JOB MARKET PAPER
Collusion with Private Information and Fixed Costs
In this paper, I research the possibility of collusion among price competing firms that try to obtain private information about each other by observing a third party public information (such as media publication, accounting report or the like). Athey and Bagwell (2001, 2008) have shown that collusion among infinitely Bertrand competing firms with asymmetric and unknown marginal costs is possible under proper inter-temporal market sharing agreements between firms. They suggest schemes to implement the first-best outcome that supports a Perfect Public Equilibrium. In my paper, I assume a similar set-up, but also assume that firms pay an avoidable fixed cost of entry in the period they decide to participate in the market. This set-up is widely present across industries such as the airlines industry where firms have to renew their terminal lease agreements every period before competing on price. In line with Athey and Bagwell (2001, 2008), I maintain that in each period firms receive an iid cost shock and are allowed to communicate before making their entry decisions, but to be more consistent with the wider reality present in today’s economy, I do not allow for explicit market sharing agreements. As a result, and unlike Athey and Bagwell (2008), the stage game in this set-up has permanent inefficiencies (Patra, 2015) where either the market is not served with positive probability or the entering firm earns a negative profit with positive probability. But with infinite interaction, the collusive equilibrium (a PPE) presented in my paper develops a strategy to restore market efficiency where the market is always served and the entering firms receives its share of the monopoly profit. Allowing for communication among firms facilitates a self-enforcing collusive agreement among competing firms and I study the value of this communication both from collusion and efficiency perspective. I provide a characterization of the PPE and show that there exists a discount factor strictly less than one for which this equilibrium exists. The conclusion that emerges then is that the presence of the avoidable fixed cost makes it easier for the firms to collude, and market efficiency is achieved in this PPE in the sense that, among the firms who enter, only lowest cost firms produce. A numerical illustration is also provided.
A Model of Bertrand Competition with Unknown Costs
Baye and Kovenock (2008) and several others that establish that, under equal market sharing rule, the existence of pure strategy equilibrium in a standard Bertrand game with avoidable fixed cost is difficult. Saporiti et al (2010) show that an equilibrium with pure strategies is possible when cost functions of firms are not sub-additive. However, when marginal costs are unknown and due to the fundamental discontinuity of the game, Sharkey et al (1993) and Spulber (1993) indicate that the existence of a pure strategy equilibrium is not possible. In my paper, I show that when firms are allowed to monitor each other’s entry decision in the market, pure strategy equilibrium exists. The paper investigates the equilibrium in a dynamic Bertrand duopoly where firms do not know the cost of other firms and firms face an avoidable sunk cost when they decide to enter the market. In this model, firms are allowed to monitor rival's entry decision before making their pricing decision. Firms are also allowed to communicate with each other via announcements before they make the entry decision. I show that there exists two classes of Pure-Strategy Bayesian-Nash equilibria in this game. In one class of equilibrium (symmetric) only the low cost firms enter, and in the other class of equilibrium (asymmetric) only one firm enters while the other (inefficient firms) stay out irrespective of their cost types. This is a new existence result and the paper provides full characterization of the Perfect Bayesian Equilibria. The paper also explores the effect of pre-play communication in the game to see whether this brings cooperation among firms, however, the results indicate that such communication is ‘cheap talk’ and has no effect on the set of equilibria.
WORK IN PROGRESS
Repeated Collusion with Hidden Investment (with Satoshi Fukuda)
Stochastic Utility in Ramsey Model (with Hans Werner van Wyk and V.L. Raju Chinthalapati)
Information Revelation and Collusion in a Bertrand Set up with Unknown Costs (with Rajeev Sooreea) (Work in progress)
1. Statistical Fluctuations Along the Lennard-Jones Melting Curve (with David Heyes) (Accepted for publication at Computational Methods in Science and Technology, December 2015)
WORK IN PROGRESS
1. A Model of Hybrid Dynamic Beam Movements with Specific Application to Wind Mills (with David L. Russell and David Heyes)