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 (risky asset) and depositing money into a savings account (risk-free asset). Bankruptcy is possible only for the risky asset. We define 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 profits by choosing a bankruptcy rule. Our agents are differentiated by their incomes. We consider three most prominent bankruptcy rules in our base model: the proportional rule, the constrained equal awards rule and the constrained equal losses rule. We show that only the proportional rule is a part of any pure strategy subgame perfect Nash equilibrium. This result is robust to changes in income distribution in the economy and can be extended to a larger set of bankruptcy rules and multiple types. However, extension to multiple company framework with competition leads to equilibria where the noncooperative support for the proportional rule disappears.