I presented my research at the Department of Mathematics of the Faculty of Applied Science in Pilsen, Czech Republic, the university where I did my Bachelor in mathematics. The first 20 minutes is in English, the remaining 40 minutes is in Mathematics.
Abstract: I 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 and novel feature of my model is that the research progress of each firm is assumed to be its private information. Hence, a firm does not know the progress of its rival. Instead, it has a posterior believe over it. The model leads to a system of nonlinear ordinary differential equations that needs to be analyzed without having a closed-form solution. I conclude that a firm keeps decreasing its research efforts as it is giving up over time before making the first discovery. To the contrary, a firm increases its effort as it is aggressively striving to patent after making the first discovery. I also consider the settings in which the firms have the option to reveal about being successful, and I find the circumstances under which they would want to do so.
