Nash vs. coarse correlation

We run a laboratory experiment with a two-person game with unique pure Nash equilibrium which is also the solution of the iterative elimination of strictly dominated strategies. The subjects are asked to commit to a device that randomly picks one of three symmetric outcomes in this game (including the Nash equilibrium) with higher ex-ante expected payoff than the pure Nash equilibrium payoff. We find that the subjects do not accept this lottery (which is a coarse correlated equilibrium as in Moulin and Vial, 1978), instead, they choose to play the game and then coordinate on the pure Nash equilibrium. However, given an individual choice between a lottery with equal probabilities of the same outcomes and the sure payoff as in the Nash equilibrium, the lottery is chosen by the individuals. The result is robust against variations like (i) a lottery choice for a pair of individuals, (ii) different payoffs in the game and (iii) the fixed-match between pairs.