Global games of regime change-coordination games of incomplete information in which a status quo is abandoned once a sufficiently large fraction of agents attack ithave been used to study crises phenomena such as currency attacks, bank runs, debt crises, and political change. We extend the static benchmark examined in the literature by allowing agents to take actions in many periods and to learn about the underlying fundamentals over time. We first provide a simple recursive algorithm for the characterization of monotone equilibria. We then show how the interaction of the knowledge that the regime survived past attacks with the arrival of information over time, or with changes in fundamentals, leads to interesting equilibrium properties. First, multiplicity may obtain under the same conditions on exogenous information that guarantee uniqueness in the static benchmark. Second, fundamentals may predict the eventual fate of the regime but not the timing or the number of attacks. Finally, equilibrium dynamics can alternate between phases of tranquility-where no attack is possible-and phases of distress-where a large attack can occur-even without changes in fundamentals.

This section shows that the equilibrium of the action game in section 1 of the main text is unique.It does that by adapting an argument first made Angeletos and Pavan (2007, propositions 1 and 3) to our environment. The idea of the proof is that there is a social planner problem such that every equilibrium of our model is also a solution to this planning problem. The planning problem is strictly convex, meaning that it has a unique minimum. Since the planning problem has a unique solution and every equilibrium is a solution to the planning problem, the equilibrium of the model must be unique.We begin by setting up some notation for the proof. We letp (·) denote the candidate equilibrium function characterized by equation (4) in the main text, and will make use of the fact that s = b ω. We let F (ω) denote the prior distribution of ω, with density f (ω). We let µ denote the distribution of the agents' information choices, and φ (Xz|ω) the distribution of observed signals, conditional on the state ω. Together, µ and φ determine the distribution F (I|ω)of information sets I = (χ, Xz), conditional on the state ω. The agents' posterior beliefs conditional on I are defined by the pdfφ.Proposition 1 Let P denote the set of functions p for which

This paper introduces signaling in a global game so as to examine the informational role of policy in coordination environments such as currency crises and bank runs. While exogenous asymmetric information has been shown to select a unique equilibrium, we show that the endogenous information generated by policy interventions leads to multiple equilibria. The policy maker is thus trapped into aWe are grateful to the editor, Nancy Stokey, and two anonymous referees for suggestions that greatly helped us improve the paper. For comments we thank

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