Philip LaPorte
mathematics phd candidate, uc berkeley
From simultaneous to leader-follower play in direct reciprocity
URL: https://academic.oup.com/pnasnexus/advance-article/doi/10.1093/pnasnexus/pgag005/8425146
Summary
In a basic repeated game, two players choose actions simultaneously in a sequence of rounds. When one player is forced to move first within each round, several interesting things happen. First, the possible payoff outcomes of the game simplify in a satisfying way. This allows one to analyze which Nash equilibria of the original game are still Nash in the new one. Indeed, this is an effective way to find equilibria in the first place. Second, one finds that simple equilibria, like cooperative memory-1 strategies, remain stable under modifications to simultaneity. More complicated ones may not.
Some people may find this paper useful purely as a reference sheet for memory-1 Nash equilibria in 2x2 games with discounting. (We describe the important classes of symmetric Nash equilibria. Note that pairing two such strategies from the same class, e.g. two different conditional cooperators, also yields asymmetric Nash equilibria.)