Utilizing Prisoner’s Dilemma In Business And The Economy

By Elvis Picardo, CFA AAA

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, and formalized and named by Princeton mathematician Albert William Tucker. Prisoner’s dilemma basically provides a framework for understanding how to strike a balance between cooperation and competition, and is a very 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.

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, 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 confess, 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 the 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 prison sentence (as symbolized by the negative sign; obviously the lower 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; this is shown in cell (a).
  • If A confesses but B does not, A goes free and B gets three years cell (b).
  • If A does not confess but B confesses, A gets three years and B goes free cell (c).
  • If A and B both confess, both get two years in prison cell (d).

Therefore if A confesses, he either goes free or gets two years in prison. But if he does not confess, he either gets 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 the Prisoner’s Dilemma

The prisoner’s dilemma elegantly shows that when each individual pursues his or her own self-interest, the outcome is worse than if they had both cooperated. In the above example, cooperation – wherein A and B 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 himself or herself would generally prefer to defect, rather than cooperate. If both choose to defect assuming the other wouldn't, instead of ending up in cell (b) or (c) like each of them hoped to, they would end up in cell (d) and earn two years in prison each. 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. But 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, as discussed below.

Applications to Business

A classic example of prisoner’s dilemma in the real world is encountered when two competitors are battling it out in the marketplace. Many sectors of the economy have two main rivals. In the U.S., for example, the fierce rivalry between Coca-Cola (NYSE:KO) and PepsiCo (NYSE:PEP) in soft drinks, and Home Depot (NYSE:HD) versus Lowe’s (NYSE:LOW) in building supplies, has given rise to numerous case studies in business schools. Other fierce rivalries include Starbucks (Nasdaq:SBUX) versus Tim Horton’s (NYSE:THI) in Canada, and Apple (Nasdaq:AAPL) versus Samsung (SSNLF) in the global mobile phone sector.

Consider the case of Coca-Cola versus PepsiCo, and assume that the former is thinking of cutting the price of its iconic Coke drink. If it does so, Pepsi may have no choice but to follow suit for its Pepsi 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 therefore 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 Coke drinks.

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/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 ad 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 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, government shutdown, etc.) 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 obviously 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 less if you simply walked in and paid 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 employer.

Conclusion

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.

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