Stylised models of the policy game between monetary policy makers and the private sector have suggested that discretionary policy regimes suffer from an inherent inflationary bias and that pre-commitment to a target rate of inflation may be desirable. This paper shows that in the presence of labour unions, the monetary policy game can lead to radically different results: a central bank that is completely indifferent to the level of inflation may obtain outcomes with high employment rates and zero inflation while 'prudent', inflation-averse, central banks generate stagflation with positive inflation and low rates of employment