Policy Rule Nash Equilibria

We study how different types of instrument rules affect the outcome of a monetary policy game between the central bank and the private sector. Policy rules can be independent of output and a shock, functions of the shock, or functions of output. We rank the Nash equilibria generated by different types of policy rules according to the central bank's ex ante expected loss. If both players can condition on output, then the following is true: no equilibrium exists if the central bank cares much about output stability and little about price stability, and infinitely many equilibria exist otherwise