I study repeated competition among oligopolists. The only novelty is that firms may go bankrupt and permanently exit: the probability that a firm survives a price war depends on its financial strength, which varies stochastically over time. Under some conditions including no entry, an anti‐folk theorem holds: when firms are patient, so that strength levels change relatively quickly, every Nash equilibrium involves an immediate price war that lasts until at most one firm remains. Surprisingly, the possibility of entry may facilitate collusion, as may impatience. The model can explain some observed patterns of collusion and predation.

Repeated games with unknown payoff distributions are analogous to a single decision maker's “multi-armed bandit” problem. Each state of the world corresponds to a different payoff matrix of a stage game. When monitoring is perfect, information about the state is public, and players are sufficiently patient, the following result holds: For any function that maps each state to a payoff vector that is feasible and individually rational in that state, there is a sequential equilibrium in which players experiment to learn the realized state and achieve a payoff close to the one specified for that state.

The Coase conjecture (1972) is the proposition that a durable-goods monopolist, who sells over time and can quickly reduce prices as sales are made, will price at marginal cost. We show that an arbitrarily small deviation from Coase's assumptions—a deviation that applies in almost any practical application—results in the failure of that conjecture. In particular, we examine that conjecture in a model where there is a vanishingly small cost for production (or sales) capacity, and the seller may augment capacity in every period. In the “gap case”, any positive capacity cost ensures that in the limit, as the size of the gap and the time between sales periods shrink, the monopolist obtains profits identical to those that would prevail when she could commit ex ante to a fixed capacity. Those profits are at least 29.8% of the full static monopoly optimum.