Firm Learning and Market Equilibrium.

• Author: Pakes, Ariel

One goal of the field of industrial organization is to predict the response of markets to environmental or policy changes. A market, for our purposes, is a collection of firms that produce and sell competing products or services. Since the consequence of, say, a price change by a given firm depends on the prices of competing firms, realism requires analyzing these changes in the interacting agent frameworks supplied to us by our game theory colleagues. If a firm had set a profit maximizing price before an environmental change, that price was unlikely to be optimal after, say, a tariff or merger induced a price change by a competitor. It is important to take account of the price adjustments that followed the initial price change.

An explicit model of firm behavior might let the price change by firm A lead to a response by firm B, which would lead to a further price change from firm A, and so on. Rather than following this modelling strategy, a substantial body of applied work focuses on finding the Nash equilibrium after an environmental change. There is an intuitive appeal to proceeding in this way. Sticking with the pricing example, in a Nash equilibrium each firm's price maximizes its own profits given the prices of every other firm. So as long as firms are trying to maximize profits, the Nash equilibrium will constitute a "rest point" to any model of how the responses to the change actually occur. In a Nash equilibrium, no firm has an incentive to change its price (to "deviate"), and away from such an equilibrium at least one firm has an incentive to change its price, so further changes are likely to occur.

My research, spanning several decades, has focused on the use of the Nash equilibrium concept in empirical research and the estimation of demand and production functions that are key inputs to firm behavior. Early contributions on estimating demand functions with Steven Berry and James Levinsohn, (1) on estimating production functions with G. Steven Olley, (2) and on the use of Nash equilibrium in dynamic contexts with Richard Ericson, (3) led to shifts in the paradigms used to analyze price and productivity responses to environmental change. However, when the concept of Nash equilibrium was extended to analyze investment responses, the cognitive requirements of both agents and researchers seemed unrealistic. (4) This led Chaim Fershtman and me to consider how firms learn to achieve their goals. (5)

Understanding the learning process has two further advantages. First, it takes time to get from one equilibrium to another, and if we only analyze equilibria, we give up on investigating how long that takes and what is likely to happen in the interim. There is also a more subde point: In many situations there can be more than one Nash equilibrium. If firm A chooses x it may well be an equilibrium for firm B to choose x', while if firm A had chosen y which differs from x, we would expect that firm B's equilibrium response would differ from x'. Since the different equilibria can have different properties, this not only impacts our ability to predict the implications of a given...