Oligopolistic equilibrium and financial constraints

We provide a model of dynamic duopoly in which firms face financial constraints and disappear when they are unable to fulfill them. We show that, in some cases, Cournot outputs are no longer supported in equilibrium, because if these outputs were set, a firm may have incentives to ruin the other. In these cases, standard grim-trigger strategies in which collusion is sustained by infinite reversion to Cournot outputs cannot be used. We show that there is a stationary Markov equilibrium in mixed strategies where predation occurs with a positive probability. We also obtain a modified "folk theorem". We show that any bankruptcy-free outputs (outputs in which no firm can drive another firm to bankruptcy without becoming bankrupt itself) that attain individually rational profits (reflecting bankruptcy consideration) can be supported by a subgame perfect Nash equilibrium when firms are sufficiently long-sighted.