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Game Theory: The Prisoner’s Dilemma and Personal Finance

For those unfamiliar with the Prisoner’s Dilemma, it’s essentially a hypothetical scenario where a prisoner has to choose between two alternatives – rat out his accomplice or say nothing. The prisoner selects which action to take based on the potential payoff or outcome from either alternative.

The Prisoner’s Dilemma is a common way to explain a branch of economics called Game Theory or Industrial Organization, popularized in the movie A Beautiful Mind. John Nash realized that to reach an optimal outcome, no participant can be made better off by choosing a different course of action. Essentially, everyone is in the best place that they can be.

So how does this apply to personal finance?

Let’s use credit card companies as an example. ACME Credit Cards has a large marketing department who has one simple responsibility – convince you that the optimal outcome is using a credit card.

So let’s use game theory to analyze the true payoffs of using and not using credit cards. I’ll then show you how ACME Credit Cards has distorted the truth hoping that you’ll choose a non-optimal solution (though certainly optimal for them).

Setting up the participants and outcomes

Step 1 is setting up the game with the possible choices that each participant has.

Choices in Prisoner's Dilemma

As shown above, Consumers have the option to either use credit cards or use cash for purchases. For the purpose of this illustration, I am narrowing the Credit Card Issuer’s options to make money from either interest charges or transaction fees charged to merchants (this assumes that the Consumer pays off the balance in full each month).

Step 2 is setting the payoffs that each participant can expect depending on the outcome of the choices made.

Real Outcomes from Prisoner's Dilemma

Here is a recap of the outcomes:

  • If the Consumer chooses to use credit cards and not pay off the balance each month, then the Consumer pays interest charges and the Credit Card Issuer makes huge profits. Bad outcome.
  • If the Consumer chooses to use credit cards and pay off the balance each month, then the Consumer still pays more since Consumers spend on average 18% more when using credit cards versus cash and the Credit Card Issuer still makes money. Bad outcome.
  • If the Consumer chooses to use cash only, then he or she saves money and the Credit Card Issuer goes broke no matter what it chooses. Good outcome.
  • Optimal Outcome: The Consumer should always choose to use cash instead of credit.

Step 3 is setting up the outcomes as Credit Card Issuers would have you believe them.

Outcomes according to Credit Card Issuers

Here is a recap of the outcomes:

  • If the Consumer chooses to use credit cards and not pay off the balance each month, then the Consumer  was able to get just what he or she needed when he or she needed it and the Credit Card Issuer is the good guy. Good outcome.
  • If the Consumer chooses to use credit cards and pay off the balance each month, then the Consumer was still able to get just what he or she needed when he or she needed it and the Credit Card Issuer is the good guy. Good outcome.
  • If the Consumer chooses to use cash only, then he or she misses out on all of the rewards and fun that everyone else is taking advantage of and the Credit Card Issuer goes broke no matter what it chooses. Bad outcome.
  • Optimal Outcome: The Consumer should always choose to use a credit card instead of cash.

Avoiding the marketing traps

Do not be fooled by slick advertising. Although Credit Card Issuers paint a very pretty picture of instant gratification, reasonable fees and interest rates, and a mass of incentives (e.g. miles, points, cash back), the reality is that they are making a lot of money. Visa posted profits of $713mm just for the first three months of 2010!

Meaning, they are doing a great job of distorting the truth. As shown above, the actual outcomes are not fun and fancy free living. Rather, avoiding credit and debt is the sure path to financial stability and growth.

This same logic and process aptly works for other areas of personal finance as well. I just like picking on credit cards.

Also, listed below are several articles and ideas on how to avoid debt and save money:

What are some other examples where the optimal outcome is being distorted by clever marketing? Also, sign-up for our RSS Feed for timely updates on this and other financial topics.


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  • Debrah

    There is no prisoner’s dilemma in the above examples. In fact, there isn’t even much of a game since the credit card company’s choices are not mutually exclusive (either-or). For there to be a game you need the payoffs of the consumer’s choices to depend on the choices of credit card companies. In your “games” the consumer’s payoffs depend on her choices only: if she uses the credit card she loses (first game) if she doesn’t, she gains. In the second game you reverse these outcomes. What role do the “choices” of credit card companies play? Now suppose we allow your matrices to be called games, they would still not, NEVER, be prisoner’s dilemmas. In technical words (I assume you will understand them, given the authority with which you speak): in a prisoner’s dilemma you have a unique Nash equilibrium in dominant strategies, which happens to be Pareto-dominated by some other outcome. In simple words: your games should have as “optimal outcome” (using your terminology) only one cell out of the four in the matrix (this already fails), and it should be the case that there is some other cell in the matrix that would actually make BOTH participants happier than the cell containing the optimal outcome. IF YOU CREATE A PAGE MEANT TO FREE CONSUMERS FROM MISLEADING INFORMATION BY CORPORATIONS, PLEASE START BY NOT GIVING MISLEADING INFORMATION YOURSELF!

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