Continuous-Time Option Games: Review of Models and Extensions

Guimarães Dias, Marco Antonio; Teixeira, José Paulo

Volume 14, Numbers 3 & 4 / September/December , Pages 153-317

Multinational Finance Journal, 2010, vol. 14, no. 3/4, pp. 219-254

Marco Antonio Guimarães Dias , PUC-Rio, Brazil Corresponding Author

José Paulo Teixeira , PUC-Rio, Brazil

Abstract:
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.

Keywords : option games; real options; game theory; duopoly under uncertainty; preemption
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