We study the interaction of multiple large economies in dynamic stochastic general equilibrium. Each economy has a monetary policymaker that attempts to control the economy through the use of a linear nominal interest rate feedback rule. We show how the determinacy of worldwide equilibrium depends on the joint behavior of policymakers worldwide. We also show how indeterminacy exposes all economies to endogenous volatility, even ones where monetary policy may be judged appropriate from a closed economy perspective. We construct and discuss two quantitative cases. In the 1970s, worldwide equilibrium was characterized by a two-dimensional indeterminacy, despite U.S. adherence to a version of the Taylor principle. In the last 15 years, worldwide equilibrium was still characterized by a one-dimensional indeterminacy, leaving all economies exposed to endogenous volatility. Our analysis provides a rationale for a type of international policy coordination, and the gains to coordination in the sense of avoiding indeterminacy may be large.