Strategic real options
Abstract I study hidden investment in quality in a dynamic persuasion game. A seller, such as a project manager or startup company, controls an asset and wants to convince a potential buyer, such as an acquiring company or a regulator, that it has high quality. The buyer observes exogenous news with quality-dependent drift and holds a call option on the asset; the seller is privately informed about quality and can wait (at a flow cost), upgrade (at a fixed cost) or exit the market. For low upgrade costs, multiple equilibria exist and exhibit novel reputational dynamics — resetting barriers and skew Brownian motion, a generalization of a reflected stochastic process. In one type of equilibrium, a seller with low quality waits until his reputation hits “rock bottom” and then upgrades with some probability, inducing upward reputational jumps in equilibrium; the seller may exit at an intermediate reputation. In a second type, the low quality seller mixes over exiting at low reputations and upgrading in an intermediate “sweet spot” region. The results suggest a social benefit to setting high expectations for effort when agents start with low reputations and help explain why agents respond to adversity in drastically different ways across environments.