This paper proposes a method for evaluating a patent race in a three-firm asymmetric model. Previous research has evaluated patent races between two firms using a game-theoretic real options approach; however, very little research has been done on the evaluation of R&D races in patent acquisition when three or more major firms exist in the market. Furthermore, the synergy created by technical cooperation has not been considered. Therefore, the present research expands on the previous research to formulate and evaluate a patent race model between three asymmetric firms using a game-theoretic real options approach. We formulated and evaluated one situation in which all three firms subject to evaluation are competing for patent acquisition and another situation in which two of the three firms are engaging in technical cooperation. In the situation in which two of the three firms engage in technical cooperation, we used numerical examples to consider the influence of a reduction in R&D cost due to the synergy created by the cooperation. Our research showed that the cost of cooperative R&D is within a realistic range in situations where technical cooperation is desirable.