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Stackelberg equilibrium with many leaders and followers. The case of zero fixed costs

Antonio Tesoriere

Research in Economics, 2017, vol. 71, issue 1, 102-117

Abstract: I study a version of the Stackelberg game with many identical firms in which leaders and followers use a continuous cost function with no fixed cost. Using lattice theoretical methods I provide a set of conditions that guarantee that the game has an equilibrium in pure strategies. With convex costs the model shows the same properties as a quasi-competitive Cournot model. The same happens with concave costs, but only when the number of followers is small. When this number is large the leaders preempt entry. I study the comparative statics and the limit behavior of the equilibrium and I show how the main determinants of market structure interact. More competition between the leaders always displaces the followers. Instead, how a stronger threat of entry affects the equilibrium depends on the technology. With strictly convex costs it is the followers that eventually displace the leaders.

Keywords: Stackelberg equilibrium; Cournot equilibrium; Existence of the equilibrium; Supermodular games; Entry preemption; Endogenous market structures (search for similar items in EconPapers)
Date: 2017
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