What Game Theory Can Teach Us About RICO Prosecutions

This famous thought experiment describes a situation in which two people who have committed a common crime are now separated and unable to communicate with each other. Each person faces a choice: they can remain silent or confess and present evidence of the common crime in exchange for a lighter sentence. If a smart prosecutor gets the rewards and punishments right, confession becomes a better strategy for each person acting alone—though silence works better for the couple jointly.

The prisoner’s dilemma is one of the first concepts students of game theory learn—and for good reason, he explains Ehud Kalaiemeritus professor of managerial economics and decision science at the Kellogg School.

“It shows the power of game theory,” he says. “We can design rules that make criminals confess, and we can create incentives that make people want to do things they wouldn’t normally want to do.” In the case of the prisoner’s dilemma, the game can also produce a socially desirable outcome by encouraging the guilty to confess their crimes.

Of course, the classic prisoner’s dilemma is a mostly theoretical exercise. In the real world, crime is usually not so tidy, nor are the motives so clear. Consider the Racketeer Influenced and Corrupt Organizations Act (RICO), the law perhaps most famously used against the Mafia. In RICO prosecutions, there can be dozens of co-conspirators with different incentives to testify (or not) against the boss.

But game theory can still be used to elicit confessions even in these more complex situations. That’s the finding from Kalai’s new paper, which explores strategies for making confession an attractive prospect in multiplayer games like RICO prosecutions.

“How can we make this method more realistic and applicable to more than two players?” explains. “This is my paper.”

The next best thing to a dominant strategy

In game theory, there is sometimes what is called a “dominant strategy”: an action by one player that is optimal regardless of the actions chosen by the opponents.

For example, consider a two-party prisoner’s dilemma game in which the rewards and punishments are defined as follows: if both players remain silent, they are both convicted of a lesser charge and both serve one year. If one confesses and the other does not, the person who confesses is not punished with imprisonment and the person who refuses serves five years. And if they both confess, they both serve three years.

In this scenario, confession is the dominant strategy for each player, since there is always an incentive for each player to confess, regardless of what the other player does. For example, consider the decision from the perspective of Player 2: If Player 1 confesses, Player 2 is punished with three years in prison if he confesses and five years in prison if he remains silent. If Player 1 remains silent, Player 2 receives no jail time if he confesses, but a one-year sentence if he remains silent. In both cases, confession works best. The same logic applies to player 1’s choice. (The paradox of the game is this both Keeping the players silent yields the best overall outcome—just two years total served by the two criminals—but neither player has an individual incentive to make that choice.)

However, not every game has a dominant strategy. Imagine that the judge insists that both players get no jail time if they both remain silent, while if one player confesses and the other doesn’t, the confessor still gets a year on a lesser charge and the denier gets five years. If they both confess, they both serve three years.

In this second game, no player has a dominant strategy. Their optimal move depends on what the other player is doing. If your opponent remains silent, your best option is to remain silent, and if your opponent confesses, your best option is to confess.

As games become more complex, it becomes more difficult to design rules in which the desired outcome—confession—is a dominant strategy for the guilty. In the case of RICO prosecutions, for example, it is difficult to construct sentences that would be acceptable to a judge and make confession a dominant strategy.

But it turns out that you don’t always need a dominant strategy to make confession seem attractive to the guilty. Instead, as Kalai shows in the paper, prosecutors can cause a reversal in another way that is easier to achieve. He calls this “next best” approach a “contagious strategy”—a scenario in which it is optimal to confess if other players confess. As the number of players—or conspirators—increases, so does the effectiveness of this tactic.

Contagious Strategies and RICO Prosecutions

Consider the case of a mastermind, M, who could have recruited ten conspirators to commit a crime. For the prosecutor the aim is to give M a five year sentence if he is guilty. For conspirators, the goal is to be found not guilty – or, short of that, to receive a lighter sentence, such as no jail time or community service.

The prosecutor presents M’s alleged co-conspirators with a deal: If they all remain silent, they—and M—will all be found not guilty. (If M and his compatriots are truly innocent, they will obviously choose this option.) However, if some do confess, the confessors get a light sentence (community service), the deniers get five years in prison, and M also gets a five-year penalty.

Of course, anyone remaining silent would have the best outcome for the group as a whole (and for each individual)—resulting in a plea of ​​not guilty. However, silence is not a very comfortable option for any individual player. After all, if only one person confesses, whoever remained silent spends five years behind bars.

In this game, then, confession is not a dominant strategy in the mathematical sense—it does not produce a better outcome in a situation where all other players remain silent—but it is certainly much more attractive than silence because it is “safer, ” or, in Kalai’s terminology, more durable.

Although not a dominant strategy, this “contagious strategy,” which exploits the fear (and indeed the possibility) of defection, is very successful in making confession seem like the best option. And contagious strategies, Kalai points out, are much easier to create than dominant ones.

The fragility of denial

Kalai says the idea for the paper was sparked by news coverage RICO Prosecution of President Donald Trump in Georgia. At first, he couldn’t understand why the prosecutor in the case, Fannie Willis, wanted to try all 18 of Trump’s alleged co-conspirators at once. But he saw the logic—Willis was trying, in essence, to make confession a contagious strategy.

“The more people on trial, the more fragile the overall denial,” he explains. “If you’re on trial with 17 other people, the fear that someone else will confess becomes much more realistic.”

Beyond the criminal justice system, contagion strategies—and the logic behind them—are everywhere, Kalai says. “It is related to other fears, such as the fear of fears. Run to the banks, inflation mentality, etc.’

Contagious strategies also apply to simple economic interactions, such as price competition. Consider, for example, ten identical sellers offering the same good in a market. Each seller posts an asking price and each buyer buys from a seller who posts the lowest price. Posting the “lowest possible profitable price” (lpp) is a non-dominant contagion strategy. For example, if all nine sellers post a price equal to lpp+2, then the best choice for the tenth seller is to post the price lpp+1. But it’s easy to see that if even one seller publishes lpp, it becomes very attractive for every other seller to do so as well—just as it becomes attractive for other conspirators to flip after the first confesses.

Thus, the very same logic that can be used to induce a confession in a RICO trial explains why a greater number of competing sellers in a market tends to yield a low price.

“This is part of a bigger picture,” says Kalai.