The aftermath of the Global financial crisis has seen two types of monetary policy concerns. Some economists (e.g. Paul Krugman) worry primarily about possible deflation caused by a secular stagnation. In contrast, others (e.g. John Taylor) worry about excessively high inflation caused by quantitative easing and monetization of fiscal imbalances. We show that some countries should fear both - deflation in the short term and high inflation in the long term - whereas some countries are unlikely to experience either. This is done in a game theoretic framework with dynamic leadership (stochastic revisions of actions). Such framework enables us to examine strategic monetary-fiscal interactions as well as policymakers' incomplete information about the economic recovery (such as during 2010-2014). Our empirical section then quantifies indices of monetary and fiscal leadership for high-income countries to assess their deflationary/inflationary prospects. It is shown, for example, that undesirable departures from price stability, both in the short term and long term, are much more likely in the United States and Japan than in Australia or New Zealand.