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We study an optimal patent problem in the spirit of Hopenhayn, et al (2006), but where all innovations arise from two repeated innovators. Following Hopenhayn, et al (2006) we divide patent regimes into those that are exclusive, in the sense that only one firm ever has a claim on the current market, and non-exclusive regimes where both firms simultaneously have ongoing claims to market leadership at a given instant. We show that in the exclusive regime, the long run treatment of the firms depends crucially on the investment technology: when it has no fixed costs, no firm is ever excluded, but with fixed costs one firm is excluded in finite time. We characterize non-exclusive regimes numerically and show that they may or may not lead to monopolization in the long run.
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