Economics of football penalty shots
A soccer penalty is a good example of a situation where two choices made at the same time determine each other’s success or failure. Since the ball moves so fast, the goalkeeper has to move as soon as the striker moves. If a striker is likely to shoot to the left, it is in the goalie’s interest to move in that direction. But if the goalie is going to do that, then it is in the striker’s interest to shoot to the right, and so on.
It can be shown mathematically that the optimum for both players is to choose the left, right or centre unpredictably. Two studies by economists compare the behaviour of real professional football players to this ideal behaviour identified by economic theory, and find a good approximation. In other words the football players are doing good intuitive economics.
Look it up: I. Palacios-Huerta (2003) “Professionals Play Minimax” Review of Economic Studies, 70, pp. 395-415.
P.-A. Chiappori, S. Levitt, and T. Groseclose (2002) “Testing Mixed-Strategy Equilibria When Players Are Heterogeneous: The Case of Penalty Kicks in Soccer” The American Economic Review, vol. 92 no. 4, pp. 1138-1151.
Found via Tim Harford’s “Dear Economist” column in the Financial Times.