Continuous-Time Option Games: Review of Models and Extensions

This paper discusses a selected literature on continuous-time option games models, providing new insights and extensions. The paper analyzes both symmetrical and asymmetrical duopoly under uncertainty, including issues like preemption, non-binding collusion, perfect-Nash equilibriums, first-mover advantage, mixed strategies, probability of mistake with simultaneous exercise, competitive advantage effect, etc. In the first model, the demand follows a stochastic process, whereas in the second model the exchange rate follows a stochastic process. This paper presents two equivalent ways to calculate the leader and follower values and thresholds, the differential and the integral methods. The paper extends the Joaquin and Buttler’s model by considering mixed strategies in asymmetric duopoly and other extensions.