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Published: February 24, 2003

 
 

Finding Sanity with Game Theory

The branch of game theory that’s most widely discussed is noncooperative theory. It explores situations in which we interact with small numbers of other players whose strategic choices directly affect our payoffs, as well as situations in which our choices will determine the kind of market we are in. Most such situations involve “noncooperative games” because each player is choosing the strategy that will benefit that player individually. There are no cooperative agreements being made between players that will allow them to maximize their gains collectively. Noncooperative games are usually characterized by payoff tables that list what each player will receive, depending on the strategy that player chooses and the strategies the other players choose.

Dr. Nash’s big contribution was to provide some concepts for characterizing the outcomes of these games. In particular, he demonstrated that noncooperative games can result in something called a Nash equilibrium. This is when each player makes the optimal choice given what the other players might choose, even though these choices don’t necessarily result in the best outcomes for everyone, or even for anyone. In other words, playing the game out move by move gets you to a result you wouldn’t choose if you could make some kind of cooperative deal.

The best known noncooperative game is “the prisoner’s dilemma.” This is a scenario in which two prisoners who have committed a crime together each confess and implicate the other, accepting a moderate prison term. They do this in order to avoid the very long sentence one of them would have to serve if only the other had confessed. The kicker is that if neither had confessed, they would each have drawn very short terms. But confessing is the “dominant strategy” because it gives each player the best payoff for each of the other player’s choices. The resulting double confession illustrates the Nash equilibrium because neither player could unilaterally improve his payoff by adopting a different strategy.

Businesses experience something like the prisoner’s dilemma every time a move by a competitor drives them to do things that leave each business worse off than it would have been otherwise. A business will launch an expensive promotion, for example, in order to match a competitor’s price promotion, even though each might have been better off without any promotion. Sometimes customers are the beneficiaries of this competitive dilemma. But exactly who benefits and what the best strategies will be depends on the exact way the game is formulated or defined in a specific business situation.

Because this branch of game theory is by far the most developed, there are quite a few books that explain it and apply it to business problems. Two textbooks presenting noncooperative game theory are especially readable: Joel Watson’s recently published Strategy: An Introduction to Game Theory and Prajit K. Dutta’s Strategies and Games: Theory and Practice. Both use a significant amount of math, but they keep it simple. The writing is accessible enough so that, with a little patience, you can dip into them and learn a great deal, without having to take a formal course.

For readers who want a more popular treatment, one of the best is Avinash K. Dixit and Barry J. Nalebuff’s Thinking Strategically: The Competitive Edge in Business, Politics, and Everyday Life. This book uses payoff tables, simple graphs, and decision trees, but avoids all mathematical equations. Its examples move from military campaigns to tennis matches to Hollywood movies. John McMillan’s Games, Strategies, and Managers: How Managers Can Use Game Theory to Make Better Business Decisions is also excellent and has the advantage of focusing more specifically on business problems. It discusses such matters as the design of contracts and the management of subcontractors.

 
 
 
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