On the Equivalence of Synchronous Coordination Game and Asynchronous Coordination Design

Abstract: This paper establishes the equivalence between synchronous and asynchronous coordination mechanisms in dynamic games with strategic complementarities and common interests. Synchronous coordination, characterized by simultaneous commitments, and asynchronous coordination, defined by sequential action timing, are both prevalent in economic contexts such as crowdfunding and fund management. We introduce Monotone Subgame Perfect Nash Equilibrium, MSPNE, to analyze least favorable equilibrium outcomes. We provide a recursive characterization for synchronous coordination and a graph-theoretic representation for asynchronous coordination, demonstrating their equivalence in terms of the greatest implementable outcome. Our results show that the structure of commitment, whether simultaneous or sequential, does not affect the achievable welfare outcome under certain conditions. Additionally, we discuss computational aspects, highlighting the general NP-Hardness of the problem but identifying a significant class of games that are computationally tractable. These findings offer valuable insights for the optimal design of coordination mechanisms.