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Game theory: the prisoner’s dilemma

How can game theory: the prisoner’s dilemma support strategic choice or positioning?

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Contents

Firms don’t always think directly about what is right for their customers; sometimes they also think strategically about how their competitors will behave, and adapt their own behaviour accordingly.

Game theory analyses decisions in which each participant’s outcome depends partly on what others choose. The prisoner’s dilemma is its best-known illustration of a social dilemma: individually rational choices can produce a result that is worse for everyone.

When to use it

To structure a consequential choice involving strategic rivals or partners.

To anticipate competitor responses rather than treating them as fixed.

To prepare negotiations, auctions, market entry, pricing or cooperation.

Origins

John von Neumann’s 1928 work helped establish modern game theory, and his 1944 book with Oskar Morgenstern connected it to economic behaviour. At RAND, Merrill Flood and Melvin Dresher devised the interaction now known as the prisoner’s dilemma in 1950; Albert Tucker supplied the prison-sentence story and memorable name. Research then expanded into equilibrium, repeated interaction, bargaining, auctions, politics and business. A Nash equilibrium is a set of choices in which no player can improve its payoff by changing alone, given what the others do.

What it is

A “game” specifies the players, available actions, information, order of moves and payoffs. A payoff may represent profit, market share, time, risk or another outcome valued by the player.

In the prisoner’s dilemma, two suspects decide separately whether to confess. If both confess, each receives ten years. If only one confesses, that person receives one year and the other receives 25 years. If neither confesses, each receives three years.

Confessing is individually dominant under those payoffs: it produces a better personal outcome regardless of the other prisoner’s choice. Both therefore confess and receive ten years, even though mutual silence would have given both a better result. The model shows how incentives and inability to make a credible cooperative commitment can defeat collective welfare.

Real business games differ. Interaction may be repeated, moves may be sequential, information may be incomplete and payoffs uncertain. Some games are zero-sum, while others allow participants to create additional value through cooperation. The model is useful only when those differences are represented explicitly.

How to use it

Define the players and the decision each can actually make. Keep the initial model small enough to understand, but include alternatives that could change the result.

Construct a payoff matrix. For pricing, for example, each competitor may choose high or low, and each cell records the estimated outcome when the choices interact. State whose payoff appears first, the time horizon and the assumptions behind every value.

Look for:

a dominant strategy, which gives a player a better payoff for every relevant action by others;
a dominated strategy, which is always worse than another available action;
a Nash equilibrium, where no player benefits from changing alone;
an opportunity for credible commitment, communication, repeated reciprocity or rule design to produce a better outcome.

Eliminate strictly dominated choices where justified, then analyse the remaining game. In repeated or uncertain settings, consider reputation, learning, trust, retaliation and the value of future interaction. In negotiation, explore how the game can be redesigned to align incentives rather than merely predicting conflict.

Use ranges and alternative opponent models when payoffs or sophistication are uncertain. Game theory organises judgment; it does not read minds or remove the need for evidence.

Top practical tip

Draw a compact payoff matrix before debating tactics. Test the result under a naive, strategic and differently motivated opponent, and ask whether communication, sequencing or a credible commitment changes the incentives. The simplest useful model is often enough to expose a hidden dependency.

Top pitfall

Do not assume the other party shares your information, payoffs or sophistication. Auction design can also create a winner’s curse: in the UK mobile-licence auction of 2000, four successful bidders paid a combined £22.5 billion, far above expectations. Winning the game as defined may still destroy value if the payoff estimates are wrong.