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Prisoner's Dilemma—Game Theory And Self-Interest

Prisoner's Dilemma—Game Theory and Self-Interest

By William R Thomas

Question: How would an Objectivist respond to the Prisoner's Dilemma? Peter Singer, in his book A Darwinian Left: Politics, Evolution, and Cooperation, uses it for an attack on rational self-interest. His version of it is as follows:

"You and another prisoner are languishing in separate cells of the Ruritanian Police Headquarters. You have no way of contacting him. The police are trying to get you both to confess to plotting against the state. An interrogator offers you a deal: If the other prisoner continues to remain silent, but you confess, implicating him in your crime, you will be freed and he will be locked away for twenty years. If, however, you refuse to confess, and the other prisoner does, you will be the one who gets twenty years and he will go free. You ask: 'What if we both confess?' The interrogator says that then you will both get ten years. 'And if neither of us confesses?' Reluctantly, the interrogator admits that he will not be able to get convictions, but they can, and will, hold you for another six months under the government's emergency powers legislation. 'But think about it,' he adds, 'whether the other guy sings or not, you'll be better off if you do—you can walk straight out of here if he doesn't, which is better than staying here for another six months, and you can get ten years rather than twenty if he does. And remember, we've offered him exactly the same deal. So what are you going to do?'"(p. 48)
 
Singer goes on to write, "There is no solution to this dilemma. It shows that the outcome of rational, self-interested choices by two or more individuals can make all of them worse off than they would have been if they had not pursued their own short-term self-interest. The individual pursuit of self-interest can be collectively self-defeating"(p. 48).
 
I sense that there might be an equivocation on Singer's part with "self-interest," but how would an Objectivist respond to this?
 
Answer: First, let me remark that you are right that Objectivism doesn't share Singer's idea of interest. We can see this by looking at the real-life relevance of the Prisoner's Dilemma as Singer describes it. Formally speaking, Singer is wrong that "there is no solution" to this dilemma. In terms of one's own interests, there are correct courses of action to take depending on what the other person will do. These are known in game theory as "Nash equilibria." Unfortunately, the Prisoner's dilemma set up makes confessing the best course of action. But when both do it, they both end up poorly. This is perverse, since if the prisoners could only reliably commit to not confess, they would both be better off. But they can't, so they should confess.
 
Now is this a real problem for the Objectivist ethics of rational self-interest? There are two things to say about this: First, the Prisoner's Dilemma is a game, not real life. Second, it's a peculiar kind of game, a one-shot game. Let's look at each of these points.
 
"The Prisoner's Dilemma is a game, not real life."
 
A formal game scenario is just that, a scenario. It radically simplifies the real complexities of information and the "pay-offs" or benefits we get in life. There is no reason to think that a game scenario applies to many cases in real life, unless it can be shown to do so. In the case of the prisoner's dilemma, there is a story associated with the game (and Singer recounts it well in the quotation you offer). But the game may in fact not connect to many real situations, and it may fail to do so in several key respects.
 
First, consider that the perverse game result depends on a crucial assumption: the prisoners have no means of committing to cooperate. Each one has two choices: confess, or don't confess. That's it. There is nothing else either can really do.
 
But in real life, there are all sorts of means of cooperating, including side-payments, contracts, credible threats, reputation effects, and so on. (By the way, the Prisoner's Dilemma is a case of "non-cooperative" game theory. This just means the actors can't be forced to cooperate. When I use the term "cooperate," I mean voluntary cooperation. So I am still talking about "non-cooperative" scenarios).
 
Second, most real interactions are not of a "lose/lose" character, like this game. They aren't even of an "I win/you lose" character. Most real interactions almost always present us with a potential to end up at least somewhat better off. And in most real interactions, there is always the choice of "don't play." Will taking that job make you miserable? Don't take it.
 
The prisoner's dilemma is just not the right game to model real life interaction on most issues. It gets the pay-off sets wrong, and forces the actors into perverse lose/lose interactions that normally they simply do not have to engage in. Despite the fascination of philosophers with the Prisoner's Dilemma, it is really just one kind of game-theory scenario. There are many, many others.
 
Even in the highly stylized context of the Prisoner's Dilemma game, there is one very crucial aspect to the game's assumptions, which also shows how little real life application it is likely to have. This is my second major point:
 
"It's a one-shot game."
 
In real life, one reason we don't rat out our fellows is that we have to meet them tomorrow. In the future, they might rat on us right back. The standard Prisoner's Dilemma game is a one-shot model. This means that not only do the prisoners only have the choice of confess vs. don't confess, they also never, ever interact in any way again. If we relax this assumption, and assume they play this game over and over, the results can change very radically.
 
In particular, if the game is played repeatedly without any known end-point (even if it does end randomly at some point), then there are usually Nash equilibria that involve neither party confessing. For example, if one party plays "tit for tat," and only confesses if the other confesses, he can induce his opponent to never confess. After all, if you confess against a person who offers you tit-for-tat, you know that person will confess in reaction to your confession, and then you all are both in the soup! In that case, it makes more sense to not confess. Tit-for-tat won't confess either, because it's not in his interest to do so.
 
(To see this point in its full glory, I recommend a textbook by a former professor of mine, Ken Binmore. It is called Fun and Games and was published by D.C. Heath in 1992. I am sure there are many other good textbooks as well. )
 
Since most of our important interactions are of this repeated, indefinite-duration character, this really should be the standard way formal games are set up. Certainly no one should make much hay out of a game result if it comes from a one-shot game. True one-shot interactions are rarely of much importance. And the ability to take even a perverse set up and turn it to mutual benefit in the repeated, indefinite duration game shows in one respect how, in fact, there can be a harmony of interests among rational people over the long term and in the full context.
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William R Thomas has written on topics in politics, ethics, and epistemology, and has spoken internationally on the theory of individual rights and Ayn Rand’s philosophy of Objectivism. His works include Radical for Capitalism, and, as editor, The Literary Art of Ayn Rand. He is the director of programs for The Atlas Society. Thomas is currently a lecturer in the Department of Economics of the University at Albany.