Achieving Risky Coordination in the Electronic Mail Game

The electronic mail game [8] or “email game” is a coordination game with two possible states, a and b. In each state, players are trying to coordinate their actions so that both play A (in a) or B (in b). The first case happens more than half the time, and the second is not only less frequent but also carries a penalty if only one player chooses B. So in the absence of extra information, it makes sense to pick A. However, in the email game, player 1 (and only player 1) has access to the ground truth about whether the state is a or b. Whenever the state is b, player 1 automatically sends a message to player 2, allowing them to try to coordinate on B. Messages have a chance of being dropped, so players send confirmation messages (and confirmations of confirmations) until a message is dropped. Surprisingly, this additional information does not help players coordinate on B: it is a strictly dominant strategy to ignore the messages and always play A. In this paper, we present the proof from [8] which says that coordination on the risky action (B) is impossible. Then we present results from the literature which show how changing assumptions about the email game can get around the impossibility result. Finally, we analyze the email game under an alternative paradigm for reasoning about uncertainty, called possibility measures. This new way of looking at the original email game also sidesteps the impossibility result and allows coordination in the risky case.