Rational coordination with no communication or conventions

Coordination games ([16]) are games in strategic form with several pure strategy Nash equilibria with the same or comparable payoffs for every player. In these games, all players have the mutual interest to select one of these equilibria. In pure coordination games ([16]), aka games of common payoffs ([17]), all players in the game receive the same payoffs and thus the players have fully aligned preferences to coordinate with each other in order to reach the best possible outcome for everyone. In this paper we study one-step pure winlose coordination games (WLC games) in which all payoffs are either 1 (i.e., win) or 0 (i.e., lose). Clearly, if players can communicate when playing a pure coordination game with at least one winning outcome, then they can simply agree on a winning strategy profile, so the game is trivialised.