Stochastic Reaction Strategies in the Barro-Gordon Framework : Support for a Low Inflation Equilibrium

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 model, we assume that rather than playing a one shot game, the monetary authority and private sector interact with each other repeatedly for an infinite number of times. Both, the monetary authorities'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 classical Non-Nash low inflationary state. In contrast to Barro and Gordon (1983a) we show that the low-inflationary state can be realized as a Nash-equilibrium in our model and in contrast to Barro and Gordon (1983b) we do not rely on punishment strategies, therefore addressing the concerns on credible punishment raised by al-Nowaihi and Levine