferable utility games the players face the challenge to split up some good among them using cooperation. This essay is an introduction to the existing link between cooperative game theory and the so called rationing problems or bankruptcy problems. This problem is based in using division rules to allocate a quantity of good among some creditors taking into account that the sum of the claims exceeds the quantity available to allocate. We will prove that the Shapley value (Shapley 1953) and the Nucleous (Schmeidler 1969) of the cooperative game associated to the bankruptcy problem corresponds to the random arrival rule (O’Neill 1982) and the Talmud rule (Aumann and Maschler 1985) of the bankruptcy problem respectively.