On rational expectations and dynamic games

We consider the problem of uniting dynamic game theory and the rational expectations hypothesis. In doing so we examine the current trend in macroeconomic literature towards the use of dominant player games and offer an alternative game solution that seems more compatible with the rational expectations hypothesis. Our analysis is undertaken in the context of a simple deterministic macroeconomy. Wage setters are the agents in the economy and are playing a non-cooperative game with the Fed. The game is played with the wage setters selecting a nominal wage based on their expectation of the money supply, and the Fed selecta the money supply based on its expectation of the nominal wage.

We find it is incorrect to use the rational expectations hypothesis in conjunction with the assumption that wage setters take the Fed's choices as an exogenous uncontrollable forcing process. We then postulate the use of a Nash equilibrium in which players have rational expectations. This results in an equilibrium that has Stackleberg properties. The nature of the solution is driven by the fact that the wage setter's reaction function is a level maximal set that covers all possible choices of the Fed.

One of the largest problems we encountered in applying rational expectations to a dynamic game is the interdependence of the players' expectations. This problem raises two interesting but as yet unresolved questions regarding the expectations structures of agents: whether an endogenous expectations structure will yield rational expectations; and can endogenous expectations be completely modelled.

In addition to the questions mentioned above we also show that the time inconsistency problem comes from either misspecifying the constraints on the policy maker or an inconsistency in interpreting those constraints. We also show that the Lucas critique holds in a game setting and how the critique relates to the reaction functions of players.