Dynamic Duopoly with Intertemporal Capacity Constraints

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Working paper
Anita H.J.van den Berg , P. Jean-Jacques Herings and Hans J.M. Peters
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Maastricht University
We analyze strategic firm behavior in settings where the production stage is followed by several periods during which only sales take place. We analyze the dynamics of the market structure, the development of prices and sales over time, and the implications for profits and consumer surplus. Two specific settings are analyzed. In the first, a firm can commit up-front to a sales strategy that does not depend on the actual sales of its competitor. In this case there is a unique Nash equilibrium and price increases over time. In the second setting, there is no commitment and firms can adjust their sales in response to observed supply of their competitor in the previous period. It is shown that in this case a subgame perfect Nash equilibrium does not always exist. Equilibria can have surprising features. For some parameter constellations, price may decrease over time. It is also possible that the firm increases its profit by destroying some of its production. When firms have equal size, the equilibrium outcome is the same in both the commitment and the non-commitment setting. In general, the setting without commitment is beneficial to the larger firm, whereas the setting with commitment leads to higher profits for the smaller firm.
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