Preempting an Alert Rival: Strategic Timing of the First Plant by Analysis of Sophisticated Rivalry

This paper examines the strategic rivalry in a duopoly where firms must correctly time the construction of the first plant in a growing market. We explicitly model rivalry for market share. Firms recognize the effect of the rival's actions on their profits; they behave noncooperatively to maximize discounted profits over the infinite horizon. For the timing problem we develop an appropriate solution concept. It is a Nash equilibrium in the space of sequential decision rules which specify each firm's correct action as a function of the state of the world. We then show how the equilibrium can be computed by backward induction dynamic programming. Numerical examples illustrate the sequential Nash solution and characterize the rivalry to be the first to build. Parametric analysis of the example enables us to explore the competitive dynamics of capacity choice in new markets.