What Game Theory Can Teach Us about RICO Prosecutions

This famous thought experiment describes a situation in which two people who have committed a joint crime are now separated and prevented from communicating with one another. Each person faces a choice: they can remain silent, or they can confess and present evidence of the joint crime in exchange for a lighter sentence. If a clever prosecutor sets the rewards and punishments correctly, confession becomes a better strategy for each individual acting alone—even though silence yields a better outcome for the pair jointly.

The prisoner’s dilemma is one of the first concepts students of game theory learn about—and for good reason, explains Ehud Kalai, a professor emeritus of managerial economics and decision sciences 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 will make people want to do things they wouldn’t want to do normally.” In the case of the prisoner’s dilemma, the game can also produce a socially desirable outcome, encouraging guilty people to confess to their crimes.

Of course, the classical prisoner’s dilemma is a mostly theoretical exercise. In the real world, crime is not usually so tidy, nor the incentives so clear. Consider the Racketeer Influenced and Corrupt Organizations (RICO) Act, the law perhaps most famously used against the Mafia. In RICO prosecutions, there might be dozens of conspirators with differing motivations for testifying (or not) against the boss.

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

“How can we make this method more realistic and applicable to more than just two players?” he explains. “That’s what my paper is about.”

The next-best thing to a dominant strategy

In game theory, there is sometimes what’s called a “dominant strategy”: an action of a 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 penalties are set 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 doesn’t, the person who confesses gets no jail time and the denier serves five years. And if both confess, both serve three years.

In this scenario, confession is the dominant strategy for each player, in that there is always an incentive for each player to confess, no matter what the other player does. For example, consider the decision from Player 2’s point of view: If Player 1 confesses, Player 2 receives a three-year sentence if she confesses and a five-year sentence if she remains silent. If Player 1 remains silent, Player 2 receives no jail time if she confesses, but a one-year sentence if she remains silent too. In both cases, confession yields the better outcome. The same logic applies to Player 1’s choice as well. (The paradox of the game is that both players staying silent yields the best joint 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 one year on a lesser charge and the denier gets five years. If both confess, both serve three years.

In this second game, neither player has a dominant strategy. Their optimal move is dependent on what the other player does. If your opponent stays silent, your best choice is to stay silent, and if your opponent confesses, your best choice is to confess.

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

But it turns out you don’t always need a dominant strategy to make confession seem appealing to the guilty. Rather, Kalai shows in the paper, prosecutors can elicit flipping 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 any other players confess. As the number of players—or coconspirators—increases, so does the effectiveness of this tactic.

Contagious strategies and RICO prosecutions

Consider the case of a mastermind, M, who might have recruited ten conspirators to commit a crime. For the prosecutor, the goal is to impose a five-year sentence on M if he is guilty. For the conspirators, the goal is to be declared innocent—or, short of that, to receive a lighter sentence, such as no jail sentence or community service.

The prosecutor presents M’s alleged conspirators with a deal: If they all remain silent, they—and M—will all be declared innocent. (If M and his compatriots are truly innocent, they will presumably choose this option.) However, if some people confess, the confessors get a light sentence (community service), the deniers get a five-year sentence, and M also gets a five-year sentence.

Of course, everyone remaining silent would produce the best outcome for the group as a whole (and for each individual)—it would result in a declaration of innocence. Still, silence is not a very comfortable option for any one individual player. After all, if only one person confesses, anyone who stayed silent gets 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 case where all other players remain silent—but it is certainly much more appealing than silence, because it is “safer,” or, in Kalai’s terminology, more resilient.

Despite not being a dominant strategy, this “contagious strategy,” which leverages the fear (and, indeed, likelihood) of defection, is very successful at 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 the RICO prosecution against President Donald Trump in Georgia. At first, he could not understand why the prosecutor in the case, Fani Willis, wanted to try all of Trump’s 18 alleged coconspirators simultaneously. But he came to see the logic—Willis was trying to, in essence, make confession a contagious strategy.

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

Beyond the criminal-justice system, contagious strategies—and the logic underlying them—are everywhere, Kalai says. “It’s related to other fears, like the fear of fears. Run on banks, inflation mentality, et cetera.”

Contagious strategies are also applicable to straightforward 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 asking price. Posting the “lowest possible profitable price” (lpp) is a contagious strategy that is not dominant. For example, if all nine sellers post a price equal to the lpp+2, then the best choice for the tenth seller is to post the price lpp+1. But it is easy to see that if even one seller posts lpp, it becomes very appealing for every other seller to do so too—just as it becomes appealing for other coconspirators to flip after the first one confesses.

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

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