Strategy

Game theory: the prisoner’s dilemma

Game theory provides a set of models, such as the ‘prisoner’s dilemma’, which help a firm plan its strategy, taking all such factors into account

Firms don't always consider what is best for their clients; they also consider how their competitors will act and adjust their own behavior accordingly. Game theory provides a collection of models, such as the "prisoner's dilemma," that assist a company plan its strategy while considering all of these issues.

When to use it

● To choose a course of action in a highly competitive situation.
● To anticipate your competitors' next movements.
● To assist you in your negotiations.

Origins

Game theory has a long history in academia. It was invented in the field of mathematics by John von Neumann, who published an introductory 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' refers to any competitive situation in which two or more players are attempting to make decisions that affect each other.

While game theory has many subfields, the focus here is on one well-known type of game called the "prisoner's dilemma." Merrill Flood and Melvin Dresher of the RAND Corporation in the United States developed the first mathematical analysis of this game in 1950. Its relevance to Cold War politics and the use of nuclear weapons was obvious because it entailed two sides attempting to foresee how each other would act. Throughout the 1950s, research in this subject exploded, with many various sorts of games being studied. The concept of a 'Nash equilibrium,' or the result of a game in which neither player has an incentive to reverse their decision, was established around this time.

Game theory concepts were gradually introduced into the corporate world and used to a number of situations. Game theory, for example, is highly useful for understanding how firms create strategies in oligopolies, or markets with a small number of competitors who closely monitor each other. It's also helpful for comprehending individual and corporate negotiations.

What it is

Game theory is a means of looking at how people make decisions in situations where they have competing or conflicting goals. If your company is competing with another company, for example, the price you charge is influenced not only by what customers would pay, but also by your competitor's pricing. In such a case, you must think strategically, which entails getting inside your competitor's head and acting in a way that considers its anticipated decision.The 'prisoner's dilemma' is the most well-known model in game theory. Consider the case of two suspected criminals who are apprehended by the police and interviewed in different rooms. They are each told: (a) if you both confess, you will each serve 10 years in prison; (b) if just one of you confesses, he will serve one year in prison and the other will serve 25 years; and (c) if none of you confess, you will each serve three years in prison.

This game is designed to demonstrate how difficult these kind of 'games' can be. If neither of the inmates confesses, they will each receive three years in prison. However, because they are unable to communicate with one another, their best individual decision is to confess, with the net outcome (if they both confess) being ten years in prison for each of them. To put it another way, maximizing individual achievements does not always equate to optimal collective welfare.

This model can be extended and modified in a variety of ways. Many real-life 'games,' for example, are actually recurring interactions between people, so what you do in one game affects what you do in the next. Sequential rather than simultaneous moves are used in some games. Some games are 'zerosum,' meaning there is a fixed amount of value to be distributed, while others are 'non zero-sum,' meaning you can enhance the amount of value by cooperating.

How to use it

The mathematics involved in game theory is difficult to grasp, and most people in the corporate sector don't have the time or motivation to do so. However, several simple rules of thumb can be derived from the prisoner's dilemma analysis.

First, consider all of your options as well as the options available to the other party. In the prisoner's dilemma, each party has two options (confess or not confess), with extremely apparent consequences for each. You have to make some calculated estimates in the actual world. For instance, you might choose a 'high' or 'low' price for your new product, your opponent could do the same, and you could calculate the potential market share and profits from each scenario. This is referred to as a 'pay-off matrix.'

Then you examine the data to see if your company has a 'dominant strategy,' defined as one with pay-offs so high that no alternative strategy would result in a higher pay-off regardless of other parties' choices. Obviously, if you have a strong approach, you should employ it. You can also observe if some 'dominant strategies' exist that are plainly worse than others, regardless of what the other parties do. These can be done away with.

These steps can help you understand your options. If you eliminate one dominated approach, for example, it may become evident that you have a dominating strategy that should be followed. You repeat this process until a dominant strategy emerges or the game can no longer be simplified. In the latter instance, you must next make a decision based on whatever other criteria you believe are relevant.

Top practical tip

Because the ideas are simple and the applications are broad, game theory has become immensely popular. For example, you may find yourself competing with particular coworkers for a promotion opportunity, which requires you to work together while also competing. You may have to choose between being the first to market with a new product (and risking it failing) or being the last to market. You can find yourself competing for a government contract against a few tough competitors, and having to make difficult decisions about pricing or service.

In all of these situations, game theory ideas can help you think about how your choices and those of your competitors interact with one another. In most cases, a simple back-of-the-envelope reward matrix and a search for dominant and dominated strategies is all that is required.

Top pitfall

One thing to keep in mind is how advanced the opposing party's analysis is likely to be. You may lose out if you do your calculations expecting the other side is highly strategic but they turn out to be relatively simple-minded. The opposite is also true: don't underestimate your competitor's intelligence. In 2000, the UK government held an auction for third-generation mobile telecommunications licenses, which became a notable illustration of the latter scenario. With only four licenses available and five prospective bidders, the auction was meticulously planned. It raised £22.5 billion, far more than planned, and all four 'winners' were overpaid as a result.