This paper provides recursive methods for analyzing the credible equilibria of an incomplete information monetary policy game. The policy game is one in which a discretionary government has a short-run temptation to engage in a surprise monetary expansion. It also has the opportunity to imitate a government that always implements the ex ante optimal monetary policy actions. We derive an algorithm for computing the set of credible equilibrium payoffs. We use this algorithm to explore the idea that incomplete information monetary policy games of this kind have fewer equilibria and less indeterminacy than their complete information counterparts.