A Noncooperative Approach to Bankruptcy Problems with an Endogenous Estate

We introduce a new class of bankruptcy problems in which the value of the estate is endogenous and depends on agents’ investment decisions. There are two investment alternatives: investing in a company and becoming a shareholder (risky asset) and depositing money into a bank (risk-free asset). Bankruptcy is a possible event only for the risky asset. We de…ne a game between agents each of which aims to maximize his expected payoff by choosing an investment alternative and a company management which aims to maximize the investment in the company by choosing a bankruptcy rule. There are two types of agents in our model, who are differentiated by their incomes. We, first, consider three well-known bankruptcy rules: the proportional rule, the constrained equal awards rule and the constrained equal losses rule. We show that there always exists a pure strategy subgame perfect Nash equilibrium, which involves the proportional rule. This result is independent of the income distribution in the economy and holds even under one-sided uncertainty on the income distribution. We also show that our results can be extended to a larger set of rules containing the Talmud rule along with other rules that belong to the TAL-family. Our results provide, at least, a partial explanation from a strategic point of view for the popular use of the proportional rule in allocating bankrupt companies’ assets to shareholders.