Speculative Attacks with Multiple Targets

This paper examines a global games model of speculative attacks in which speculators can choose to attack any one of a number of targets. In the canonical global games model with a single target, it is well known that there exists a unique equilibrium that survives the iterative deletion of dominated strategies, characterized by the threshold values of the private signal and the fundamentals. This paper shows that with two targets, iterative deletion of dominated strategies yields a unique combination of threshold signal functions that are nondecreasing in the private signals of the other target's fundamentals, and threshold fundamentals functions that are increasing in the other target's fundamentals. The result is shown to extend to environments with any N symmetric targets. The key argument is to combine the iterative deletion procedure with the contraction mapping theorem. The paper then goes through a number of numerical examples and shows, among other results, that more accurate private signals have a decoupling effect on the outcomes of attack on different countries. Finally, this paper introduces public information and shows that the sufficient condition for unique equilibrium threshold functions is very similar to that for a unique equilibrium in the single-target model.