We provide here a brief introduction to game theory, which might better be called the theory of conflict and cooperation. An earlier article in this series (Bratvold and Begg, 2009) discussed the application of decision analysis in the oil and gas industry. Classical decision analysis is more widely applicable to one-person games, involving a single player (individual or organization) against nature, than to strategic interactions, which are more appropriately addressed by game theory.
What Is Game Theory?
Game theory comes in two flavors. Cooperative game theory was invented by John von Neumann and Oskar Morgenstern. Their 1947 book, which also lays out the foundations of utility theory—a central element in decision theory—provided an analogy between decision problems that people and organizations face and parlor games such as poker or bridge. Cooperative game theory assumes people will do what they say they will do—a promise made is a promise kept. In real-world decision situations, this is far too optimistic. Cooperative game theory works well for zero-sum games, where one side’s loss equals the other side’s gain, but most actual decision making situations are more complex.
By the early 1950s, mathematician John Nash had extended the field to create noncooperative game theory, which addresses how people and organizations interact in an effort to achieve their own goals. Nash, later the subject of the book and movie A Beautiful Mind and the winner of the 1994 Nobel Prize in economics, drew attention to people’s tendency not to cooperate. Promises are kept only when people or organizations believe it is in their interest. When promises and interests differ, people renege on their promises, break their word, and do whatever it takes to maximize their benefits. As it can be costly to break promises, the costs as well as benefits must be taken into account.
Game theory formalizes the interaction among multiple players, where each player has a strategy set from which one or more strategies can be chosen with specified probabilities. The payoff (utility, profit) to each player depends on the combination of strategies chosen by all the players. Game theory prescribes the optimal strategies for each player. Players may disagree on who should expend resources to regulate costs, profits, and risk, or they may free-ride on the investment decisions made by the other players. Conflicts leading to reactions and counterreactions by players affect their individual as well as collective payoffs. Even if players can agree on an objective, they may disagree on how much each should invest toward achieving it. The Nash equilibrium is defined as a state from which no player prefers to deviate unilaterally.
A game theory analysis is useful if (i) at least two players are present, where each player maximizes an objective, (ii) at least one of the players has the opportunity to choose between at least two strategies, and (iii) the payoff to each player depends on the combinations of strategies chosen by all players. The theory assumes that partners or players in a relationship can have different interests, objectives, and influence. The optimal choice for any individual player might not be optimal for fellow players, who may try to prevent it. However, understanding the objectives and influencing opportunities of the fellow players enables a player to judge sensibly whether to try to change the outcome of the game.
Example: The Oil Producer’s Dilemma
One of the most basic and best known games is the prisoner’s dilemma, where two players independently choose between two alternatives, and the payoff for each player depends on the choices made by both. For the purpose of this article, the dynamics of this classical game have been cast as the oil producer’s dilemma, in which two oil producing countries produce the amount of oil that each believes will maximize its oil revenues. The two countries are assumed to provide a dominant proportion of the world’s total production, that is, their production determines the price of oil. Fig. 1 depicts the change in the price of oil relative to total production. In our example, each of the two countries can choose to produce either 10 or 20 bbl of oil. The possible price outcomes are shown in Fig. 2.
Were the two countries to agree to produce only 10 bbl each, to keep the oil price high, each country would have an incentive to violate the agreement by producing 20 bbl. Here is how it works. Each country realizes that the other country may break the promise. Country A knows that if country B is true to its word and limits its production to 10 bbl, country A will make USD 1,500 by producing 20 bbl (20 bbl x USD 75/bbl). If instead country A sticks to its agreement and limits its production to 10 bbl, it will make a maximum of USD 1,400 if country B sticks to the deal. However, if country B breaks the deal, country A will only make USD 750 by sticking to the deal, while it will make USD 800 by breaking the agreement. The same logic applies for country B. Game theory takes a dim view of human nature. Each of the countries looks out for itself, and no matter what the other country decides—to stick to the deal or break it—the best option is to break the deal.
This produces the dilemma. If both countries stick to the deal they would make apparently reasonable revenue of USD 1,400 and be better off than if both break the deal. The problem is that neither one benefits from taking a chance, knowing that it is always in the other country’s interest to break the deal. Consequently, despite the two countries’ promise to each other, neither can expect the other to stick to its commitment to limit production to 10 bbl, without some additional contractual or enforcement process.
Game Theory Applications in the Oil and Gas Industry
Game theory applications in the oil and gas industry tend to fit one of three broad classes. First is competitive bidding, where companies are competing for limited opportunities. Second is the joint venture partnership, where several companies must cooperate to bring a project or other opportunity to fruition. Third is the negotiation among partners, customers and suppliers, and governments, where each party is trying to obtain the largest possible share. Game theory can provide insights on each of the classes.
Competitive Bidding. Bidding in auctions are classic game theory problems. In the oil and gas industry, most major new opportunities are made available by host countries through a sealed bid process. The simplest form may be bonus bidding, such as in the U.S. offshore, where companies offer an upfront cash bonus and the largest bid wins. Far more complex is work commitment bidding, where companies bid to perform a set amount of work in return for an opportunity to participate in the development and production of new reserves. In general, game theory cannot calculate what an opportunity is worth to a company, which is the role of conventional decision analysis and valuation techniques. However, once a company understands the value it sees in an opportunity, game theory will help the company understand how to capture that opportunity without sacrificing the very value it wishes to capture. The analysis will shed light on how the seller (usually a national government) views the payoff, based on its objectives, what tradeoffs may be attractive, and the amounts that other players may be willing to offer. In some cases, game theory can provide insights that result in a winning bid; in others, game theory can provide the clarity to convince a company not to bid. Both insights can be equally valuable, as not all games are worth winning.
Joint Ventures. Most major projects and opportunities in the oil and gas industry are structured as joint ventures between competitors. A typical partnership could consist of several major international energy companies, national oil companies, the government, and other investors. Partnerships of four or five entities are not unusual. The partners in these joint ventures often have conflicting objectives, values, and priorities. However, for a project to be successful, the partners must find common ground on which to agree and proceed with the effort. This creates an ideal setting for the application of game theory methods to analyze the project decisions and find solutions that allow a company to create value for itself while other partners also see incentive to proceed. Instead of a simple two-player game as in the producer’s dilemma above, these games are played out in five or six dimensions. Game theory provides a methodology to evaluate the games and develop strategies and tactics to “win” or at least achieve the best attainable outcome.
Negotiations. Many are familiar with the saying, “You don’t get what you deserve, you get what you negotiate.” Negotiation techniques focus on how to get what you want. Game theory can help a company understand its position, its degree of power, and the leverage points it can use to achieve the best outcome. Game theory allows the analyst to look at the negotiation from all sides and discover key tradeoffs and acceptable terms. Although many negotiations are viewed as basic zero-sum games, game theory analysis can reveal ways to change the game, possibly creating win/win solutions. Negotiators armed with a thorough game theory analysis have a significant advantage in understanding their best alternative.
Summary
This discussion focused briefly on three broad classes of game theory applications. However, each game theory analysis must focus on the specific objectives and preferences of the players involved. Much of the literature on game theory focuses on basic two-player games, where players have mutually exclusive options such as play A or B or some mixed strategy playing each a fraction of the time. The real games we face in the oil and gas industry often involve four to six players, each having multiple options that are not mutually exclusive. This greatly complicates the game, although the fundamentals may not change. The simple game of the oil producer’s dilemma has four outcomes; a five-player game where each player has five independent options (each presenting two choices) has 225 or 33,554,432 possible outcomes. The challenge in applying game theory in oil and gas problems is to maintain the critical elements of the game while simplifying it so that it can be analyzed.
References
Bratvold, R.B. and Begg, S.H. 2009. Would You Know a Good Decision if You Saw One? SPE The Way Ahead 5 (2): 21–23.
Willigers, B.J.A., Bratvold, R.B., and Hausken, K. 2009. A Game Theoretic Approach to Conflicting and Evolving Stakeholder Preferences in the E&P Industry. SPE Econ & Mgmt 1 (1): 19–26. SPE 124178-PA. doi: 10.2118/124178-PA.
• Recommended Reading From TWA Economist’s Corner Team: Harrington, J.E. Jr. 2009. Games, Strategies, and Decision Making. Worth Publishers.
