Symmetrical Duopoly under Uncertainty - The Huisman & Kort Model - With Excel spreadsheet to download!
This section focuses option games models, the combination of option pricing theory with game theoretic models. Option games models are useful for managerial decisions, specially (real) investment decisions when both exogenous uncertainty and competition matters.
Option pricing tools addresses the optimization (maximization of value)
under uncertainty problem, given the stochastic processes modeling
uncertainties and given the relevant options.
Game theoretic tools addresses the optimization problem given the
competitors actions and given the incomplete information (Bayesian games
case) available.
In short, option pricing and game theory are complementary
theories. The first one dealing with maximization of value but without
consider the strategic interaction effect from the others market players.
Game theory fills this lacuna.
Generally, game theoreticians analyzes the complexities of the equilibriums and the payoffs are "mere details", generally players’ utility functions without any relation with market values. Real options approach fills this gap by setting up the payoff value under uncertainty, considering market values and the flexibility of response by the optimal exercise of the options.
This special webpage has the intention to help people to awake for the large potential of option games models in both academy and industry. There are many topics below, and the reader will find in the option-games webpages a lot of models discussion, charts, and even Excel spreadsheets to download.
The following topics are freely available:
Symmetrical Duopoly under Uncertainty - The Huisman & Kort Model - Asymmetrical Duopoly under Uncertainty - The Extended Joaquin & Buttler Model - Oligopoly under Uncertainty - The Grenadier Model - Option Games Bibliography Paper: Continuous-Time Option Games: Review of Models and Extensions - Part 1: Duopoly under Uncertainty. By Dias & Teixeira. New Paper: Continuous-Time Option Games - Part 2: Oligopoly and War of Attrition under Uncertainty. By Dias & Teixeira. Duopoly: Extended Dixit & Pindyck Model Exploratory Option-Game Model
This section presents the abstract and the link to download this paper, by Marco A.G. Dias & José P. Teixeira named "Continuous-Time Option Games: Review of Models and Extensions - Part 1: Duopoly under Uncertainty".
This paper was especially written for the 7th Annual International Conference on Real Options, Washington, July 2003.
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 wit 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.
Download the compressed (.zip) Word for Windows file: dias_teixeira-option-games.zip, with 313 KB.
This section presents the abstract and the link to download this paper, by Marco A.G. Dias & José P. Teixeira named "Continuous-Time Option Games: Review of Models and Extensions - Part 2: Oligopoly and War of Attrition under Uncertainty".
This paper is related with the author dissertation and was especially written for the 8th Annual International Conference on Real Options, Montreal, June 2004.
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.
Download the latest version of this paper (July 25th, 2004). It is a compressed (.zip) Word for Windows file: dias-teixeira_part2_option-games.zip, with 315 KB.
Download the Montreal presentation file (Powerpoint-2000 for Windows file): dias-teixeira_part2-ppt.ppt, with 609 KB.