UC Santa Barbara

We study a class of stochastic duopoly games inspired by the two time-scale feature of many markets. The firms convert their short-term “local” advantage driven by exogenous infinitesimal shocks into a more durable gain through long-term market dominance. As an extension of existing literature, we consider two asymmetric players each of whom adopts timing strategies to increase her profitability and possibly bring negative externality to the rival. In turn, this leads us to more general settings of nonzero-sum games. Characterizing Nash equilibrium as a fixed-point of each player’s best-response to her rival, we construct threshold-type Feedback Nash Equilibrium via best response iteration. Our main contribution is explicitly constructing equilibria for types of duopoly games that represent a wide range of industries. Motivated by the competition among sectors of power generators, we consider a duopoly of producers with finite options to increase their production capacity. We study nonzero-sum games in which two players compete for market dominance via switching controls. We also study mixed switching and impulses games inspired by the vertical competition among the producers and consumers of a commodity. Our analysis quantifies the dynamic competition effects and brings economic insights.