The Prisoner's Dilemma is a well-known game theory problem that translates well into our real life experience. The idea is that two people who will optimize their individual and collective outcomes by cooperating can, under specific circumstances, decide not to cooperate.

Can the two prisoners solve their dilemma by mutually binding each other to silence with an enforceable civil contract of the nature of a Non-Disclosure Agreement?

Prisoner's Dilemma Description

Two members of a criminal gang are arrested and imprisoned. Each prisoner is in solitary confinement with no means of communicating with the other. The prosecutors lack sufficient evidence to convict the pair on the principal charge, but they have enough to convict both on a lesser charge. Simultaneously, the prosecutors offer each prisoner a bargain. Each prisoner is given the opportunity either to betray the other by testifying that the other committed the crime, or to cooperate with the other by remaining silent. The offer is:

If A and B each betray the other, each of them serves two years in prison

If A betrays B but B remains silent, A will be set free and B will serve three years in prison (and vice versa)

If A and B both remain silent, both of them will only serve one year in prison (on the lesser charge).

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I don't think the following analysis applies:

It would not "solve" the problem, because the contract would not be enforceable. See this question on enforceability. In particular, Lachman v. Sperry-Sun Well Surveying Company, 457 F.2d 850

A bargain, performance of which would tend to harm third persons by deceiving them as to material facts, or by defrauding them, or without justification by other means is illegal.

But I do not think that analysis applies because there is no deception or fraud involved. Both parties have a fifth amendment right to not self-incriminate. The agreement would be for both parties to exercise their constitutionally protected rights by remaining silent. Prosecutors often solve this with immunity agreements for "unindicted co-conspirators" plus subpoenas to compel testimony and otherwise cooperation with investigation. However, I don't think that tactic can displace an individual's constitutionally protected right to "remain silent."

  • 2
    What is the penalty for breaking the NDA? If it's less than 1 year in prison, it's still advantageous to do so. – Nuclear Wang Sep 28 '18 at 18:04
  • 2
    The difficult issue here is "enforceable". The state has no interest in helping the prisoners with their dilemma, in fact it exploits it and encourages (e.g. immunity in exchange of declaring in trial, whistleblower protections, ...). And if the enforcer isn't the state, this is not different from the classical "if you talk to the cops you will sleep with the fish" legal approach. – SJuan76 Sep 28 '18 at 18:11
  • @NuclearWang: If the penalty makes a difference in your analysis, describe it in your answer. The minimum penalty would be "damages" but it is theoretically possible the two could agree to "liquidated damages" of an arbitrarily large sum. There is also the possibility of injunctive relief and strict enforceability. But either of those mechanisms for relief would need to be enforced pre-emptively somehow. – Mowzer Sep 28 '18 at 18:33
  • By the way, a grant of immunity can absolutely override your right to remain silent (which is really just part of the right against self-incrimination; you can't incriminate yourself if you have immunity.) The problem for the prosecution if they go that route is that they don't know what you'll say once on the stand; if you proclaim the other guy's innocence, that makes it even more difficult to convict him. – D M Sep 28 '18 at 23:31
  • If you consider a more generic version, not involving crimes and confession and prison but merely some other situation where cooperation is good but betrayal is better, then certainly contracts can help. – Nate Eldredge Sep 29 '18 at 14:40

The contract is almost certainly not valid. The answer you linked references the 2001 Federal Circuit case Fomby-Denson v. Dept of the Army. The court, in its opinion, quoted from the 1948 Supreme Court case Hurd v. Hodge:

[t]he power of the federal courts to enforce the terms of private agreements is at all times exercised subject to the restrictions and limitations of the public policy of the United States . . . . Where the enforcement of private agreements would be violative of that policy, it is the obligation of courts to refrain from such exertions of judicial power.

It is clear that, in the case you propose, the enforcement of such a contract would go against the public interest. Quoting from the 1972 Supreme Court case Branzburg v. Hayes, the Fomby-Denson decision said:

it is obvious that agreements to conceal information relevant to commission of crime have very little to recommend them from the standpoint of public policy.

It further notes this clause from the First Restatement of Contracts:

[a] bargain in which either a promised performance or the consideration for a promise is concealing or compounding a crime or alleged crime is illegal.


Not a bad question but a contract would change the outcomes of the prisoners dilema more than it would the nash equillibrium directly, at which point would it still be the prisoners dilema?

Looking past this existential conundrum, economic analysis would show that to change the equilibrium, the contract would probably have to be at least as harsh as 2 or 3 years in prison for talking or provide a reward worth 2-3 years in prison to work (I say "probably" because were talking about human behavior) and be enforceable.

Enforcability is your bigger issue and a bit hard to answer yes or no. As D M's answer explains, courts will likely not uphold a contract that goes against the public policy. There is also the issue of whistle-blower statues that protect people from retaliation for bringing crimes to light. On the other hand current events have shown that you can buy silence in cases of sexual harrasment, so it's not outlandish to think in certain circumstances paying off a witness is legal and enforceable but certainly rare.

That said to some extent this is what happens with gangs and cartels in the real world. There is a contract. i.e. You forbear from testifying and I will forbear from causing harm to you and everyone you love. I don't think the word "civil" is the best word for this case, and it would not be enforceable in a court of law, but still technically a contract, and usually people making these kinds of contracts operate outside the law.

  • "you can buy silence in cases of sexual harrasment" - Well, sort of. If a person has a possible civil case against you, you can pay them an amount up to what they could have reasonably sued you for, and include a nondisclosure agreement to prevent them from going to the media with the story. That still doesn't stop them from reporting the crime to the police or testifying against you (and any contract that purported to do so would likely be viewed as bribery/extortion) but perhaps the other person is less likely to do so if they are being compensated. – D M Sep 30 '18 at 14:24

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