Game theory: diner's dilemma

Matthew Lynn at Marketwatch applies game theory to the Greek crisis (link). He first mentions a game of chicken and the diner's dilemma, which I had not heard of until today. Perhaps others have not either. One key point is that each diner doesn't really like the others, and tends to be selfish.

A group of real friends probably wouldn't try to do each other that way. The European union is a bunch of selfish countries that don't really like each other. Many have fought and killed each other, and those bad feelings remain.

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... the “diner’s dilemma.” Ten of us go out for dinner. We split the cost equally. Each of us decides to order the most expensive thing on the menu even though it is only marginally better than the cheapest — because once the extra cost is split 10 ways it is a trivial sum. But if all 10 of us make the same calculation, we end up ordering 10 of the most expensive dishes — and a far more expensive night out than any of us actually wanted.
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Another economic model is the real life problem of the commons. Back in old England, some parcels of land were set aside as common land. The common land was overgrazed, overused and abused, because each sheep herder would overgraze on the common land while preserving their private land.

Yet a third thing to think of is unintended consequences. Markets are not static. Punish or tax certain behaviors, and less of that occurs. Reward, bailout or subsidize certain behaviors and those behaviors tend to multiply. Politicians seem to have a very hard time with second order thinking, or perhaps do know and rely on voters being stupid enough not to think ahead. C'est la vie.

Another game I recently heard about was a crowded bar. In this game optimal is 60% occupancy. People must choose a few days ahead whether to go or not. If more than 60% choose to go, everyone will have a bad time, more than 70% and it will be terrible. If 60% or fewer go, everyone has a good time, less than 50% best time ever. The game theory sets up groups of people that have different algorithms for choosing. A small core group almost always will go. Some tend to go if they had a good time last week, some won't go if they had a bad time last week. Some ask their friends if it was crowded last week and rely on those reports.

Set up a simulation with those factors and the crowd will oscillate around an average of 60%, with many weeks over 70% and a miserable time for all, and many weeks under 50% and a wonderful time for those that went. The analogy to markets is for a particular investment. A good investment that gets too crowded may no longer be a good investment. People tell their friends, or learn from experience.

At one of the many talks at the local Schwab office that I've been attending, one of the presenters says it is always the same. After the stock market has a good up move, a good year, many clients come in and want to be more aggressive. After a down move, a bad year, the opposite, they want to be more conservative. It is close to the model of the crowded bar. When too many people are in it, bad times tend to follow. When a lot of investors leave, good times tend to be ahead.

Investment cycles are rarely as simple and short as one night events at a bar. So more complex models might be added. Some might track the attendance at the crowded bar and only go when there is a certain pattern, such as three crowded weeks in a row, or three sparse weeks in a row. In the stock market, this manifests in the form of those that move in and out based on price moving averages.

A long winded post, but game theory can be a useful way for market participants to do thought experiments to try and think about likely outcomes. Keep in mind, that top analysts are playing the same game, so it is not only trying to figure out what is likely to happen, but what others think is likely to happen, and staying in front of that curve. For example, the U.S. deficit and gold, best time to buy gold in recent memory was when the U.S. had a federal surplus back in 1999. The current trillion dollar deficits are factored into today's price which is up over 500% from the lows.