Week 6: The theory paper in focus this week is the iconic "Electronic mail game" by @arielrubinstein.bsky.social. It is characteristic Rubinstein---communicating a big idea with elegant simplicity. It brought into focus failures of common knowledge, by extension failures in coordination. - ThreadSky

rohitlamba.bsky.social • 16 days ago

Week 6: The theory paper in focus this week is the iconic "Electronic mail game" by @arielrubinstein.bsky.social. It is characteristic Rubinstein---communicating a big idea with elegant simplicity. It brought into focus failures of common knowledge, by extension failures in coordination.

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rohitlamba.bsky.social•16 days ago

In both games below, there are two pure Nash equilibria one of which is Pareto dominant. If players fail to coordinate, then the player who played B gets -L. Thus, it is dangerous for a player to play B unless he is confident enough that his partner is going to play B as well.

rohitlamba.bsky.social•16 days ago

Player 1 knows the exact realization of the game. Without any pre-play communication, you can have two equilibria: (i) P2 plays A, and P1 plays A in both states, with expected payoff (1-p)M; (ii) P2 plays B, and P1 plays B in both states, with expected payoff pM.

rohitlamba.bsky.social•16 days ago

If however, the information about the exact realization of the state could become common knowledge, they could coordinate on (A,A) in state a, and (B,B) on state b, and get a higher payoff of M each.

Let's allow them to communicate through an email system.

rohitlamba.bsky.social•16 days ago

Only if state is b, an email is sent by P1 to P2. If P2 gets the email, a confirmation is sent to P1. If P1 gets confirmation, then a confirmation of the confirmation is sent to P2, and so on. With small probability \epsilon, any of the emails gets lost & communication stops.

rohitlamba.bsky.social•16 days ago

If infinite number of emails are sent, the state becomes common knowledge. However, for any positive, \epsilon, with probability 1, only finite number of messages are sent. Let T_i be number of message sent by player i's computer.

rohitlamba.bsky.social•16 days ago

How should we think about information at the end of the communication phase? If P1's screen reads T1=2. Then it is either the case that P1's second email didn't reach P2 or P2's second email didn't reach P1. So, T2=1 or T2=2.

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