8 - An experimental test of the consistent-conjectures hypothesis

Summary

A common way of analyzing multiperiod oligopoly models without dynamic interactions in the payoff structure is to compute a Nash equilibrium for each period taken separately. Many economists believe that behavior in a repeated market game cannot be predicted accurately with a period-by-period sequence of such “static” Nash equilibria, but an explicitly dynamic analysis can be extremely difficult unless the class of feasible dynamic strategies is restricted.

There is an embarrassing multiplicity of alternative oligopoly “solutions” that are computationally less complex than game-theoretic approaches to multiperiod games. Many of these alternative solutions can be classified as conjectural variations models in which firms are assumed to conjecture that changes in their own decisions will induce reactions by other firms. These reactions are typically assumed to be characterized by functions that are locally linear. Almost any configuration of decisions can be an equilibrium for some conjectured reaction functions, so these models have little empirical content unless the reaction functions themselves are determined endogenously.

Timothy Bresnahan (1981) has proposed a consistency condition that can often be used to determine specific conjectured reactions. Martin Perry provides a clear explanation of this consistency condition in the context of a duopoly in which firms' decisions are output quantities:

Each firm's first-order condition defines its profit-maximizing output as a reaction function on (1) the output of the other firm and (2) the conjectural variation about the other firm's response. Thus a conjectural variation by one firm about the other firm's response is consistent if it is equivalent to the derivative of the other firm's reaction function with respect to the first firm's output at equilibrium.

[1982, p. 197]