Game theory is based on the premise that no matter what the game, no matter what the circumstances, there is a strategy that will enable you to succeed. If you are formulating business

strategy to increase market share, playing poker, negotiating salaries or bidding in an auction, rules are at work, however elusive and intangible they might be. Georgina Peters reports

BUSINESS STRATEGY REVIEW

GAME Game theory was conceived not in the classroom or in the boardroom but in the casino. In the 1930s, when he was a student at Princeton and Harvard, John von Neumann was an attentive spectator at poker games. Von Neumann was a mathematical genius rather than a gambler and the result was game theory, a unique mathematical insight into the possibilities and probabilities of human behaviour.

Prisoner’s dilemma

While von Neumann went on to apply his genius to the development of the US’s nuclear arsenal and the frst computer, game theory developed its own Zen-like language of dilemmas and riddles. Te most famous of these is the prisoner’s dilemma.

Invented by Princeton University’s Albert Tucker in 1950, the prisoner’s dilemma is an imaginary scenario. Two prisoners are accused of the same crime. During interrogation in diferent cells they are each told that if one confesses and the other does not, the confessor will be released while the other will serve a long prison sentence. If neither confesses, both will be dispatched to prison for a short sentence and if both

confess they will both receive an intermediate sentence.

Working through the possibilities, the prisoners conclude that the best decision is to confess. As both reach the same decision, they receive an intermediate sentence.

Te prisoner’s dilemma has a fundamental faw: game theory is rational, reality is not. Companies that have expressed an interest in game theory tend to be from tightly regulated industries – such as power generation; ones where there is limited competition or cartels (such as OPEC in the oil industry). With a limited number of players, playing by accepted rules and behaving in a rational way, game theory can make sense of what the best competitive moves may be.

Broader interest in game theory was reignited in 1994 when the Nobel Prize for economics was awarded to three renowned thinkers – John Nash, John Harsanyi and Reinhard Selten. Harsanyi has shown that even if players in a particular game are not well informed about each other the game can still be analysed in the same way as other games. Te precociously brilliant Nash (brought to life on the big screen by

Russell Crowe in A Beautiful Mind) has carved the most notable academic furrow and is the creator of the Nash equilibrium, an idea developed in his PhD thesis.

Te Nash equilibrium is the point when no player can improve his or her position by changing strategy. Players in a game will change their strategies until they reach equilibrium. (In the prisoner’s dilemma the Nash equilibrium is reached when both prisoners confess – they can no longer improve their situation by changing their strategy as this would send them to prison for a longer period.)

Interdependent interaction

In one classic example, an industry includes two competing companies. Each determines the price of its product. If both were to set high prices they would maximise their profts. Similarly, if both set their prices at lower levels they would remain proftable. Te trouble comes when they choose diferent price levels. If one sets a high price and the other a low price, the company with the low price makes far more money. Te optimal solution is for both to have high prices. Te trouble

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where the full range of uncertainties is evident. Game theory ofers a means of rationally interpreting the possibilities of cooperation as managers grapple with the myriad of intangibles produced by win-win relationships.

American academics Adam Brandenburger and Barry Nalebuf suggest the new onus should be on “co-opetition,” an inelegant combination of competition and cooperation. Tey argue that “looking for win-win strategies has several advantages. First, because the approach is relatively unexplored, there is greater potential for fnding new opportunities. Second, because others are not being forced to give up ground, they may ofer less resistance to win-win moves, making them easier to implement. Tird, because win-win moves don’t force other players to retaliate, the new game is more sustainable. And, fnally, imitation of a win-win move is benefcial not harmful.”

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HEORYis if one company has a high price, the other will undercut it and vice versa. Eventually, both companies end up with low prices and lesser profts.

Te key lesson from this and other scenarios explored by game theory is simply that the interactions of companies and other organisations are interdependent.

In fact, game theory encompasses some of the fundamental truths of decision making. If a company decides to make an investment it should consider how others – whether they be competitors, customers or suppliers – will react. Game theory acknowledges that real life is not conducted in a vacuum. Instead, companies must visualise and anticipate the reactions and responses of their competitors. In the jargon, putting yourself in the shoes of your competitors, considering their future moves and their likely impact, is labelled “allocentrism”.

Win-win relationships

Game theory is more than rational rules for an irrational world. Behind its rationality lies a world of daunting irrationality and maddening paradox. It is best seen as a way of thinking about

the future, a tool to get people to think. As a rationalist’s guide to business paradoxes, game theory can be a useful business weapon. Instead of seeking out strategies driven by win-lose scenarios, companies begin to explore the merits of other strategies, which may be win-win with mutual benefts for themselves, their customers, suppliers and even their competitors.

Tis enables escape from the “negative sum games” evident in many industries where promotions and advertising are quickly countered by yet more promotion and advertising. In such scenarios, the costs of doing business increase, profts fall and market share tends to remain distressingly static. Game theory is dismissive of such short-term, knee-jerk reactions. If you are going to play the game you have to think ahead. You make your move in anticipation of what you have calculated the competition will do.

One potential growth area for game theory’s as yet minimal usage lies in partnerships. Nash’s initial work tackled non-cooperative games where competitors didn’t communicate. Now, game theory has spread its tentacles to embrace the growing trend for partnerships, an area

ResouRces Robert Axelroad, Te Complexity of Cooperation, (Princeton UP, 1997); Adam Brandenburger and Barry Nalebuf, Co-Opetition (Doubleday, 1996); Martin Osbourne and Ariel Rubinstein, A Course in Game Teory (MIT Press, 1994)

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