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

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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.
Lingua originaleEnglish
pagine (da-a)102-117
Numero di pagine16
RivistaDefault journal
Volume71
Stato di pubblicazionePublished - 2017

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Follower
Stackelberg equilibrium
Fixed costs
Costs
Threat
Guarantee
Stackelberg game
Cournot model
Pure strategies
Cost function
Market structure
Comparative statics

All Science Journal Classification (ASJC) codes

  • Economics and Econometrics

Cita questo

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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.",
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