Capacity games in Cournot's duopoly model of complements

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We analyze a capital accumulation game in a dynamic version of Cournot duopoly model of complements. In this game, firms' instant profits are discontinuous and therefore one cannot use standard optimal control approaches to study dynamic equilibria. We find that in contrast with Reynolds' (1987) seminal analysis of capacity games in Cournot quantity duopoly model, an open-loop Nash equilibrium generally does not exist. Existence of equilibrium only holds when firms cannot disinvest and have the same initial production capacity. These conclusions diverge from the finding that a Nash equilibrium always exists in the static version of the Cournot model of complement with capacity constraints.

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