Folk theorem under bankruptcy

Abstract

In this paper, we examine Subgame Perfect Nash Equilibria (SPE) within an infinite horizon oligopolistic market, accounting for the possibility of firm bankruptcy. Central to our dynamic analysis is the concept of Bankruptcy-Free (BF) allocations. The consideration of bankruptcy introduces several distinctive features not encompassed by standard models of infinitely repeated games. Notably, when firms are sufficiently patient towards future outcomes, achieving certain collusive outcomes as equilibria may not be possible. We discern qualitatively different results depending on the number of firms in the market; in a duopoly, only specific BF allocations can be sustained as SPE, while in scenarios with more than two firms, allocations outside the BF set can also be sustained as SPE. In both instances, it is crucial that the payoffs are above the minimax BF payoff, a condition more restrictive than the standard minimax payoff advocated in Folk Theorems.