Coordination and Signal Design: The Electronic Mail Game in Asymmetric and Multiplayer Settings

We examine the nature of the coordination failure in Rubinstein’s Electronic Mail Game, a classic game-theoretic paradox in which parties are unable to coordinate on a mutually beneficial action, and we propose a principle for designing more successful signaling protocols. When signaling technology is such that signals fail to reach their destination with small probability, it is important that the signaling protocol be designed so that when there is signal failure, the parties largely agree on where the failure took place. This agreement over information in turn allows the parties to coordinate their actions. To illustrate this principle, we show that if one party is able to send a stronger signal than the other, the asymmetry leads to agreement over the source of signal failure, and hence permits coordination. We then extend the model to multiplayer settings. If a central party is communicating separately with multiple parties, or if a central party is communicating with a group via correlated signals, an asymmetry in signal strength arises naturally from the many-to-one nature of the model and the coordination problem is again resolved.