Sunday, December 9, 2007

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.
--
Jim Devine

16 comments:

YouNotSneaky! said...

"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..."

Well, I'm not sure who the Orthodox economists are here but I presume the non-game theory (since GT has all kinds of ways of modeling the scenario you describe) kind where perfect competition is assumed. But it's precisely the competition itself (more specifically agents facing perfectly elastic supply and demand (what Ostroy and Makowski refer to as PEDS) or reaction functions) that makes Cain and Abel UNABLE to screw each other (play "rat" in PD), because it creates outside options for all players.

"Orthodox economics (Orthonomics?) simply assume it away."

It assumes it away by assuming perfect competition. But the point of the IH result is that competition disciplines players, agents, business people, citizens, etc. so that this kind of mess doesn't result. The competition IS the invisible hand.

rosserjb@jmu.edu said...

Nash equilibria and competitive equilibria are generally not identical.

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kevin quinn said...

Jim: This is perhaps not what you had in mind, but there is an obvious PD when it comes to trading at a distance. I agree to send you money if you send me the good. The trade at the price we agree on we'll assume is mutually beneficial. Each of us (assumed "rational") has a dominant strategy of reneging. I don't want to send money if you send the good; and I certainly prefer not to send the money if you are NOT going to send the good. SO the trade doesn't occur.

Solutions involve either Leviathan or reputation through repetition. Cf. Ebay's rating system.

Shane Taylor said...

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.

Jim, could you elaborate on this point? How does thinking in terms of transaction costs mislead here?

YouNotSneaky! said...

Of course in general they're not identical. But with many sellers and buyers (or the right market structure - Bertrand competition) they are. Or at least approximately so. Maybe. Hopefully. Sort of.

rosserjb@jmu.edu said...

yns,

Yes, well Scarf's Core Theorem promises ultimate convergence at infinity under the right conditions.

Barkley

J.Goodwin said...

I prefer the converse of the Locke capitalists run the state scenario.

The residents seize the state and the state nationalizes capital assets.

Talking about the workers is starting to seem just as discriminatory to me as talking about "landowners" or "citizens" or "capitalists."

The the increasing insulation of those in de facto power from those in nominal power (we the people) is becoming a serious problem. No simple answers there unfortunately. Certainly not at this stage.

YouNotSneaky! said...

That's more about cooperative allocations linking up with competitive allocations. It's related, but I think this is more about something like the Cournot convergence, or even Bertrand price competition.
The main point being that competition (roughly speaking, large number of actors) can in some (many?) instances solve the PD without the need for any kind of coordination, cooperation or other external mechanisms. Which is what the whole IH story, I think, is about.

As far as Scarf's (and Aumann's too) theorem, yeah, you need infinite agents and other stuff (in Aumann's case, a continuum) but it's hard to say exactly what the real world implications of these assumptions are. It's a bit like Zeno's paradox. When you shoot an arrow at a target in the real world, it does reach that target even though it has to travel half the distance first and all that. And if you go by Vernon Smith's experiment then you only need something like 5 people to get the competitive solution, not infinity.

Anonymous said...

Jim,
You should look at the work of Avner Greif (sp?) who uses game theory to explore mutually advantageous trade in an economic
historic context. Also Thomas Schelling has written about credibility issues underlying exchange. There's a nice discussion by Dixit and Nalebof (sp!) in the Schelling Festschrift
volume; I think some of this can be found in their Thinking Strategically.

rosserjb@jmu.edu said...

yns,

The Smith result depends on the right institutional setup of the market, with double auction being the one that brings convergence to the competitive equilibrium most quickly and straightforwardly in the experiments. A lot of the experimental lit actually suggests that four may be enough, more or less.

I have heard a rumor that an old line long mumbled in the halls of the Antitrust Division of the Department of Justice in Washington regarding prosecuting (or at least trying to block) mergers is "If two, sue; if three, wait and see; if four, open the door," or something like that.

Barkley

rosserjb@jmu.edu said...

More precisely that old DOJ line was more like "if to two, sue; if to three, wait and see; if to four, open the door."

Barkley

Anonymous said...

i think the 'core' issue is that the PD is a non-zero sum game. In other words, there are equilibria in which there are dollars all over the pavement. the first one to try to pick them up will get stabbed in the back by cain, whose able. one has a market failure.

the IH which assumes perfect foresight and infinite information solves this problem by looking around for all those dollars, and spare change in the couch, on the floor, etc. using Hayek's theory of Intelligent Design. (logically, IH implies ID, or its a tautology, with a mobius topology ).

K Arrow essentially solved this awhile back, by assuming 'information is power' and from physics we know money=power. So, there is not really any 'non zero sum game' or PD in general equilibrium. (one can get rid of money too, since its just an accounting tool for measuring what exists and what is known about it (its utility)). One uses 'dynamic equilibrium' following the poincare method.

Locke's and others (Gintis) solutions to the problem of choosing which market equilibrium is most aesthetic (by Dirac-Rawls theory) , by simply using the state and law and voting how to redistribute the wealth and other property rights (an applied problem left as an excercize for the reader

see Jared Ball for President
'go green'

)

has a dual described by Proudhon. To Proudhon, an armchair philosopher and mystic well known for his pornographic ramblings written under his nom de plum 'marquis de sade', 'property is theft'. So rather than law and economics, one can have crime and economics, and abolish crime (and the problem of whether cain is able) by simply abolishing property, as a solution to the economic (and crime) problem.

Anonymous said...

me: >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.<

Shane Taylor said >Jim, could you elaborate on this point? How does thinking in terms of transaction costs mislead here?<

because there are also transactions costs associated with the IH and exchange, including setting up a large superstructure of laws, courts, and police. The latter "transactions costs" are largely paid for by the taxpayer.

Anonymous said...

I wrote: >"Orthodox economics (Orthonomics?) simply assume it [the PD] away."<

"ohyounotsneaky" replies: >It assumes it away by assuming perfect competition. <

But you can't "assume perfect competition" without assuming that property rights are guaranteed, either

(1) because the property-owners use their state power to impose these rights on others or

(2) because of the popular legitimacy of those property rights, so that no-one will steal.

But I repeat myself. Competition without guaranteed property rights of some sort leads to a Hobbesian war of each against all.

In our current empirical reality, we have partially-guaranteed property rights. What we see is that -- if the central state isn't pushed to stop this process -- individual competitors acting dynamically to internalize as many external benefits as possible (get something for nothing) and to externalize internal costs to a maximal extent (pollute our lungs, destroy the earth, etc.) E.K. Hunt calls this the "Invisible Foot."

Kevin mentions the role of reputation (as on e-Bay). Reputation only works to stabilize exchange and the IH if the basic problem of respect for individual property rights has been settled. Without the property rights guaranteed, reputation becomes the same as "street cred," the reputation your gang has for being biggest and toughest.

Jim

Econoclast said...

J.Goodwin said: >I prefer the converse of the Locke capitalists run the state scenario. The residents seize the state and the state nationalizes capital assets.<

Going back to Locke's generation, this is the solution that the Swiss philosopher J-J Rousseau proposed. While for Locke, property rights defined who the citizens were, for Rousseau, the citizens defined the property rights. He didn't propose socialism, though. He saw the citizens as imposing limits to the accumulation of property on each other.

J. Goodwin: > Talking about the workers is starting to seem just as discriminatory to me as talking about "landowners" or "citizens" or "capitalists."<

I don't know about "discriminatory." But it should be made clear that "workers" is short-hand for a heterogeneous group of people who have to work for a living. Being a "worker" does not make anyone morally superior to anyone else.

>The the increasing insulation of those in de facto power from those in nominal power (we the people) is becoming a serious problem. No simple answers there unfortunately. Certainly not at this stage.<

maybe people on this blog can suggest some answers...?
Jim D.