Reasoning about "When" instead of "What": Collusive Equilibria with Stochastic Timing in Repeated Oligopoly - Grana, Justin; Bono, James; Wolpert, David (The B.E. Journal of Theoretical Economics, 2019)
We analyze a continuous time game of Bertrand competition with private monitoring that includes asynchronous signals and asynchronous actions. Unlike existing models where firms observe a signal that is imperfectly correlated with demand parameters and firms’ prices, we assume firms observe demand and prices perfectly but at times governed by independent Poisson processes. The signals only reveal information at the instant they are observed and do not contain information about past actions or states of demand. This implies that any firm’s price change will go undetected for some time or may never be detected. Firms are also allowed to engage in costless but unverifiable cheap talk. The model focuses on the strategic considerations that arise when firms reason about then timing of the signals rather than the content. We show that standard Nash reversion arguments can enforce collusion and truthful communication when signals are asynchronous and signals only reveal information about the current state of the world and do not reveal information about past states or actions. Through comparative statics, we disentangle how parameters that govern the timing of events and signals interact to either facilitate or preclude collusion. Finally, we extend the model to show that firms may collude not only to avoid Nash reversion but to prevent opposing firms from believing demand has dropped and thus lowering their price.