Playing games with economics

There has been a huge growth in game theory in undergraduate economic courses in recent years. Indeed, some universities seem to think it should form the main pillar of study. This was brought home to me when visiting a very respectable Midlands university for an open day. The head of department explained how game theory showed that free markets did not generally produce optimal results and he used the financial crisis as an example of how the pursuit of self-interest damaged welfare and how the outcome could therefore be improved upon by regulation. More on that later…

Unfortunately, his thesis was easily unravelled when the professor showed what he thought was the clinching example. He played an engaging scene from the film ‘A Beautiful Mind’ which is about the Nobel Laureate John F. Nash. A small group of men are deciding how to chat up a small group of women in a bar. They realise that, if they all like the same girl and follow their self-interest by converging on her, then it is likely that they will all be leaving the bar without any success.

One of the men (Nash, I think) then has a Eureka moment when he realises that Adam Smith was wrong, that there were gains from co-operation and that, if everybody pursues their own self-interest, then everybody will lose out. However, if they co-operate, then there might be benefits.

Well, there are no Nobel prizes for unravelling that one. Of course, Nash is correct to argue that the absence of co-operation will lead to sub-optimal results, but the Midlands professor is wrong to think that this demonstrates that regulation is better than the pursuit of self-interest in markets. Let us think in terms of a comparative systems analysis. There are two possibilities:

1.    A regulator – let’s call it ‘Offchatup’ - could try to discern, assemble and centralise all the information about people’s subjective preferences in such situations and about when such situations might arise. The regulator could then co-ordinate the activities of the men in the bar, saying ‘Mr. X should chat to Miss A at 10:05pm’, and so on.

2.    Alternatively, we could let the four people co-operatively solve the problem. They could sit round the table and think whether the four as a group should talk to the women as a group, whether they should draw lots, and so on.

Nash, as far as I understand, was merely identifying that, if the group could not come to an enforceable co-operative agreement, then the outcome could be sub-optimal. There were no normative conclusions with regard to regulation as was suggested at the university open day.

In fact, the policy conclusion should be that we should allow the greatest scope to come to enforceable co-operative agreements with others (in this respect, one thinks of the huge networks of co-operation that existed in private stock exchanges or of the way in which football is organised, but there many other examples). The market provides a great forum for co-operation. Competition is the process by which the best forms of co-operation are discovered and are copied. But it is true that enforceability is vital, though enforceability could be by tacit means (exclusion from future ventures to the bar) as well as explicit means (legal action for breach of contract).

Very often, of course, government prevents such co-operation because co-operation in the market involves collusion that is deemed detrimental to consumers. Different free-market economists will have different views on the extent to which the government should intervene here; however, it is interesting that the interventionist economists who call for regulators to solve co-ordination problems rarely seem to say that there should be exceptions to competition policy to allow the market to solve such problems through enforceable co-operative agreements. Indeed, it is worth noting one example. Until the mid-1980s, many life insurance companies colluded to cap commissions. This had the effect of ensuring that brokers would not recommend insurance policies (from this group of companies) solely on the basis of commission. This, in turn, made mis-selling less likely and thus helped promote the reputation of the industries as a whole (both the insurance and the broking industries). The arrangement was broken up by the Office of Fair Trading. Next year, the Financial Services Authority is introducing a new regime for the sales of financial products as it attempts yet again – 27 years on – to deal with the problem of insurance mis-selling that was exacerbated by the break-up of the maximum commission agreement.

Now, of course, co-operation in the market may not always produce the theoretically optimal result. But, the market is the forum where people will solve these problems most effectively. As von Mises said in Human Action, markets are places where people are ‘competing in co-operation and co-operating in competition’ in order that people can find the position from which they can best serve society. The idea that regulators can centralise all the necessary knowledge and act purely in the public interest (and not be captured by outside interests) suggests that the alternative of government regulation to promote the optimal outcomes is not promising. After all, with regard to the financial crash, some people say that banks were over-regulated; some say that they were under-regulated; some say that they were badly regulated. However, nobody argues that regulators lacked powers. Government regulation of the financial system did not produce optimal outcomes. Government regulators have, though, bull-dozed private regulatory mechanisms that might have been more effective. It is imperative that theoretical economics professors consider wider political economy issues, otherwise they will jump to dangerous reductionist conclusions from ground-breaking work that has subtle implications.

Yes; and regulators tend to crowd out personal responsibility as those who are regulated get into the habit of thinking 'what are we allowed to do?' rather than 'what would it suit us best to do?' Indeed, regulators have a paternalist attitude: they often genuinely think they are doing the rest of us a favour while actually limiting our options. I wonder if regulators, on average, have fewer children than the average? If so that might help explain why they seem so unwilling to permit, even encourage, trial and error as the most effective way of advancing learning.
The prof. has drawn entirely the wrong lesson from this simple example, seemingly taking a basic Prisoners' Dilemma game and then extrapolating far beyond its relevance. Any number of extensions would undermine his conclusion. 1. This game is zero sum. Voluntary trade, as in a marketplace, benefits both parties. 2. This game is non-cooperative - that is, it is predicated on the idea that parties cannot sign contracts, or make side payments. If these are allowed, much of the problem disappears. 3. This game is not repeated. Repeated Prisoners' Dilemma games often allow players to reach the "Good" outcome with simple cooperative strategies. 4. Social conventions and norms evolve spontaneously to solve such coordination problems. Lots, turns, bidding etc. Allowing many institutions to compete helps find dynamically efficient solutions, rather than imposing a single solution 5. This game has a small number of players competing for a single outcome. In more realistic "matching" models, efficient outcomes are reached. Game Theory, when properly taught, can illustrate all these phenomena. Like anything, it can be misrepresented.
thanks, Bill, for putting this so clearly.
As I recall the scene from the film, I don't even see why cooperation is the solution. The choice was between all the guys approaching the hottest woman, or else approaching different women, right? It seemed to me that at least most of them could individually improve their expected return by passing up on approaching the hottest woman. That strikes me as simply following individual self interest, no cooperation required. Am I misremembering the example?
That is correct, John. However, I think they all had sufficient self-belief that they believed that the best-looking woman would be within their grasp. That is, of course, at least a possible situation, regardless of whether it was realistic in that particular case.
The professor clearly needed to get out more. Groups of men approaching groups of women with a generally successful outcome has been going on forever (else likely there would never have been a professor). The less hot men might take a few repeat lessons to learn their limitations, but repeated failure teaches them in the end. And even in the example, there was no regulator involved. A good job I'd say- the chances of a regulator knowing which man was most fancied by the ladies are remote. Probably the ladies would all have been disappointed in his choice, and they'd have to start again somewhere he couldn't reach. And where did Adam Smith rule out co-operation? I thought he noted that people co-operate whenever it is in their mutual self interest to do so- and warned that people of a given trade often do so at the expense of the public.

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