Measuring agents' reaction to private and public information in games with strategic complementarities

In games with strategic complementarities, public information about the state of the world has a larger impact on equilibrium actions than private information of the same precision, because the former is more informative about the likely behavior of others. This may lead to welfare-reducing 'overreactions' to public signals. We present an experiment based on a game of Morris and Shin (2002), in which agents' optimal actions are a weighted average of the fundamental state and their expectations of other agents' actions. We measure the responses to public and private signals and find that, on average, subjects put a larger weight on the public signal. However, the weight is smaller than in equilibrium and closer to level-2 reasoning. Stated second order beliefs indicate that subjects underestimate the information contained in public signals about other players' beliefs, but this can account only for a part of the observed deviation of behavior from equilibrium. In the extreme case of a pure coordination game, subjects still use their private signals, preventing full coordination. Reconsidering the welfare effects of public and private information theoretically, we find for level-2 reasoning that increasing precision of public signals always raises expected welfare, while increasing precision of private signals may reduce expected welfare if coordination is socially desirable.