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The prisoner’s dilemma is a paradox 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 the concepts can sometimes be 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
- The prisoner’s dilemma describes a situation where, according to game theory, two players acting selfishly will ultimately result in a sub-optimal 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 a prisoner’s dilemma can result in more favorable outcomes.
- This setup allows one to balance both competition and cooperation for mutual benefit.
How to Use the Prisoner’s Dilemma in Business
Understanding the Prisoner’s Dilemma
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, you will go free, and the other suspect will serve three years.
- If you do not confess but the other suspect does, you will be convicted and serve three years while they go free.
- 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.
Basic Concepts of the Prisoner’s Dilemma
There are a handful of basic concepts that must be present for the prisoner’s dilemma paradox to work. These concepts include:
- There must be two players. The scenario involves two individuals or entities who are implicated in a shared situation, such as committing a crime together or facing a mutual decision.
- Decisions are made at the same time. Both players make their decisions without knowledge of the other’s choice. This simultaneous decision-making is a crucial aspect of the dilemma, as each party must make its decision without regard to the other party’s decision.
- There must be a combination of outcomes. A payoff matrix is a table that outlines the possible combinations of choices made by both players and the associated payoffs or outcomes for each player. It helps to visualize the consequences of different decisions. We’ll talk more about a playoff matrix later.
- There can be mutual cooperation or mutual betrayal. Players have the option to either cooperate with each other (choosing a mutually beneficial outcome) or betray each other (choosing a self-serving outcome). The tension behind the prisoner’s dilemma comes from the conflict between individual and collective interests.
- Each player has a dominant strategy. That strategy is the option that provides the best outcome for them, regardless of the other player’s choice. This dominant strategy is often the rational choice for an individual, leading to a suboptimal outcome when both players follow it.
- Players are assumed to be rational decision-makers. This means that people tend to maximize their own self-interest. This assumption is a fundamental aspect of game theory and the rational choice model, as it drives the conflict between options.
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 (as for example, 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.
| Prisoner’s Dilemma – Payoff Matrix |
Suspect B |
||
| Cooperate |
Defect |
||
| Suspect A |
Cooperate |
(a) -1, -1 |
(c) -3, 0 |
| Defect |
(b) 0, -3 |
(d) -2, -2 |
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.
Implications of Prisoner’s Dilemma
The prisoner’s dilemma elegantly shows that 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 prison sentence of one year. All other outcomes would result in a sentence of either two or three 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 A’s confidence in B’s staying silent 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.
Fast Fact
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) and Tim Horton’s (QSR) in Canada and Apple (AAPL) and 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 higher 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):
|
Coca-Cola vs. PepsiCo –
Payoff Matrix |
PepsiCo |
||
|
Cooperate |
Defect |
||
|
Coca-Cola |
Cooperate |
500, 500 |
0, 750 |
|
|
Defect |
750, 0 |
250, 250 |
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 a 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:
|
Car Buyer vs. Salesman –
Payoff Matrix |
Salesman |
||
|
Cooperate |
Defect |
||
|
Buyer |
Cooperate |
(a) 7, 7 |
(c) 0,10 |
|
Defect |
(b) 10, 0 |
(d) 3, 3 |
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 lower 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 unwilling 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.
Example of Prisoner’s Dilemma in Economics
We’ll wrap up the article by talking through how the prisoner’s dilemma appears in economics. A macroeconomic example of the prisoner’s dilemma can be found in the context of government fiscal policies during an economic downturn. When there’s an economic recession, individual governments face the choice of implementing expansionary fiscal policies to stimulate economic growth. However, the effectiveness of these policies depends on the actions of other governments.
Consider if all countries simultaneously adopt expansionary fiscal policies. The global economy would benefit from increased aggregate demand, leading to a potential recovery. However, if one country decides to pursue a more conservative fiscal approach, focusing on austerity measures or budget cuts, it may experience short-term economic stability. However, the global impact could be detrimental.
This situation mirrors the prisoner’s dilemma, as each government must decide whether to cooperate by collectively implementing expansionary policies or defect by pursuing more conservative measures. If all countries cooperate, the global economy can recover more effectively. However, if one or more countries defect and pursue the maximum personal gain, it can hinder the recovery for all nations, resulting in a suboptimal outcome for the broader group.
What Is the Answer to the Prisoner’s Dilemma?
There is no correct answer for the prisoner’s dilemma. It is a paradoxical situation that demonstrates how individual decisions affect group outcomes.
What Is the Prisoner’s Dilemma in Simple Terms?
Two prisoners face a choice to confess or remain silent without communicating. Each one’s choice affects the other. If one confesses but the other doesn’t, the confessor is set free and the silent one receives a long sentence. If both remain silent, both receive a shorter sentence. If both confess, they both receive a medium sentence. The outcomes are both confess, only one confesses, or both remain silent. Game theory predicts that, generally, people will pick the option that benefits them the most.
What Is the Best Strategy for the Prisoner’s Dilemma?
The prisoner’s dilemma is not about the best strategy or answer. Instead, it demonstrates how two entities acting in their own self-interest do not generate an optimal income for both parties.
The Bottom Line
The prisoner’s dilemma shows us that acting in one’s own self-interest doesn’t always result in the optimal outcome. Businesses, governments, and individuals may not always get the best result when they act in their own interests, so it is best to consider how cooperating might affect the outcome of their decisions.
