Dynamic coordination with individual learning

Abstract

We study how the presence of multiple participation opportunities coupled with individual learning about payoffs affects the ability of agents to coordinate efficiently in global coordination games. Two players face the option to invest irreversibly in a project in one of many rounds. The project succeeds if some underlying state variable θ is positive and both players invest, possibly asynchronously. In each round they receive informative private signals about θ, and asymptotically learn the true value of θ. Players choose in each period whether to invest or to wait for more precise information about θ.We show that with sufficiently many rounds, both players invest with arbitrarily high probability whenever investment is socially efficient, and delays in investment disappear when signals are precise. This result stands in sharp contrast to the usual static global game outcome in which players coordinate on the risk-dominant action. We provide a foundation for these results in terms of higher order beliefs. * We thank

Strategic Delay in Global Games

“…The papers most closely related to this one are Ková^and Steiner (2013), Dasgupta (2007), and Dasgupta, Stewart, and Steiner (2012). Both Dasgupta and Ková^and Steiner focus on a continuum of agents and treat a single coordination-sensitive investment decision which may be delayed until or (for Ková^and Steiner only) reversed after the arrival of new information.…”

“…Finally, Dasgupta, Stewart, and Steiner (2012) also consider a setting with two agents, and an irreversible coordination-sensitive investment decision that can be delayed. There are several key differences: a decision can be delayed up to T times (with the sharpest results coming as T !…”

Multi-agent sequential hypothesis testing

“…The existing literature on this subject focuses on analysis in terms of high-order beliefs [11] and global games [12], whereas our work presents methods of multiagent sequential learning that neither require approximate common/higher-order beliefs nor restrict game environments. …”

Coordination, timing and common knowledge

“…There has been little formal analysis of higher order beliefs and timing in economics. An important exception is Dasgupta, Steiner, and Stewart (2012) who study how relaxing the need for perfect synchronicity in action choices weakens the nature of the approximate common knowledge of timing required for coordination. This connection between higher order knowledge and timing has been extensively studied in the computer science literature; see Halpern and Moses (1990), chapter 8 of Fagin, Halpern, Moses, and Vardi (1995) and references therein.…”

“…This connection between higher order knowledge and timing has been extensively studied in the computer science literature; see Halpern and Moses (1990), chapter 8 of Fagin, Halpern, Moses, and Vardi (1995) and references therein. Recent work in the computer science literature, Ben-Zvi and and Gonczarowski and Moses (2013), like Dasgupta, Steiner, and Stewart (2012), examines how changing the degree of synchronicity of coordination required changes the higher order knowledge requirements. 5 6 The formal model is presented in Section 2.…”