We develop a simple game-theoretic model to determine the consequences of explicitly including financial market stability in the central bank objective function, when policymakers and the financial market are strategic players, and market stability is negatively affected by policy surprises. We find that inclusion of financial sector stability among the policy objectives can induce an inefficiency, whereby market anticipation of policymakers’ goals biases investment choices. When the central bank has private information about its policy intentions, the equilibrium communication is vague, because fully informative communication is not credible. The appointment of a “kitish” central banker, who puts little weight on market stability, reduces these inefficiencies. If interactions are repeated, communication transparency and overall efficiency can be improved if the central bank punishes any abuse of market power by withholding forward guidance. At the same time, repeated interaction also opens the doors to collusion between large investors, with uncertain welfare consequences.