Essays on collusion with capacity constrained firms

Emmanuel Dechenaux, Purdue University

Abstract

The purpose of this dissertation is to analyze tacit collusion in infinitely repeated price-setting games with capacity constrained firms. The dissertation is comprised of three related essays. The first essay contributes to the literature on optimal penal codes in Bertrand-Edgeworth duopoly supergames. We characterize perfect equilibrium punishment paths with a 2-phase structure that achieve the security level for both firms for a wide range of parameter values. Such 2-phase punishment paths sustain collusion for values of the discount factor and the tie-breaking rule for which other paths analyzed previously in the literature do not. The second essay also examines the feasibility of tacit collusion in capacity constrained duopoly supergames. However, in order to deal with some of the conceptual and technical difficulties encountered in the Bertrand-Edgeworth supergame analyzed in the first essay, a different strategy space is assumed. In each period firms simultaneously set a price-quantity pair specifying the price for the period and the maximum quantity the firm is willing to sell at this price. Under price-quantity competition firms are able to ration their output below capacity. For a wide range of capacity pairs, the equilibrium path providing the smaller firm with its highest stationary perfect equilibrium payoff requires that it undercut its rival's price and ration demand. Furthermore, for some capacities and discount factors supporting security level punishments, price shading and rationing arise everywhere on the set of stationary perfect equilibrium paths yielding (constrained) Pareto optimal payoffs. In the third essay, we analyze infinitely repeated multiunit uniform price auctions in a symmetric oligopoly with capacity constrained firms. Under the Market Clearing and Maximum Accepted Price rules of determining the uniform price, we show that there exists a range of discount factors for which the monopoly outcome with equal sharing is sustainable in the uniform price auction, but not in the corresponding discriminatory auction. Moreover, capacity withholding may be necessary to sustain this outcome. These results are extended to the case where firms may set bids that are arbitrary step functions of price-quantity pairs with any finite number of price steps.

Degree

Ph.D.

Advisors

Kovenock, Purdue University.

Subject Area

Economic theory

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