When to use it

• To select a course of action in a highly competitive situation.
• To understand the likely moves of your competitors.
• To help you in negotiations.

Origins

Game theory has deep academic roots. It emerged from the field of mathematics, and its invention is typically attributed to John von Neumann who wrote an initial paper on the subject in 1928 and then a book, Theory of Games and Economic Behaviour, in 1944 (co-authored with Oskar Morgenstern). The term ‘game’ here refers to any sort of competitive scenario where two or more players are trying to make decisions that interact with each other.

While there are many subfields within game theory, the focus here is on one well-known type of game, known as ‘the prisoner’s dilemma’. The first mathematical discussion of this game was developed in 1950 by Merrill Flood and Melvin Dresher at the RAND Corporation in the USA. Because it involved two players who were trying to predict how each other might behave, its application to Cold War politics and the use of nuclear weapons, was obvious. Research in this area proliferated throughout the 1950s, with many different types of games being analysed. A key concept developed during this period was the notion of a ‘Nash equilibrium’ – the outcome of a game where neither party has an incentive to change their decision.

Gradually, the concepts of game theory were brought into the business world, and applied in a variety of areas. For example, game theory is very useful for understanding how firms develop strategies in oligopolies – that is, where there are small numbers of competitors who watch each other carefully. It is also very useful for understanding negotiations between individuals and between businesses.

What it is

Game theory is a way of understanding decision making in those situations where multiple participants have competing or conflicting objectives. For example, if your firm is competing head to head with another firm, the price you charge isn’t affected only by what customers will pay, it is also affected by your competitor’s price. In such a situation, you need to be ‘strategic’ in your thinking, which means getting inside the head of your competitor and acting in a way that takes its likely decision into account. The most famous model in game theory is ‘the prisoner’s dilemma’. Consider the situation where two suspected felons are caught by the police, and interrogated in separate rooms. They are each told: (a) if you both confess you will each go to jail for ten years; (b) if only one of you confesses, he gets one year in jail, the other gets 25 years; and (c) if neither of you confesses, you each get three years in jail.

This game is deliberately set up to expose how tricky ‘games’ of this type can be. The optimal outcome is for neither of the prisoners to confess, so they each get three years. But because they cannot communicate with each other, their best individual decision is to confess, and the net result (assuming they both do this) is that they each get ten years. In other words, maximising individual outcomes does not necessarily aggregate up to the optimal welfare for a group.

All sorts of extensions and modifications to this model are possible. For example, many real-life ‘games’ are actually repeated interactions between parties, so that what you do in one game influences what you do in the next game. Some games involve sequential moves, rather than simultaneous moves. Some games are ‘zero-sum’, meaning there is a fixed amount of value to be divided up, while others are ‘non zero-sum’, which means that by acting in a cooperative way you can increase the amount of value.

How to use it

The mathematics involved in game theory is challenging, and most people in the business world don’t have the time or the inclination to understand the details. However, it is possible to draw out some simple rules of thumb from the prisoner’s dilemma analysis.

First, try to figure out all the choices you can make and all the choices the other party can make. In the prisoner’s dilemma, each party has two choices (confess or not confess) and the consequences of each choice are very clear. In the real world, you have to make some calculated guesses. For example, you could choose a ‘high’ or a ‘low’ price for your new product, your competitor can do likewise, and you can estimate the likely market share and profits that follow from each scenario. This is called a ‘pay-off matrix’.

Next, you look at the analysis to see if there is a ‘dominant strategy’ for your firm – defined as one with pay-offs such that, regardless of the choices of other parties, no other strategy would result in a higher pay-off. Clearly, if you have such a dominant strategy, you should use it. You can also see if there are any ‘dominated strategies’, which are clearly worse than others, regardless of what other parties do. These can be eliminated.

These steps often clarify the choices you face. For example, if you eliminate one dominated strategy, it sometimes becomes clear you have a dominant strategy that should be the right way forward. You keep iterating in this way until a dominant strategy emerges, or the game cannot be simplified any further. In the latter case, you then have to make a judgement based on whatever other factors you think might be important.

Further reading

Dixit, A.K. and Nalebuff, B. (1991) Thinking Strategically: The competitive edge in business, politics, and everyday life. New York: W.W. Norton & Company.

Von Neumann, J. and Morgenstern, O. (2007) Theory of Games and Economic Behavior (60th Anniversary Commemorative Edition). Princeton, NJ: Princeton University Press.