Bankruptcy games and the ibn ezra's proposal

Resumen

This paper follows the interpretation of the bankruptcy problems in terms of TU games given in O'Neill (1982). In this context we propose the analysis of the Transition Game associated to each bankruptcy problem. We explore an old solution described by Ibn Ezra in the XII century. Firstly, we study the extension of the Ibn Ezra's proposal by O'Neill (1982), the Minimal Overlap solution. We provide a characterization of this value and show that it can be understood as the composition of the Ibn Ezra solution and the Constrained Equal Loss rule. Secondly, we introduce a new way of extending the Ibn Ezra's proposal, the Generalized Ibn Ezra solution, by imposing that the general distribution principle in which is inspired remains fixed. The characterization of our proposal clarifies the analogies and differences between the two ways of generalizing the Ibn Ezra's proposal.