Capital Structure in an R&D Duopoly: a Differential Game Approach with Randomly Generated Polynomials
Robert Beach

Abstract
This paper considers financial distress and optimal capital structure given a duopoly market characterized by an upstream firm that is primarily engaged in research and development (the R&D firm) and whose value comes from the market valuation of these activities, and a downstream firm primarily engaged in distribution and marketing (the D&M firm). This is within the context of a differential game with a finite planning horizon. A numerical solution is obtained by randomly generating parameters for second degree polynomials for the decision variables of the R&D and D&M firms and from this derives an estimate of the state equation. The results suggest that optimal capital structure for the R&D firm does not come from converging to a target debt-to-equity ratio as in tradeoff theory, but evolves over time as it responds strategically to decisions made by the D&M firm.

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