Three is a crowd – inefficient communication in the multi-player electronic mail game

In a two-player stag hunt with asymmetric information, players may lock each other into requiring a large number of confirmations and confirmations of confirmations from one another before eventually acting. This intuition has been formalized in the electronic mail game (EMG). The literature provides extensions on the EMG that eliminate inefficient equilibria, suggesting that no formal rules are needed to prevent players from playing inefficiently. The present paper investigates whether these results extend to the multi-player EMG. We show that standard equilibrium refinements cannot eliminate inefficient equilibria. While two players are predicted to play efficiently, many players need formal rules telling them when who talks to whom.