thoughts on the Prisoner's dilemma.

While trying to teach my students about the (non-repeated) "Prisoner's Dilemma" (PD) game, I had the following thoughts. I hope some of them are vaguely original -- or at least interesting.

The usual view of this "game" is that it turns Adam Smith's "Invisible Hand" (IH) on its head (or on its heel). In the Greatest Economics Story Ever Told, the IH says that in exchange, individual greed leads to the production of mutually-beneficial gains for all (or almost all) people, especially when organized by a competitive market. On the other hand, in the PD story, individual greed (possessive individualism) leads to mutual destruction of the prisoners. This occurs even though there exists a mutually-advantageous solution for them (collusion, cooperation, conspiracy, other "c" words).

There's another way of looking at the PD. The problem is that the police have set up a special social structure that pushes the prisoners to hurt each other. They aren't allowed to talk to each other. They have to make their decisions (rat[*] on each other or keep quiet) simultaneously (in effect). The cops create incentives that push each prisoner to rat. Thus, the prisoners both "defect" and suffer.

(For simplicity, I'm ignoring degrees between "ratting" and "staying mum." I'm also ignoring the honor among thieves, which can encourage tacit collusion, so that both refuse to "rat" on the other.)

This might be thought of in terms of "transactions costs" which make it extremely expensive for the prisoners to get together and strike a deal. But that would be misleading.

The problem is that exchange can also be like a PD game. Orthodox economists don't tell you that in the act of exchange, the two "players" are colluding to not rob each other. If we drop this usually-covert assumption, we see four possible choices. (Again, the choice is binary, ignoring intermediate choices between the extremes. Again, the two "traders" are assumed to embrace possessive individualism.)

1. Cain and Abel swap their goods with each other, with mutually-beneficial effects (collusion, IH result).

2. Cain slays Abel, stealing his goods. Cain gains in a big way (getting both sets of goods) while Abel obviously suffers.

3. Abel slays Cain, reversing the roles.

4. Both fire their weapons at each other, so both die (both defect, the usual PD result).

As in a PD game, the incentive is there for Cain to kill Abel. Naturally, Abel will fear this event and find that he has an incentive to preempt Cain's dirty deed (done dirt cheap). So Cain may react by shooting first. Mutual destruction ensues...

What's the solution to this mess? Orthodox economics (Orthonomics?) simply assume it away. More seriously, the English political philosopher Thomas Hobbes advocated bringing a very Visible Hand, the Leviathan, the unified state which monopolizes the means of violence. This prevents mutual destruction. It sets up incentives for the two traders to cooperate.

Another English political philosopher, John Locke, naturally enough didn't trust the state. His solution was to advocate merging the propertied class (what we would call the capitalists) with the state. The former should dominate the latter, to the maximal possible extent, natch. In this scenario, Cain and Abel _are_ the state, colluding to prevent the odious option #4.

An incentive problem still exists, however. Suppose that we see trading between the two brothers. Cain could see the benefits of having both of the guys' goods rather than simply getting Abel's goods in exchange for his own. He might then cheat or rob or kill Abel. This unhinges the collusion (or turns the game into a one-person affair, which I'll ignore).

But Locke had a solution: he proposed that people accept each others' property rights as "natural." If they accept this fiat, then trading can occur and both can benefit. It's as if he were proposing that the "honor among thieves" that allows real-world prisoners to collude in real-world dilemmas should apply to all property owners. They should see themselves as a community, with common interests.

Though Hobbes and Locke were a little silly (seeing imaginary "social contracts" as providing insight into what's happening in the real world), they captured the two main elements of what allows the IH to work, at least some of the time. These are the coercion of the state and the generally-accepted legitimacy of property rights.

The latter element, I believe, needs a lot of shoring up. After all, if profits are to be made, why accept the ideology of "natural" property rights? But there are two reinforcing elements that Karl Marx might suggest. The property owners cling to the ideology of natural property rights because it unites them against those who lack significant property rights (capital). The ideology helps maintain ruling-class solidarity. Second, if the capitalists believe it, or at least generally act as if they did, then it's easier to teach to the underclasses.

This analysis says that the mutually-beneficial exchange of the IH story is just as artificial as is the mutual destruction of the PD case. Both are based in human-made institutions. For one, the IH, the structure is created allowing collusion, while for the other, the PD, it's set up to encourage defection.

Those in power decide which activities fit in which box. For example, for you hemp-heads out there, the capitalist state in the US has decided that pot sellers belong in the PD box, while alcohol purveyors belong in the IH box.

To choose a less heady example, the social structure puts purely private goods in the IH box, while purely public goods are in the PD box. (The "public goods problem" is a version of the PD game, with a large number of participants. The "rats" are called free-riders.) Of course, in the real world, almost no products are purely public or purely private.

BTW, if this story is revealing, that indicates (once again) that game theory can say something about the world, as long as we don't obsess with equilibrium situations (Nash or otherwise).

[*] This is unfair to rats. Recent research indicates that those cute and furry creatures are more cooperatively-minded than the stereotypes say.
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Jim Devine