Pre-play communication and coordination in two-player games

The main result of this paper is that any correlated equlibrium pay-off of a two-player completeinformation game with rational parameters can be reached through an unmediated costlesspre-play conversation scheme. This problem was left open by Barany and Forges' analysis. Ourcommunication protocol does not rely on external mediators of any kind. It is also self-enforcing(in the sense that no player has an incentive to deviate if the other does not) and quasi-sure (inthe sense that a 'deviation from the rules' of a player can be detected by the other with aprobability as close as one as we want). Coordination failures that may arise in many economicsituations are solved by applying our pre-play communication scheme.