Collusion when players take turns

Traditional collusion models typically assume that players coordinatetheir actions actively during the competition process to influence the outcomes.In contrast, we consider a repeated interaction setting betweentwo players where collusion occurs through well-defined strategies: theplayers take turns, with one holding monopoly power while the other eitherrefrains from participating or behaves as if absent. We provide afull characterization of when taking turns constitutes a subgame perfectNash equilibrium in repeated games. By allowing players to discount timedifferently, we uncover a novel, non-monotonic condition on the discountfactor that sustains collusion. We apply our findings to three specificcontexts: contests, duopoly, and political competition.