The Prisoner’s Dilemma

The prisoner’s dilemma is the negative counterpart to the invisible hand.

The analysis we have just given of cartel cheating is one version of a very famous game called the prisoner's dilemma. The prisoner’s dilemma describes situations where the pursuit of self-interest leads to a group or social outcome that is in the interest of no one. The prisoner’s dilemma is the negative counterpart to the invisible hand. The pursuit of self-interest can, with the right rules, lead to the social interest—that’s the invisible hand. The pursuit of self-interest can also lead, with the wrong rules, to an outcome that no one intends and no one wants.


When Great Britain discovered large oil deposits in the North Sea, why didn’t it immediately join OPEC?

What is the surprising conclusion of the prisoner’s dilemma?

To give another example of this phenomenon, the world’s stock of fish is rapidly being depleted. To understand why, replace Saudi Arabia and Russia in Figure 15.4 with two large fishing firms or countries, say the United States and Japan. Cooperate now means “produce less fish” (instead of less oil). If both players choose Cooperate, fishing revenue can be maximized and the stock of fish will be maintained for future generations. But if one player cooperates, the other has an incentive to cheat by overfishing. And, of course, if one player cheats, the other has an incentive to cheat as well. Each player has the same incentive and so both players cheat. That reduces the stock of fish below the best possible outcome and eventually it may deplete the stock completely. That’s why so many people are concerned that the world is running out of many species of fish.

The Prisoner’s Dilemma and Repeated Interaction

The prisoner’s dilemma suggests that cooperation is difficult to maintain both when cooperation is good (preventing overfishing) and when cooperation is bad (maintaining a cartel). The situation is more optimistic and more pessimistic with repeated interactions! If the same players engage with one another repeatedly, they are more likely to cooperate than if they meet and play the prisoner’s dilemma just once. The political scientist Elinor Ostrom, who was awarded the Nobel Prize in economics in 2009, has shown, for example, that fishermen do not invariably overfish common fishing grounds. In small communities with repeated interaction, people generally find rules or norms, such as limits on how much it is okay to take, that lead to greater cooperation, and that limit the prisoner’s dilemmas. We will have more to say about overfishing in Chapter 19.


For the same reasons, however, cheating does not always break down cartels when a small number of players interact repeatedly. The asphalt industry, for example, is notorious for cartel-like behavior (asphalt is the tar-like material used for paving roads). Thousands of firms produce asphalt so you might think that cartels wouldn’t work. The problem is that asphalt is costly to transport and it has to be kept hot, so a firm can’t deliver asphalt at a reasonable price anywhere more than an hour or so away from its place of production. In rural regions, that limits the number of bidders on a road contract to just a handful of firms.

When only a handful of firms can realistically bid on a road contract, it becomes profitable to collude. For instance, the firms could secretly agree to all submit high bids, while agreeing that on each bid cycle one firm will be the “low” bidder, and then rotating the identity of this firm over time so that each firm shares in the profits. In the 1980s, the government prosecuted over 600 bid-rigging cases in the asphalt industry. What’s most interesting, however, is that there is evidence that the cartels did not disappear, even after this prosecution.

Tacit collusion occurs when firms limit competition with one another but they do so without explicit agreement or communication.

Government prosecution eliminated explicit agreements to rig bids but it didn’t solve the underlying problem. In many parts of the country, there are still only a handful of firms that can realistically bid on a contract. Moreover, the same firms face each other repeatedly and each firm understands that if they bid aggressively on every contract, then no one will ever profit very much. In this situation, strategies often evolve that can duplicate collusive outcomes even without explicit agreement. If Firm A bids low today, for example, Firm B can punish them by bidding low on the next contract. But if Firm A cooperates by submitting a high bid today, then Firm B can cooperate by submitting a high bid tomorrow. This strategy—do whatever your partner did the last period—is called “tit for tat” and it can be very effective at developing tacit collusion, collusion without explicit agreement or communication.

Another strategy is for firms to tacitly agree on territories—“I won’t underbid you in this area if you don’t underbid me in this other area.” Between 2005 and 2007, for example, over one thousand road contracts were put up for bid by the Kentucky government and a stunning 63% had only one bidder! Moreover, two clever economists, David Barrus and Frank Scott, discovered that the pattern of bids wasn’t random.1 Remember that asphalt firms have to deliver their product within about an hour of production. What Barrus and Scott discovered is that the firms weren’t bidding for every potential contract within their one-hour radius. Instead, the firms more often made bids just within the county in which the firm had its production plant. A firm might bid on a contract 40 miles away in the same county, for example, but not bid on a contract just 10 miles away but in another county. Even though county lines are irrelevant to the economics of asphalt production, they had become a focal point for firms to tacitly collude.


Most importantly, notice that it’s much harder to prosecute collusion when the colluding firms never meet or discuss an agreement and the only signal of collusion is not bidding!

The Prisoner’s Dilemma Has Many Applications

The prisoner’s dilemma has a remarkable number of applications throughout economics and the social sciences and even in biology, computer science, and philosophy. We show a few examples in Figure 15.5.


There Is Trouble with the Trees Each tree grows tall to try to grab up all the light. But when all the trees do, none gain an advantage and all expend resources in fruitless competition.
The Arms Race Few people wanted to develop the hydrogen bomb but no one wanted the other side to develop it first so we ended up in a very dangerous world.
Battle of the Brands Coke and Pepsi have spent billions trying to convince buyers that their brand is better. The war has been profitable … for the advertising agencies.
Standing Room Only At the concert everyone stands to get a better view but no one gets it (unless you have a very good friend).