Stochastic Reaction Strategies and a Zero Inflation Equilibrium in a Barro-Gordon Model

We study a game theoretic model of the conflict which arises between a monetary authority and the private sector with regard to the inflation-rate. Building on the simple static Barro and Gordon (Barro and Gordon, 1983a) model we assume that rather than playing a one shot game the monetary authority and private sector react to each other repeatedly for an infinite number of times. Both, the monetary authority's and the private sector's reactions are assumed to be stochastic in the form of fixed behavioral transition probabilities. These probabilities are interpreted as strategies in a new game. We study the set of Nash-equilibira of this new game and how these correspond to the classical discretionary Nash-equilibrium identified by Barro and Gordon as well as the non-Nash low inflationary state. In contrast to Barro and Gordon we show that the low-inflationary state can be realized as a Nash-equilibrium in our model.