“Achieving Intertemporal Rent-Sharing and Symmetry through Intratemporal Asymmetry: A Game-Theoretic Analysis of Turn Taking” by Sau-Him Paul LAU
Sau-Him Paul LAU
University of Hong Kong
Turn taking behavior is observed in many field and experimental settings. This paper develops a model to study when and how turn taking can be supported as an equilibrium intertemporal rent-sharing mechanism. Incorporating essential elements of various examples of turn taking, we study a class of symmetric two-by-two infinite-horizon repeated games, in which the players choose between Tough and Soft each period, and the two asymmetric outcomes (Tough, Soft) and (Soft, Tough) yield the highest total payoff for the players in the stage game. We determine conditions under which turn taking can be supported as equilibrium when both players use a strategy that we describe as Turn Taking with Independent Randomization (TTIR). This strategy guarantees that the players get equal treatment ex ante. We show that when the two asymmetric outcomes are Nash equilibria in the stage game, a unique TTIR subgame perfect equilibrium exists for all discount factors between 0 and 1. For the case in which the two asymmetric outcomes are not Nash equilibira, we characterize the critical discount factor δ∏such that a unique TTIR subgame perfect equilibrium exists for all discount factors above δ∏. We also show that δ∏is increasing in the "degree of distributional conflict" and decreasing in the "efficiency gain from succeeding in achieving (any one of) the asymmetric outcomes" in the stage game.