The Prisoners’ Dilemma and Congress

As I write this, our Congress is locked in an argument, unable to reach an agreement over an infrastructure bill.  Since the Democratic Party has a majority in both chambers, this would seem to be a fairly simple objective, but the failure of the party to do so reminds me of a classic example of game theory:  The Prisoners’ Dilemma.

Note.  I usually try—most likely unsuccessfully—to keep my own political opinions out of this blog.  While I have strong, and probably strange, political opinions, I have never thought my beliefs were neither terribly interesting nor any of the readers’ business.  Strangely, I routinely receive letters from people across the political spectrum who have somehow managed to read between the lines and discover my “hidden” support of everything from the Masons to the Flat Earth Society.   Sorry, but I’m not Lawrence Block’s Evan Tanner, and most people would find my real political opinions rather boring.

In the Prisoners' Dilemma, imagine that the sheriff has arrested two men for a suspected bank robbery.  When he searched their car, while he discovered no evidence of the robbery, he did find two stolen handguns.  Though the sheriff cannot arrest them on the bank robbery, he can prosecute each for the stolen handgun.  

The sheriff is crafty and unwilling to let settle for just charging the two suspects with the firearms charge, so he separates the two men where they cannot communicate with each other, and makes each the same offer.

“All right, scumbag,” says the sheriff.  “We both know that you and your partner robbed the bank, but I can’t prove it.  So, here’s the deal I’m offering both of you.  If you confess and give evidence against your partner, I’ll let you go and your partner gets ten years in jail.  If he confesses, I’ll let him go and you can rot in jail for ten years.  If you both confess, I’ll prosecute both of you, and you can spend the next decade in jail together.  But if neither of you talks, I’ll prosecute both of you for the stolen firearm and you’ll both spend a year in jail.”

Clearly, the best possible outcome for the two criminals is each man to keep his mouth shut, hope that “honor among thieves” is not a myth and that his partner will also keep quiet so that each man will only spend a single year in jail.  Game theorists have a name for this, the Coase Theorem, that states that if two parties are allowed to trade freely, and in this case, it is information that they are trading, they will eventually reach an efficient outcome.

Our two criminals (let’s call them A and B since that’s easier to label on a graph) can’t communicate, and without information, each has to develop his own optimum output.  Put more simply, each man has two choices, either to talk or to remain silent, and there are only four possible outcomes, as shown on the chart to the right.  The best outcome for each man is for him to talk and hope his partner does not, and while spending only a single year in jail is better than being jailed for ten years, there is no ‘good’ outcome if he remains silent.

Since each of the two men is likely to calculate his outcomes the same way, and since the only possibility of escaping jail time is to talk, it is most likely that both men will accept the sheriff’s offer and talk, triggering the worst possible outcome for each:  serving ten years in jail.

This is exactly what is happening right now in Washington concerning the president’s new infrastructure plan (the exact details of which change almost hourly).  Since the Democratic margin in both houses is very thin, the only possibility of the bill’s being passed is for several special interest groups within the party to work together and reach a compromise.  

Theoretically, since the Democrats have a majority, all that would be necessary to pass legislation is to use Coase Theorem, negotiate among themselves, and reach an efficient outcome.  Our elected officials, unlike the two prisoners, are allowed to actually talk among themselves, and reach a compromise.   In reality, however, both parties are made up of small special interest groups, each interested more in securing legislation favorable to their group than in passing a compromise bill.  And since a large part of the communication is being done by press releases and publicized sound bites, it is not really a negotiation.

Because of the upcoming election, there is the added element of the Democrats’ desiring a legislative victory before voting begins.  The closer we get to the election, the more power this gives to a group demanding amendments to the proposed bill, and each such amendment makes the bill more unpalatable to the party as a whole.  Since there is a thin margin in both houses, the defection of even a few members negates the possibility of passing any legislation.

Unlike the Prisoners’ Dilemma, Congress has multiple participants, each seeking his own optimum efficient outcome.  There are powerful incentives against cooperation even within a party.  Opposition brings the reward of increased press exposure, the opportunity to attract more voters interested in the special interests you represent, and the very real likelihood that your party will offer you more economic carveouts for your constituents.  

You can test this yourself.  I’m fairly sure that most of us can name Democrats opposed to the proposed legislation.  Other than congressional leadership, can you name any of Democrats who have supported the legislation?  You probably cannot, and with each additional player, game theory says it is even more unlikely that any large spending bill can be passed.  If you ignore the press announcements, and just focus on game theory, the chances of Congress passing any large infrastructure bill seem remote.