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"Thinking Ahead Backward" by Schlomo Maital, Across the Board, June 1991.

Applying game theory to business strategy may be the best way of crystallizing your best available options.

Consider these decisions executives typically confront:

* Your company faces markets thinned by recession and overpopulated by new entrants. As sales slump, your main competitor slashes his prices and boosts production. How should you respond? Follow suit and mutually self-destruct? Or hold the line and lose sales and market share? Air travel, truck transport, magazines, boutiques, and personal computers are industries where such dilemmas are becoming increasingly common.

* Producing the next generation of your product will take heavy spending in research and development. Should you make the investment? Your competitors face the same decision. Should you enter a patent contest with them, when you could well lose the race and where even winning may be unprofitable if the field is crowded? Or should you stay on the sidelines and forfeit potentially rich markets?

* You have a promising new product. Should you be first to market it? You may reap the fruits of pioneering-or break trail for cautious competitors, who then profit from your errors.

Like virtually all tough choices managers make, these are examples of "games"—situations in which your payoff depends not just on what you do but also on what your competitors do. Ever since 1926, when John von Neumann, a brilliant Hungarian mathematician and physicist, published his path-breaking paper on game theory, it has been known that analytical models of games could be built. These models make it possible to find the best strategies and the best solutions for games, including ones that embody complex business dilemmas.

For decades, mathematicians played games with game theory, publishing books and papers only they could understand. But a new book called Thinking Strategically: The Competitive Edge in Business, Politics and Everyday Life (W.W. Norton) by two economists, Avinash Dixit of Princeton University and Barry Nalebuff of Yale University, uses plain language to explain how to use game theory to solve tough problems. The authors make the subject understandable and accessible with hundreds of examples drawn from daily life, including "hot hands" (scoring streaks) in basketball, the 1983 America's Cup final, Internal Revenue Service audits, the 1984 Orange Bowl, Time versus Newsweek, Robert Carnpeau's bid for Federated Stores, GATT, OPEC, Crazy Eddie versus Newmark & Lewis, United States versus Japan in high definition television, and Republicans versus Democrats.

To those faced with a tough choice their message is: "Think ahead, then look backward." What they mean is choose the outcome you think is best, then trace backward to figure out the strategy that is most likely to get you there. To apply this, think like a smart commuter. Picture yourself at work on Wall Street (your company's objective). Then figure out the best way to get there (your decision choices)—car, PATH train, NJ Transit bus—from your home in Princeton (your initial situation). In doing so, take into account your own actions and the likely responses of your competitors, who in this case are other commuters. Often, a device known as a game tree can be helpful. With a game tree, you depict each possible outcome of the situation as a branch of the tree. You then pick the best branch and figure out how to get onto it from the tree trunk.

The essence of applied game theory is the intense analysis of each game's structure. To do this, you have to simplify. Boil down your own strategies and your rivals' to two or three key ones. For example, in price-war games: "cut prices" or "hold prices steady." That means the game has just a few possible outcomes. For two strategies and two players, there are only four different ways (2x2) the game can turn out. Calculate which outcomes are best for you and which are worst, and do the same for your competitor. Then follow Dixit and Nalebuff's checklist:

* Do you have a "dominant strategy" (one that is best for you, no matter what your opponent does)? If so, use it. 

* Are there "dominated strategies" (ones that are worst for you, no matter what your rival does)? If so, eliminate them and reanalyze the game.

* Is there an "equilibrium" (an outcome in which each player's action is the best response to the other's)? If there is one such outcome, players should probably opt for it. (You're likely to end up there anyway, Dixit and Nalebuff reason, so why not head there directly?) If there are several, some type of rule or convention should be chosen to get to the best of them.

A useful technique managers can use in building game strategies is to set up a one-sentence "thumbnail" description of the game. For instance, in price-cutting games, it is often, "I am better off holding my price and being exploited than matching my rivals' price cuts and risking mutual destruction." If this game definition holds for your rivals, too, the game is one of "chicken." Whoever bluffs best, or moves fastest to cut prices, wins because rivals prefer conceding to head-on collision.

In the 1960s, Charles de Gaulle used intransigence effectively in such games. His imitators have fared less well. Saddam Hussein may have perceived the invasion of Kuwait as a deadly game of chicken, counting on the United States to concede in the face of his aggressive move. (In an earlier game of chicken, the Cuban missile crisis, the Russians blinked first.) Companies play chicken when they threaten to slash their prices, rapidly expand output in thin markets, or invade new markets that cannot support a new entrant in order to move competitors out. In some cases, the game structure is different, such as: "I would be better off slashing my prices and facing losses than letting my rival slash his and exploit me." This game is known as prisoner's dilemma. When all players think this way, price-cutting is a dominant strategy. The result is a next-to-worst-case scenario: lower prices and revenues for all players, a bad result that is, nonetheless, better than losing all your market.

The first condition for smart strategy is reading the "game map" right. If you judge the structure of the game wrongly, you will likely misjudge your opponent's behavior and hence err in setting your own responses. Saddam Hussein miscalculated. The bitter game in Kuwait &,as chicken from his point of view, but prisoner's dilemma from that of the United States. America preferred to fight than concede. Had Hussein believed that from the outset, his smartest move would have been to withdraw. But he read the game wrong.

Viewing the game from your opponent's perspective, as well as your own, is vital. Dixit and Nalebuff quote from David Halberstam's wonderful baseball book The Summer of 49 to show how the same thinking that helped Ted Williams become a great hitter can help managers get on base, too.

As a promising 17-year-old ballplayer, Ted Williams couldn't hit curve balls. After striking out once, a veteran player asked what he fanned on. "A **@@!!? slow curve," Williams said.

"Can you hit his fastball?" the veteran asked. "You bet," Williams responded. "What do you think he'll be looking to put past you next time?" the veteran asked. Williams paused. Ted Williams had not thought about pitching to Ted Williams before.

The next time at bat, he was ready and waiting. And an illustrious 25-year career began, built on an intense study of rival pitchers' minds.

There is, of course, a danger that in simplifying the structure of games, managers may distort them or err seriously. To analyze the game correctly, its essential elements must all be captured. Leaving out something important, like neglecting a possible strategy your foe may adopt, is like skipping the baking powder in the ingredients for a cake—a recipe for failure.

Dixit and Nalebuff imply that the game-theory perspective, when adopted by managers, generates a new and helpful business philosophy. In situations of conflict, they say, it is not from cutthroat competitive rivalry that society gains, but from cooperation. In politics, business, and world affairs, interdependence often means that hard-nosed competitive strategy leaves everyone worse off, while efforts to coordinate goals and strategies among players with common interests can help everyone do better.

A University of Michigan scholar, Robert Axelrod, demonstrated this fact when he ran a prisoner's dilemma tournament with algorithms (computerized sets of decision rules) playing against one another. The game the algorithms played was structured like a price war--if one player slashed prices and played competitively, while others did not follow suit, that player won; but if other players followed suit, driving down revenues, everyone lost. Cooperation- holding the line on prices--was a good result for all players, but brought the temptation to cut prices unilaterally, exploiting the good nature of competitors until in self-defense they followed suit. The winning algorithm was the simplest: Start with a cooperative move, then do what your opponent did the previous round. This approach has a key quality—it is forgiving. If your opponent signals "cooperation," then you follow suit. It is also nice—it starts by cooperating. Being nice and forgiving are not often considered winning business strategies, but if your market structure is one in which hardheaded rivalry causes mutual destruction, they are demonstrably unbeatable.

Managers have long understood that cooperation among workers inside firms is a determinant of corporate success. They are realizing increasingly that this is also true in relations among firms—a notion that may require a radical revision of antitrust laws, especially as the global nature of markets expands playing fields far beyond a country's borders.

Perhaps the most important area in which companies compete best by cooperating is in so called technology races, where companies invest in costly programs to research, develop, and patent new products and processes. New types of joint ventures and cooperative agreements linking competitors with one another and with universities and government are finding increasing use in Japan, Germany, and the United States. In next month's column, I will discuss how managers can structure R&D alliances to help their companies become more competitive.


Copyright © 2008 by Avinash Dixit and Barry Nalebuff