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 / Spring 2003 / Issue 30(originally published by Booz & Company)


Finding Sanity with Game Theory

Since Dr. Nash wrote his seminal papers, a huge analytic effort has focused on the sort of noncooperative games that result in one or more Nash equilibria. John Harsanyi expanded the theory of Nash equilibria to encompass games in which the players have incomplete information about the other players’ preferences. Reinhard Selten showed how the idea of Nash equilibria could be applied to games unfolding over time through the selection of certain outcomes that are more reasonable than others. The relevance of this work for economics was acknowledged in 1994 when the Nobel Prize was awarded jointly to Nash, Harsanyi, and Selten for their development of the idea of equilibria in noncooperative games. Currently, noncooperative game theory is being used to design auctions and other online interactions, and to help align corporate incentives with corporate interests. (See “Beating the B2B Odds,” by Tim Laseter and David Evans, s+b, Second Quarter 2001.)

The other main branch of game theory may have even more applications to business practice. It is called cooperative game theory because it deals with situations in which players can make cooperative agreements, enabling them to carry out joint strategies and to share the resulting payoffs. Since this is what businesspeople do every time they put together a new business or a new combination of businesses, these activities are prime subjects for cooperative game theory.

Cooperative game theory does not focus on the specific moves or strategies that a player will choose as the game is played out. Instead, it focuses on the way players interact and can arrange themselves into different groups to create different amounts of value. Cooperative game theory is especially useful when it comes to deciding which people and assets to include in a business, which businesses to include in a corporation, and which corporations to include in an alliance. Furthermore, it will predict how much value each of these units can expect to collect in exchange for its participation. This makes cooperative game theory a powerful tool for assessing the viability of new ventures, products, technologies, channels of supply and distribution, and markets.

Because cooperative game theory focuses on groupings, rather than moves or strategies, the concepts it employs are very different from those used in noncooperative game theory. In place of payoff tables for individual actions, cooperative game theory is concerned with the “characteristic function,” which describes the value that would be created by each possible combination of players. And instead of identifying the Nash equilibria, cooperative game theory seeks to identify “the core” — groupings likelier to be stable because the players won’t be able to do better by defecting to another group.

When people describe a noncooperative game in business, they are almost always assuming there is some cooperative game that takes place earlier and determines the structure of the noncooperative game. This is because cooperative games are generally necessary to produce the value that noncooperative games use for their payoffs, and because the way that value is created determines the bargaining power of the participants. If the players are organized into different cooperative groupings, then the amount of value created and the way it gets divided will often be drastically different.

Take the classic prisoner’s dilemma, for example, and look at how the results change if the prisoners start playing a cooperative game among themselves. Suddenly, they have a way of getting to the optimum payoff. If there are more than two prisoners and the different prisoners can command different payoffs, the cooperative games that can be established become even more important.

This less-restricted version of the game is more like real life than the classic prisoner’s dilemma. Most business is conducted with unrestricted bargaining, except where the government rules that it would get in the way of other bargaining. The sheer creativity of businesspeople means that they are constantly producing the sort of new combinations that are the subject of cooperative game theory.

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