Sunk Costs Entry And Exit In Dynamic Oligopoly

This paper develops a dynamic econometric framework for the analysis of entry, exit, and competitive conduct in oligopolistic markets. This framework only requires panel data on the demand and producer counts of geographically dispersed markets over time. It is a dynamic extension of Bresnahan and Reiss's (1990, 1991) framework for the analysis of static competition in a cross-section of markets. Our extension to the infinite-horizon model facilitates the empirical analysis of the dynamic determinants of market structure and competition: sunk entry costs and uncertainty. Moreover, it is needed for the consistent measurement of static market primitives, such as the toughness of competition. Our model's timing and expectation assumptions help to select an essentially unique Markov-perfect equilibrium that can be computed quickly by solving a finite sequence of dynamic programming problems with low-dimensional state spaces. We apply our model to the empirical re-analysis of sunk costs and the toughness of competition in the US market for dental services, using Bresnahan and Reiss's (1993) panel data on the number of dentists across geographical markets in the US.

Most of the theoretical work on collusion and price wars assumes identical firms and an unchanging environment, assumptions which are at odds with what we know about most industries. Further that literature focuses on the impact of collusion on prices. Whether an industry can support collusion also effects investment incentives and hence the variety, cost, and quality of the products marketed. We provide a collusive framework with heterogeneity among firms, investment, entry, and exit. It is a symmetric information model in which it is hard to sustain collusion when either one of the firms does not keep up with the advances of its competitors, or a low quality' entrant enters. In either case there will be an active firm that is quite likely to exit after it deviates, but if one of the competitors is near an exit state the other incumbent(s) has an incentive to price predatorily (that is to deviate themselves). We use numerical analysis to compare an institutional structure that allows for collusion to one which does not (perhaps because of an active antitrust authority). Price paths clearly differ in the two environments; in particular only the collusive industry generates price wars. The collusive industry offers both more and higher quality products to consumers, albeit often at a higher price. The positive effect of collusion on the variety and quality of products marketed more than compensates consumers for the negative effect of collusive prices, so that consumer surplus is larger in the collusive environment.

This paper extends the static analysis of oligopoly structure into an infinite-horizon setting with sunk costs and demand uncertainty. The observation that exit rates decline with firm age motivates the assumption of last-in first-out dynamics: An entrant expects to produce no longer than any incumbent. This selects an essentially unique Markov-perfect equilibrium. With mild restrictions on the demand shocks, sequences of thresholds describe firms' equilibrium entry and survival decisions. Bresnahan and Reiss's (1993) empirical analysis of oligopolists' entry and exit assumes that such thresholds govern the evolution of the number of competitors. Our analysis provides an infinite-horizon game-theoretic foundation for that structure.

We investigate the relationship between competition and innovation using a dynamic oligopoly model that endogenizes both the long-run innovation rate and market structure. We use the model to examine how various determinants of competition, such as product substitutability, entry costs, and innovation spillovers, affect firms' equilibrium strategies for entry, exit, and investment in product quality. We find an inverted-U relationship between product substitutability and innovation: the returns to innovation initially rise for all firms but eventually, as the market approaches a winner-take-all environment, laggards have few profit scraps to fight over and give up pursuit of the leader, knowing he will defend his lead. The increasing portion of the inverted-U reflects changes in firm's investment policy functions, whereas the decreasing portion arises from the industry transiting to states with fewer firms and wider quality gaps. Allowing market structure to be endogenous yields different results compared to extant work that fixes the market structure.

This paper studies the contribution of demand, costs, and strategic factors to the adoption of hub-and-spoke networks in the US airline industry. Our results are based on the estimation of a dynamic oligopoly game of network competition using data from the Airline Origin and Destination Survey with information on quantities, prices, and entry and exit decisions for every airline company in the routes between the 55 largest US cities. As methodological contributions of the paper, we propose and apply a method to reduce the dimension of the state space in dynamic games, and a procedure to deal with the problem of multiple equilibria when implementing counterfactual experiments. Our empirical results show that the most important factor to explain the adoption of hub-and-spoke networks is that the sunk cost of entry in a route declines importantly with the number of cities that the airline connects from the origin and destination airports of the route. For some carriers, the entry deterrence motive is the second most important factor to explain hub-and-spoke networks.

An infinite-horizon, stochastic model of entry and exit with sunk costs and imperfect competition is constructed. Simple examples provide insights into: (1) the relationship between sunk costs and industry concentration, (2) entry when current profits are negative, and (3) the relationship between entry and the length of the product cycle. A subgame perfect Nash equilibrium for the general dynamic stochastic game is shown to exist as a limit of finite-horizon equilibria. This equilibrium has a relatively simple structure characterized by two numbers per finite history. Under very general conditions, it tends to exhibit excessive entry and insufficient exit relative to a social optimum.

This paper presents an estimable dynamic structural model of an oligopoly retail industry. The model can be estimated using panel data of local retail markets with information on new entries, exits and the size and growth of incumbent firms. In our model, retail firms are vertically and horizontally differentiated, compete in prices, make investments to improve the quality of their businesses, and decide to exit or to continue in the market. The model extends in two important ways the entry-exit model estimated in Aguirregabiria and Mira (2007). First, it includes firm size and growth as endogenous variables. And second, the empirical model has two sources of permanent unobserved heterogeneity: local-market heterogeneity and firm heterogeneity. This allows the researcher to control for potentially important sources of bias when using firm panel data with many local markets and several time periods.