Pre-play Communication and Credibility: A Test of Aumann's Conjecture

Abstract

The effectiveness of pre-play communication in achieving efficient outcomes has long been a subject of controversy. In some environments, cheap talk may help to achieve coordination. However, Aumann conjectures that, in a variant of the Stag Hunt game, a signal for efficient play is not self-enforcing and concludes that an agreement to play [the efficient outcome] conveys no information about what the players will do. Harsanyi and Selten (1988) cite this example as an illustration of risk-dominance vs. payoff-dominance. Farrell and Rabin (1996) agree with the logic, but suspect that cheap talk will nonetheless achieve efficiency. The conjecture is tested with one-way communication. When the sender first chooses a signal and then an action, there is impressive coordination: a 94% probability for the potentially efficient (but risky) play, given a signal for efficient play. Without communication, efforts to achieve efficiency were unsuccessful, as the proportion of B moves is only 35%. I also test a hypothesis that the order of the action and the signal affects the results, finding that the decision order is indeed important. Aumann's conjecture is rejected when the signal is determined prior to the action. However, the signal's credibility diminishes when the sender is known to have first chosen an action, supporting the conjecture, as the results are not statistically distinguishable from those in the no signal case. Some applications and issues in communication and coordination are discussed.