NON-COOPERATIVE STRATEGIES FOR DYNAMIC POLICY GAMES AND THE PROBLEM OF TIME INCONSISTENCY

Abstract

COMPETITION between decision makers is often characterised in economics as a noncooperative game. But when the decisions of a finite number of agents are linked over time in a multiperiod problem, as typically happens in policy models or market models of disequilibrium behaviour, the conventional solutions become dynamically inconsistent because they fail to allow for the noncausal effects, on current decisions, of rational expectations of the endogenised future choices. This has left the economist with the problem of determining what decision rule is best, and the decision maker with the problem of how to justify actions which are predictably inconsistent dynamically as well as suboptimal (Buiter (1981)). Many of the controversies of economic theory have been concerned with the behaviour of a small number of self-interested decision makers, or with economic behaviour when the assumptions of perfect competition are not appropriate. For example, Keynesian demand analysis recognises that government action can systematically influence the income level; but the monetarists doubt this, at least for the long term. The Philips curve suggests that organised labour may be able to influence the wage-unemployment trade-off; and so on. Then collective bargaining, international trade policy, or oligopolistic firms, provide further examples.' But the literature has yet to provide a detailed structural analysis of the optimal strategies for such dynamic policy games. This paper derives the optimal strategies for a two player nonzero sum dynamic game. Starr and Ho (1969) have used numerical examples to show that conventional recursive optimisation techniques (e.g. dynamic programming) can produce suboptimal decisions. By using a different optimisation method we find that dynamic programming generally produces suboptimal decisions because this kind of constrained optimisation problem lacks the time-recursive structure necessary for recursive optimisations. Hence the 'noncausal' effects (defined below, in Section 5.2) are ignored. These results are used to assess the impacts of the associated suboptimality on competitive decisions. It appears that strategies which ignore noncausal effects can be inferior even to those which ignore the game or misspecify the equilibrium conditions.