Tacit Collusion in the Presence of Cyclical Demand and Endogenous Capacity Levels, joint with Christopher Knittel, NBER Working Paper No. 12635, Revisions requested from The International Journal of Industrial Organization.

ABSTRACT
We analyze tacit collusion in an industry characterized by cyclical demand and long-run scale decisions; firms face deterministic demand cycles and choose capacity levels prior to competing in prices. Our focus is on the nature of prices. We find that two types of price wars may exist. In one, collusion can involve periods of mixed strategy price wars. In the other, consistent with the Rotemberg and Saloner (1986) definition of price wars, we show that collusive prices can also become countercyclical. We also establish pricing patterns with respect to the relative prices in booms and recessions. If the marginal cost of capacity is high enough, holding current demand constant, prices in the boom will be generally lower than the prices in the recession; this reverses the results of Haltiwanger and Harrington (1991). In contrast, if the marginal cost of capacity is low enough, then prices in the boom will be generally higher than the prices in the recession. For costs in an intermediate range, numerical examples are calculated to show specific pricing patterns.

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Kreps and Scheinkman Meet Judo Economics  
 PDF  In Submission


ABSTRACT
We simplify and generalize the Kreps and Scheinkman (1983) Theorem based on the Gelman and Salop (1983) idea of judo economics. For a symmetric two-stage game, where firms first choose capacities, then compete in prices, Kreps and Scheinkman (K&S) prove that under efficient rationing the Nash equilibrium coincides with the Cournot equilibrium. We generalize this in three ways: (i) proving the K&S result extends to firms with asymmetric costs, (ii) proving the capacity choice game is dominance-solvable, just like the Cournot game, and (iii) providing a simple necessary and sufficient condition under which the K&S result extends to proportional rationing. Unlike K&S, our method of proof is based on intuitions from judo economics, which depend on neither symmetry nor efficient rationing.

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Cournot outcomes under Bertrand-Edgeworth competition with demand uncertainty 
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ABSTRACT
In this paper, we examine the effect of demand “noise” on the well known result of Kreps and Scheinkman (1983). We study a two-stage game in which firms initially choose capacity levels when demand is uncertain, then, when demand is realized, compete in prices. We consider games with both efficient and proportional rationed residual demand. In both cases, there is an equilibrium outcome coinciding with an uncertain Cournot equilibrium outcome if and only if (i) the fluctuation in absolute market size is small relative to the cost of capacity, or (ii) uncertainty is such that, with high probability the market demand is very large and with the remaining probability the market demand is extremely small. Otherwise, equilibria involve mixed strategies. Further, we show that condition (i) is sufficient for an uncertain Cournot outcome to be the unique equilibrium outcome of the two-stage game. The results make prominent the nature of demand uncertainty, the costs of capacity, and the demand rationing scheme in determining the character of the equilibria of the two-stage game.

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Cournot and Bertrand-Edgeworth competition when rivals’ costs are unknown
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ABSTRACT 

We study a two-stage game with capacity precommitment followed by price competition where firms have incomplete information about their rival's marginal cost. The game has a Cournot outcome if and only if the lowest possible marginal cost is sufficiently high relative to the expected marginal cost.


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