Abstract: We study the competition of two firms developing a specific technology. Firms make costly research efforts in order to increase their chance of making a discovery. Two consecutive discoveries are needed to be able to file a patent, and only the firm completing the discoveries first wins the patent. An essential feature of our model is that the research progress of each firm is assumed to be its private information. A firm does not observe the progress of its rival, so it updates its posterior believe over it. We find that the game has unique Nash Equilibrium. We conclude that each firm should keep decreasing its research effort as it is giving up over time before making the first discovery, and to the contrary, it should keep increasing its effort as it is aggressively striving to patent after making the first discovery. We also consider the setting in which the firms have the option to reveal about being successful, and we find three types of equilibria depending on the research difficulty.
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