Gradual Guaranteed Coordination in Repeated Win-Lose Coordination Games

We investigate repeated win-lose coordination games and analyse when and how rational players can guarantee eventual coordination in such games. Our study involves both the setting with a protocol shared in advance as well as the scenario without an agreed protocol. In both cases, we focus on the case without any communication amongst the players once the particular game to be played has been revealed to them. We identify classes of coordination games in which coordination cannot be guaranteed in a single round, but can eventually be achieved in several rounds by following suitable coordination protocols. In particular, we study coordination using protocols invariant under structural symmetries of games under some natural assumptions, such as: priority hierarchies amongst players, different patience thresholds, use of focal groups, and gradual coordination by contact.