As noted before, I’ve never understood a lot of the attraction behind game theory. In particular, I’ve never heard a convincing argument for why Nash equilibria should be considered especially interesting. The only argument I know of for choosing your side of a Nas equilibria in a one-shot game involves assuming, while deciding what to do, that the other guy knows what decision you will make. This doesn’t even make sense as an idealisation. There’s a better chance of defending the importance of Nash equilibria in repeated games, and I think this is what evolutionary game theorists make a living from. But even there it doesn’t make a lot of sense. In the most famous game of all, Prisoner’s Dilemma, we know that the best strategy in repeated games is __not__ to choose the equilbrium option, but instead to uphold mutual cooperation for as long as possible.

The only time Nash equilibria even look like being important is in repeated zero-sum games. In that case I can almost understand the argument for choosing an equilibrium option. (At least, I can see why that’s a not altogether ridiculous heuristic.) One of the many benefits of the existence of professional sports is that we get a large sample of repeated zero-sum games. And in one relatively easy to model game, penalty kicks, it turns out players really do act like they are playing their side of the equilibrium position, even in surprising ways.

bq. Testing Mixed Strategy Equilibria When Players Are Heterogeneous: The Case of Penalty Kicks in Soccer (P.A. Chiappori, S. Levitt, T. Groseclose). (paper, tables) (Hat tip: Tangotiger)

Some of you will have seen this before, because it was published in __American Economic Review__, but I think it will be news to enough people to post here. The results are interesting, but mostly I’m just jealous that those guys got to spend research time talking to footballers and watching game video. I haven’t heard any work that sounded less like research since I heard about that UC Davis prof whose research consists in part of making porn movies.