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Yesterday, Nick introduced us to a classic problem of game theory: the Prisoner’s Dilemma. A standard PD goes something like this:

Two suspects are arrested by the police, who, having insufficient evidence for a conviction, separate the prisoners and offer each of them a deal: If one testifies against the other (who remains silent) the first goes free while the second receives a 10-year sentence. If both refuse to testify, both receive a six month sentence. If each betrays the other, each receives a five-year sentence. No prisoner can know what choice the other has made before the end of the investigation.

The Prisoner’s Dilemma, he noted, often provides grist for the dominant argument here in late capitalism that any rational player in an economic game should act unethically. This is because, in the form of a single PD game, a self-interested player (who wants the least possible amount of jail time) will always do better for himself by ratting out his partner.

For example, let’s say you are Prisoner A, and your accomplice Prisoner B can make the following choices: stay silent or betray you. Assume B is silent: If you also stay silent, you get a 6-month sentence; if you betray your pal you get no jail time at all. A self-interested agent, here, should betray. Now assume B betrays you: If you stay silent, you get a ten year sentence, and if you betray him, you get a five year sentence. Again, you should betray. Betraying is thus what game theoreticians call a strictly dominant strategy.

So far so bad, clearly, for the advocate of adopting an ethical stance in business. However, the picture is not so clear in the real world. Why? Well, for one thing, the world of business does not involve a single isolated economic exchange. If it is a prisoner’s dilemma at all, it is a continuously iterated one, for which it is not clear at all that such a strategy is optimal.

However, it seems to me much more likely that real-world business exchange takes the form of a stag hunt. “What’s a stag hunt?” you ask. Well, it’s another kind of game:

Two individuals go out on a hunt. Each can individually choose to hunt a stag or hunt a hare. Each player must choose an action without knowing the choice of the other. If an individual hunts a stag, he must have the cooperation of his partner in order to succeed. An individual can get a hare by himself, but a hare is worth much less than a stag.

This differs from a prisoner’s dilemma in that in the PD, if two people cooperate, each is choosing less rather than more (which is irrational). In the stag hunt, what is rational for one player to choose depends on his beliefs about what the other will choose.

Detail from Tea with Stag by Jana Paleckova.

The philosopher Thomas Hobbes famously (and informally) argued that those who view individual economic exchanges as instances of the prisoner’s dilemma not playing the relevant game, which is fundamentally due to their shortsightedness (their failure, I might note, to take the future into account).

Hobbes’ point is this: Suppose that the probability that the prisoner’s dilemma will be repeated another time is constant. Now suppose that an economic player – mistaking the continuously iterated games of business as discrete – always chooses to defect. Assume further that the other players, on observing this behavior, will retaliate (go, tit for tat).

Here is an example payoff matrix for a PD-type economic exchange (assume you are the red player):

We can see that the smart play here is to always defect: it will always net you one point more than cooperating. But now let’s assume that after any given game, the probability of another game is 0.6. This turns a two-person PD into a two-person stag hunt:

In other words, over indefinitely many games, the always-defect strategy (or, as Nick has it, the unethical play) is actually going to be consistently worse from a purely self-interested perspective.