"Need to Know" Versus "Spread the Word": Collective Action in the Multi-Player Electronic Mail Game

As shown by Rubinstein (1989, AER), in the two-player electronic mail game,
players are better off if the extent to which they can check each other’s information, check each other’s information about each other’s information, etc., is limited. This paper investigates to what extent this result extends to the multi-player electronic mail game. It is shown that, contrary to the two-player game, the multi-player game has a plethora of equilibria. If players play inefficient equilibria where they require a specific communication network to be established in order to achieve collective action, then Rubinstein’s results extend. However, contrary to the two-player game, the multi-player game also has equilibria where players find many alternative communication networks sufficient to undertake collective action. If players play such equilibria, then contrary to what is the case in the two-player electronic mail game they can become better off with more information.