Multilateral Bankruptcy Rules

A classic problem in economics is the selection of a bankruptcy rule with good normative properties.  The problem as usually specified is given by the “estate” E which is to be divided among the “claims” c= (c₁, ….c_n). It is assumed that the estate is insufficient to satisfy the claims – that is E<S c_i. Many rules have been developed with different, mutually conflicting, properties.

Multilateral bankruptcy problems have not been studied from this perspective at all.  I define a multilateral problem by a matrix of debts, X and a vector of exogenous wealths W. Each player i owes a debt x_ij to the other players j. They can fulfill these debts by accessing their exogenous wealth W_i and the income that they collect from  the debts that others owe to them.  However, the others may experience bankruptcies and thus the collected amount may fall short of the debt. The bankruptcy rule reduces the payments of a player who has more debts to pay than his total income. A solution to the multilateral bankruptcy problem is a rule which determines actual debt repayments for all bankrupt players, and endogenously determines the set of bankrupt players and the set of solvent players.

Rules are to be compared according to whether they avoid or mitigate “bankruptcy cascades”, and according to how they allocate the available exogenous wealth as a function of the matrix of debts X. Good bankruptcy rules should be neutral with respect to the “declaration” of bankruptcy.  In a dynamic setting a player may have negative net worth but may still be able to fulfill his debts for a while by running down his assets. Invariant rules yield the same results no matter which time the bankruptcy is “declared” and the rule imposed.