A Simulation on the Bankruptcy Problem As A Convex Game

There are a large number of contributions to the bankruptcy problem (cf. the references in Curiel et al. (1987) and Thomson (2002)). This paper examines this problem from the game-theoretic viewpoint in the context of coalitional game. Suppose that a person dies with property left and the property is valued $P. Furthermore, he (or she) owes to n persons with the total debt, valued $D. When P<D, there remains the problem of how the property should be divided between the creditors. Let di be the value of debt to the creditor, i (i=1,...,n), so that D=Úi=1 n di. One of the ways to divide and distribute $P to the creditors is the Proportional Division principle: PD principle. According to the PD principle, each creditor, i, receives Pdi/D (i=1,...,n). The origin of PD principle dates back to Nicomachean Ethics by the Greek philosopher, Aristotle. This principle is not the only distribution principle. The Contested Garment principle: CG principle, is also known. The example of the distribution of $P to d={d1,...,dn} by CG principle was provided in Mishnah of the Talmud, the collection of Jewish dictum. The extension of this example to the general principle was attempted by Aumann and Maschler [1985], in the context of coalitional game. It is well known that the distribution according to the Shapley values is also possible. The final distribution principle is defined the SV principle. The aim of this paper is to examine the relation among the PD principle, the CG principle and the SV principle, in terms of simulation approach.