Coordination via correlation: an experimental study

We report on an experiment exploring whether and how subjects may learn to use a correlation device to coordinate on a correlated equilibrium of the Battle of the Sexes game which Pareto dominates the mixed-strategy Nash equilibrium of that game. We consider a direct correlation device with messages phrased in terms of players’ actions as well as an indirect device with a priori meaningless messages. According to the revelation principle, it does not matter whether the correlation device is direct or indirect so long as it implements a correlated equilibrium. However, we find that subjects had an easier time coordinating on the efficient correlated equilibrium with a direct rather than an indirect device. Nevertheless, subjects were able to learn to use the indirect device to better coordinate their play. We further find that, when paired with a fixed partner, subjects utilized history-contingent strategies (e.g., “alternation”) as a coordinating device and were more likely to ignore the correlation device in this setting; the fixed-matching protocol can thus serve as a substitute for a correlation device in achieving an efficient coordination outcome.