Game Theory and Privacy

Earlier this week in “The Flawed Logic of Secret Mass Surveillance” I presented some thinking about the dynamics of mass surveillance and what that suggests about how things are likely to play out in the future with regards to the NSA’s spying. It seems to me that there’s an essential structure to privacy that is reminiscent of game theory. And this could provide additional hints about how things are likely to play out over the long term—especially with regards to spying among nations. As I wrote in the earlier piece, spying confers power over others, and it is in my interest to secretly observe you, and for you not to secretly observe me.

In particular, these circular incentives of spying create a structure of conflict that brings to mind the canonical “game” of game theory: the Prisoner’s Dilemma. The Prisoner’s Dilemma is a theoretical situation in which two criminals are arrested and interrogated separately, and must each choose whether to confess.

• If A and B both confess their crime, each of them serves 2 years in prison (lose-lose)
• If A confesses but B denies the crime, A will be set free whereas B will serve 3 years in prison, and vice versa (big win, big lose)
• If A and B both deny the crime, both of them will only serve 1 year in prison (win-win)

If we take two parties—let’s say two nation states for now—the situation is in many ways parallel:

• If nations A and B both decide to spy on each other, both parties pay the budgetary and diplomatic and possibly public relations costs of doing so, while likely gaining little net advantage over time (lose-lose)
• If A refrains from spying on B, but B spies on A, then A will be placed at a significant advantage and B at a significant disadvantage in relations between the two, and vice versa (big win, big lose).
• If A and B both refrain from spying, then neither will incur either the costs or the advantages of spying (arguably win-win).

The Prisoner’s Dilemma has formed the basis of much of the mathematical discipline of game theory. (This is an area in which John Nash, portrayed by Russell Crowe in the movie A Beautiful Mind, did pioneering work. My knowledge of this comes from a book, “The Prisoner’s Dilemma,” by William Poundstone, which I highly recommend.) Many real-world studies and theoretical analyses have been done of the game, and the conclusion that mathematicians have reached is that the most theoretically rational thing to do within a round of the game is to betray the other person (i.e., confess). In my parallel, that would be: spy.

Interestingly, however, that changes when the game is played over and over again against the same opponent, in what is called “iterated Prisoner’s Dilemma.” In that situation, even mutually anonymous, online human players of the game, after an initial unstable period of mutual and one-sided betrayals, usually end up groping their way over time to a strategy of consistent mutual cooperation—a “cooperative equilibrium.” And in computer Prisoner’s Dilemma contests, the optimal strategy is to cooperate with the other person in the first round, and then to imitate their move in each round thereafter (a strategy dubbed “tit for tat”), which produces the same cooperative outcome against any opponents utilizing the same—optimal—strategy.

You can see where I’m going with this: if we view privacy as a game-theoretical situation in which mutual betrayal is punished, mutual cooperation rewarded, and one-sided betrayal rewarded even more, that suggests that the leading nations of the world will, over time, reach a cooperative equilibrium in the area of surveillance. After a period of trying to one-up one another, they will over time gravitate towards, and eventually settle upon, on the collectively optimal strategy, which is to not spy on each other at all.

Perhaps we are seeing the earliest signs of such a dynamic in the recommendations issued yesterday by the president’s NSA advisory panel. The panel suggested that with respect to “closely allied governments,” the government should explore “understandings or arrangements regarding intelligence collection guidelines and practices with respect to each other’s citizens.”

All of this would only apply in the absence of any persistent technological advantage by one party or another, which would disrupt the game-theoretical structure of the situation by tilting the “game.” Clearly the United States possesses such an advantage at the moment. But as I argued in my recent piece, such an advantage is not likely to persist for us now, or for any party in the future.

So far I’ve confined this discussion to the dynamics of how surveillance plays out among nation states. When it comes to relations between individuals, cooperative equilibrium is probably reflected in the intricate manners, social norms and legal rules that we already have around privacy. Although each person stands to gain important insights from spying that can give them a leg up in social, professional, or other contexts, we long ago recognized that it is better if we all refrain from attempting to do so. And so many forms of spying among individuals (electronic eavesdropping through the planting of bugs, for example) are illegal, and socially, at least, “gentlemen don’t read each other’s mail.” Which is not to say there aren’t betrayals, and technological means that everyone uses to help protect privacy; life will always be complicated, but I think that cooperative equilibrium is part of the underlying logic of the situation, and it can help illuminate where we are and where we are likely to go.

When it comes to relations between individuals and the state, there can be no game-theoretical analysis, because the parties are far too unequal in power for there to be anything resembling a game. Instead, in a democracy, the theory is that the people collectively have the power to decide how much power the state shall have over them individually. In the case of mass spying, we’ll have to see how that works out.