For ye Publick Goode: Blackmaile Moust Foule

Here's one for all you recreational game theorists out there. Solve this and then ask yourself where on the euvoluntary spectrum blackmail should sit.

Player 1: the sovereign.
Player 2: a trusted agent of the sovereign, with access to sensitive, embarrassing documents.

Strategies available:
P2 first selects (blackmail; not blackmail)
P1 then selects (pay; not pay)
P2 then selects (leak; not leak)
P1 then selects (punish; not punish)

You could extend this game by adding a pre-selection stage where P1 chooses (hire; not hire) and then nature assigns (trustworthy; not trustworthy) with some probability, but Bayesian games get confusing pretty quick, so let's instead consider our moral intuitions behind some of the payoff combinations.

Here's the thing, if we're the public and we're interested in the dynamics of this game, we may want to maximize the probability that agents of the sovereign will leak information that demonstrates violations of public trust. That is to say that if the crown is spying on honest yeomen, the sheriff who blabs performs an act of public charity. This act of public charity is necessarily worth something. Perhaps the individual value isn't all that much. I might value this knowledge at 25 cents, Mungo at a buck and a half, and ol' JR that keen-eyed goshawk at $3.75. Add all this up all the way across the population and you've got the dollar-denominated value of a leak. Note that in some cases, this value could well easily be negative.

With this knowledge in hand, and working her way up the game tree, P2 sets about deciding whether to blackmail the state and if so, how much to charge. Here's the curious thing: there's no way to judge the economic efficiency of this transaction ex ante. I can't suss if I actually value this knowledge at $0.25 until I know what it is. To us, it's worth a total of five and a half bucks. So the blackmail then becomes a bet between P1 and P2. The blackmailer wants to pick the maximum value without going over what she believes the sovereign estimates the public value to be. The sovereign should be willing to transfer up to the public value of the information to keep it a secret. And then to punish, of course. That's almost another game tree in itself.

It's obvious that as long as there's a positive public value for a leak then the (not blackmail | leak) strategy is more or less okay when it comes to our moral intuitions. Sure, there are plenty of folks for whom any leak of classified state documents is costly, no matter how malfeasant the program, but we're looking at adding up value across all constituents, not just at those loud wagging tongues we hear on the ol' teevee.

But what about a blackmail bet gone south? How should we feel about (blackmail | leak)? Does attempted blackmail so tarnish the character of the leaker that the leaked information itself loses value? If we have some instrumental preferences over good governance, shouldn't we actively encourage insiders to do as they must to increase the probability of a righteous leak, even if it means blackmailing the state?

I think the answer is at least partly in that final stage. There's a combination of the probability of detection and the severity of the punishment that will allow escape from sunk cost risks. There's also the question of lowering these frictions in general. In a competitive market, the price of a commodity is equal to its marginal cost. Competition in leaking government secrets mean that even mundane crap with very low public value could be up for bid. Is it in the public's interest to haggle over marginal secrets?

And perhaps more interestingly, is there a substantial difference between private blackmail and government blackmail? Which one is more offensive? Why? Are the ethical analyses substantially different? If so, how? Also, how would you model this game if you were using it in class?