Continuous-Time Option Games Part 2: Oligopoly, War of Attrition and Bargaining under Uncertainty

This sequel paper analyzes other selected methodologies and applications from the theory of continuous-time (real) option games – the combination of real options and game theory. In the first paper (Dias & Teixeira, 2003), we analyzed preemption and collusion models of duopoly under uncertainty. In this second paper we focus on models of oligopoly under uncertainty, war of attrition under uncertainty, and the changing the war of attrition game toward a bargaining game. In the oligopoly model we follow Grenadier (2002), discussing two important methodological insights that simplify many option games applications: the Leahy’s principle of optimality of myopic behavior and the "artificial" perfectly competitive industry with a modified demand function. We discuss both the potential and the limitations of these insights. Next, we extend to the continuous-time framework the option game model presented in Dias (1997), a war of attrition under uncertainty applied to oil exploration prospects. In this model of positive externality the follower acts as free rider receiving additional information revealed by the leader’s drilling outcome. The way to model the information revelation in oil exploration is another extension of the original option game model. In addition, we analyzed the possibility of changing the game with the oil firms playing the bargaining game be perfect Nash equilibrium. Cooperation can increase the value of the firms thanks to additional private information revelation provided by a contract. We quantify the degree of information revelation with the convenient learning measure named expected variance reduction. The bargaining game strategy must be compared mainly with the follower strategy in asymmetric war of attrition. We set the game threshold window where the bargaining alternative dominates any war of attrition outcome. We also show that the option game premium can be much higher than the traditional real option premium in either war of attrition or bargaining game. This is generally the opposite of the oligopoly under uncertainty case, when the option game premium is lower than the traditional option premium, is zero in the oligopoly limit of infinite firms, and can be even negative in special preemption cases.