Strategic advance sales, demand uncertainty and overcommitment
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Strategic advance sales, demand uncertainty and overcommitment Sébastien Mitraille1
· Henry Thille2
Received: 16 July 2018 / Accepted: 13 March 2019 © Springer-Verlag GmbH Germany, part of Springer Nature 2019
Abstract We study a game in which producers can sell both before and after the realization of a random demand. Models of strategic forward trading and of advance sales to intermediaries or consumers share this structure. Demand uncertainty and committed advance sales imply that final-stage net residual demand may be so low that producers find additional sales unprofitable, or even so low that the final period price is zero, introducing some convexity into producers’ payoffs. If such an ex-post overcommitment occurs on the equilibrium path, producers reduce their advance sales, muting the pro-competitive effects found under deterministic demand. We prove existence of a unique symmetric pure-strategy equilibrium, whose nature depends on the support of the demand distribution relative to the marginal cost of production. For a narrow support, existence is assured for any distribution, while for wider support we establish a sufficient condition for existence. Our results provide a precise characterization of “minor” uncertainty, in which only the expected value of demand affects the equilibrium which is otherwise qualitatively similar to the deterministic case. Keywords Oligopoly · Advance sales · Uncertainty · Overcommitment JEL Classification C72 · D43 · L13
1 Introduction The ability of firms to commit to sales in advance of market clearing creates a strategic incentive to capture future demand through these advance sales. This leads to market outcomes that are more competitive than what occurs when advance sales are prohibited since producers are unable to commit to not make additional sales in the
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Sébastien Mitraille [email protected]
1
Toulouse Business School, University of Toulouse, 20 Bd Lascrosses, 31000 Toulouse, France
2
Department of Economics and Finance, University of Guelph, Guelph, ON, Canada
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S. Mitraille, H. Thille
future when the market clears. Examples include firms selling through forward contracts and firms selling to consumers or other intermediaries who then store for future consumption or resale. However, if the future demand is uncertain at the time the advance sales commitment is made, producers face the risk that they may have overcommitted sales if demand turns out to be lower than expected. In this case, producers may find that further spot sales are unprofitable, in which case the strategic incentive for advance sales is likely to be muted as they have no effect on rivals spot sales in these subgames. We analyze the effects of this possibility of ex-post overcommitment on the equilibrium of an advance sales game in which producers can commit to sell a quantity in a period prior to the meeting of the spot market and subsequently can produce additional output in the period in which the spot market meets. We find that the degree of uncertainty (as measured
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