Continuous-Time Option Games: Review of Models and Extensions

Abstract The theory of option games being the combination of two successful theories, namely real options and game theory, has a great potential to applications in many real situations. Although the option games literature is very recent, it has been experimenting a fast growth in the last five years. It considers in the same model, besides the key factors for investment decisions such as uncertainty, flexibility, and timing, the effect of competition with the possible strategies for each firm. This paper reviews a selected literature on continuous-time models of option games and provides some new insights and extensions. This review is divided into two parts or two papers. In this paper we analyze models of duopoly under uncertainty – both symmetrical and asymmetrical. First we present a brief survey of option games with a summary of possible equilibriums in duopoly like Cournot and Stackelberg, and types of demand function as well as the effects of this uncertainty on these functions. We discuss concepts like the preemption, non-binding collusion, main and secondary perfect-Nash equilibriums in pure strategies, first mover advantage, situations that mixed strategies are necessary, probability of simultaneous exercise as mistake, effect of the competitive advantage, etc. We show that there are two equivalent ways to calculate both leader and follower values, and two ways to calculate the follower threshold. We also extend the asymmetrical duopoly under uncertainty model analyzed by Joaquin & Buttler by considering issues like mixed strategies in asymmetric duopoly and the value of option to become a leader. In a second paper will be discussed important option games models like oligopoly under uncertainty, war of attrition and other models of positive externalities, models with either incomplete or asymmetric information, the current option-games models limitations, and suggestions for future research.