The prisoner’s dilemma, one of the most famous game theories, was conceptualized by Merrill Flood and Melvin Dresher at the Rand Corporation in 1950. It was later formalized and named by Canadian mathematician, Albert William Tucker.
The prisoner’s dilemma basically provides a framework for understanding how to strike a balance between cooperation and competition and is a useful tool for strategic decision-making.
As a result, it finds application in diverse areas ranging from business, finance, economics, and political science to philosophy, psychology, biology, and sociology.
Key Takeaways
- A prisoner’s dilemma describes a situation where, according to game theory, two players acting selfishly will ultimately result in a suboptimal choice for both.
- The prisoner’s dilemma also shows us that mere cooperation is not always in one’s best interests.
- A classic example of the prisoner’s dilemma in the real world is encountered when two competitors are battling it out in the marketplace.
- In business, understanding the structure of certain decisions as prisoner’s dilemmas can result in more favorable outcomes.
- This setup allows one to balance both competition and cooperation for mutual benefit.
Click Play to Learn the Basics of the Prisoner’s Dilemma
Prisoner’s Dilemma Basics
The prisoner’s dilemma scenario works as follows: Two suspects have been apprehended for a crime and are now in separate rooms in a police station, with no means of communicating with each other. The prosecutor has separately told them the following:
- If you confess and agree to testify against the other suspect, who does not confess, the charges against you will be dropped and you will go scot-free.
- If you do not confess but the other suspect does, you will be convicted and the prosecution will seek the maximum sentence of three years.
- If both of you confess, you will both be sentenced to two years in prison.
- If neither of you confesses, you will both be charged with misdemeanors and will be sentenced to one year in prison.
What should the suspects do? This is the essence of the prisoner’s dilemma.
Evaluating Best Course of Action
Let’s begin by constructing a payoff matrix as shown in the table below. The “payoff” here is shown in terms of the length of a prison sentence (as symbolized by the negative sign; the higher the number the better). The terms “cooperate” and “defect” refer to the suspects cooperating with each other (e.g., if neither of them confesses) or defecting (i.e., not cooperating with the other player, which is the case where one suspect confesses, but the other does not). The first numeral in cells (a) through (d) shows the payoff for Suspect A, while the second numeral shows it for Suspect B.
The dominant strategy for a player is one that produces the best payoff for that player regardless of the strategies employed by other players. The dominant strategy here is for each player to defect (i.e., confess) since confessing would minimize the average length of time spent in prison. Here are the possible outcomes:
- If A and B cooperate and stay mum, both get one year in prison—as shown in the cell (a).
- If A confesses but B does not, A goes free and B gets three years—represented in the cell (b).
- If A does not confess but B confesses, A gets three years and B goes free—see cell (c).
- If A and B both confess, both get two years in prison—as the cell (d) shows.
So if A confesses, they either go free or get two years in prison. But if they do not confess, they either get one year or three years in prison. B faces exactly the same dilemma. Clearly, the best strategy is to confess, regardless of what the other suspect does.
Implications of Prisoner’s Dilemma
The prisoner’s dilemma elegantly shows when each individual pursues their own self-interest, the outcome is worse than if they had both cooperated. In the above example, cooperation—wherein A and B both stay silent and do not confess—would get the two suspects a total prison sentence of two years. All other outcomes would result in a combined sentence for the two of either three years or four years.
In reality, a rational person who is only interested in getting the maximum benefit for themselves would generally prefer to defect, rather than cooperate. If both choose to defect assuming the other won’t, instead of ending up in the cell (b) or (c) option—like each of them hoped for—they would end up in the cell (d) position and each earn two years in prison.
In the prisoner’s example, cooperating with the other suspect fetches an unavoidable sentence of one year, whereas confessing would in the best case result in being set free, or at worst fetch a sentence of two years. However, not confessing carries the risk of incurring the maximum sentence of three years, if say A’s confidence that B will also stay mum proves to be misplaced and B actually confesses (and vice versa).
This dilemma, where the incentive to defect (not cooperate) is so strong even though cooperation may yield the best results, plays out in numerous ways in business and the economy
Albert Tucker first presented the Prisoner’s Dilemma in 1950 to a group of graduate psychology students at Stanford University, as an example of game theory.
Applications to Business
A classic example of the prisoner’s dilemma in the real world is encountered when two competitors are battling it out in the marketplace. Often, many sectors of the economy have two main rivals. In the U.S., for example, there is a fierce rivalry between Coca-Cola (KO) and PepsiCo (PEP) in soft drinks and Home Depot (HD) versus Lowe’s (LOW) in building supplies. This competition has given rise to numerous case studies in business schools. Other fierce rivalries include Starbucks (SBUX) versus Tim Horton’s (THI) in Canada and Apple (AAPL) versus Samsung in the global mobile phone sector.
Consider the case of Coca-Cola versus PepsiCo, and assume the former is thinking of cutting the price of its iconic soda. If it does so, Pepsi may have no choice but to follow suit for its cola to retain its market share. This may result in a significant drop in profits for both companies.
A price drop by either company may thus be construed as defecting since it breaks an implicit agreement to keep prices high and maximize profits. Thus, if Coca-Cola drops its price but Pepsi continues to keep prices high, the former is defecting, while the latter is cooperating (by sticking to the spirit of the implicit agreement). In this scenario, Coca-Cola may win market share and earn incremental profits by selling more colas.
Payoff Matrix
Let’s assume that the incremental profits that accrue to Coca-Cola and Pepsi are as follows:
- If both keep prices high, profits for each company increase by $500 million (because of normal growth in demand).
- If one drops prices (i.e., defects) but the other does not (cooperates), profits increase by $750 million for the former because of greater market share and are unchanged for the latter.
- If both companies reduce prices, the increase in soft drink consumption offsets the lower price, and profits for each company increase by $250 million.
The payoff matrix looks like this (the numbers represent incremental dollar profits in hundreds of millions):
Other oft-cited prisoner’s dilemma examples are in areas such as new product or technology development or advertising and marketing expenditures by companies.
For example, if two firms have an implicit agreement to leave advertising budgets unchanged in a given year, their net income may stay at relatively high levels. But if one defects and raises its advertising budget, it may earn greater profits at the expense of the other company, as higher sales offset the increased advertising expenses. However, if both companies boost their advertising budgets, the increased advertising efforts may offset each other and prove ineffective, resulting in lower profits—due to the higher advertising expenses—than would have been the case if the ad budgets were left unchanged.
Applications to the Economy
The U.S. debt deadlock between the Democrats and Republicans that springs up from time to time is a classic example of a prisoner’s dilemma.
Let’s say the utility or benefit of resolving the U.S. debt issue would be electoral gains for the parties in the next election. Cooperation in this instance refers to the willingness of both parties to work to maintain the status quo with regard to the spiraling U.S. budget deficit. Defecting implies backing away from this implicit agreement and taking the steps required to bring the deficit under control.
If both parties cooperate and keep the economy running smoothly, some electoral gains are assured. But if Party A tries to resolve the debt issue in a proactive manner, while Party B does not cooperate, this recalcitrance may cost B votes in the next election, which may go to A.
However, if both parties back away from cooperation and play hardball in an attempt to resolve the debt issue, the consequent economic turmoil (sliding markets, a possible credit downgrade, and government shutdown) may result in lower electoral gains for both parties.
How Can You Use It?
The prisoner’s dilemma can be used to aid decision-making in a number of areas in one’s personal life, such as buying a car, salary negotiations and so on.
For example, assume you are in the market for a new car and you walk into a car dealership. The utility or payoff, in this case, is a non-numerical attribute (i.e., satisfaction with the deal). You want to get the best possible deal in terms of price, car features, etc., while the car salesman wants to get the highest possible price to maximize his commission.
Cooperation in this context means no haggling; you walk in, pay the sticker price (much to the salesman’s delight), and leave with a new car. On the other hand, defecting means bargaining. You want a lower price, while the salesman wants a higher price. Assigning numerical values to the levels of satisfaction, where 10 means fully satisfied with the deal and 0 implies no satisfaction, the payoff matrix is as shown below:
What does this matrix tell us? If you drive a hard bargain and get a substantial reduction in the car price, you are likely to be fully satisfied with the deal, but the salesman is likely to be unsatisfied because of the loss of commission (as can be seen in cell b).
Conversely, if the salesman sticks to his guns and does not budge on price, you are likely to be unsatisfied with the deal while the salesman would be fully satisfied (cell c).
Your satisfaction level may be less if you simply walked in and paid the full sticker price (cell a). The salesman in this situation is also likely to be less than fully satisfied, since your willingness to pay full price may leave him wondering if he could have “steered” you to a more expensive model, or added some more bells and whistles to gain more commission.
Cell (d) shows a much lower degree of satisfaction for both buyer and seller, since prolonged haggling may have eventually led to a reluctant compromise on the price paid for the car.
Likewise, with salary negotiations, you may be ill-advised to take the first offer that a potential employer makes to you (assuming you know that you’re worth more).
Cooperating by taking the first offer may seem like an easy solution in a difficult job market, but it may result in you leaving some money on the table. Defecting (i.e., negotiating) for a higher salary may indeed fetch you a fatter pay package. Conversely, if the employer is not willing to pay more, you may be dissatisfied with the final offer.
Hopefully, the salary negotiations do not turn acrimonious, since that may result in a lower level of satisfaction for you and the employer. The buyer-salesman payoff matrix shown earlier can be easily extended to show the satisfaction level for the job seeker versus the employer.
What Is an Example of the Prisoner’s Dilemma?
This “exchange game” has the same structure as the prisoner’s dilemma, and indicates the benefits of cooperation. Greg has a green cap and would prefer a blue one, while Brenda has a blue cap and would prefer a green one. Both would rather have two caps to just one and either of the caps to no cap at all. They are each given a choice between keeping the cap they have or giving it to the other. Whether Rose keeps her cap or gives it to Bill, Bill is better off keeping his, and she is better off if he gives it to her. Whether Bill keeps his cap or gives it to Rose, Rose is better off keeping hers and he is better off if she gives it to him. The ideal is to have two caps, but that’s only possible if one person behaves selfishly—and it means one person goes capless. However, both are better off if they exchange caps than if they just keep the one they have—because it’ll be the color they prefer.
What Is the Dominant Strategy in the Prisoner’s Dilemma?
In the prisoner’s dilemma, neither suspect—let’s call them Herb and Lee—knows the decision chosen by the other suspect. Herb is afraid of remaining silent because in such a case, he can receive more years in prison if Lee blames him. If Herb chooses to blame Lee, he can be set free if Lee remains silent. However, that is not likely, because Lee is using the same rationale and she is also going to blame Herb.
So, the decision of remaining silent by both suspects (the ultimate in trust and cooperation) provides the more optimal payoff (less jail time for each). But it’s not a really rational option because both parties are bound to act in their own self-interest and blame the other person, in a shot at doing no time at all. So, the second-best strategy is for both suspects to confess. Each will get more jail time than if both had stayed silent—but less than if one stayed silent and one confessed.
How Do You Beat the Prisoner’s Dilemma?
Over time, people have worked out a variety of solutions to prisoner’s dilemmas in order to overcome individual incentives in favor of the common good. In the real world, most economic and other human interactions are repeated more than once. A true prisoner’s dilemma is typically played only once; with repetition, people can begin to predict others’ behavior and learn from mistakes and adverse outcomes.
People have developed formal institutional strategies to alter the incentives that individual decision-makers face. Collective action to enforce cooperative behavior through reputation, rules, laws, democratic or another collective decision making, and explicit social punishment for defections transforms many prisoner’s dilemmas toward the more collectively beneficial cooperative outcomes.
Also, some people and groups of people have developed psychological and behavioral biases over time such as higher trust in one another, long-term future orientation in repeated interactions, and inclinations toward positive reciprocity of cooperative behavior or negative reciprocity of defecting behaviors. These tendencies may evolve through a kind of natural selection within a society over time or group selection across different competing societies. In effect, they lead groups of individuals to “irrationally” choose outcomes that are actually the most beneficial to all of them together.
The tragedy of the commons is a prime example of the prisoner’s dilemma operating in an economy. It may be in everyone’s collective advantage to conserve and reinvest in the propagation of a common pool natural resource in order to be able to continue consuming it, but each individual always has an incentive to instead consume as much as possible as quickly as possible, which then depletes the resource.
The Bottom Line
The prisoner’s dilemma shows us that mere cooperation is not always in one’s best interests. In fact, when shopping for a big-ticket item such as a car, bargaining is the preferred course of action from the consumers’ point of view. Otherwise, the car dealership may adopt a policy of inflexibility in price negotiations, maximizing its profits but resulting in consumers overpaying for their vehicles.
Understanding the relative payoffs of cooperating versus defecting may stimulate you to engage in significant price negotiations before you make a big purchase.