### Abstract

Lingua originale | English |
---|---|

pagine (da-a) | 86-102 |

Numero di pagine | 17 |

Rivista | Journal of Mathematical Economics |

Volume | 73 |

Stato di pubblicazione | Published - 2017 |

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### All Science Journal Classification (ASJC) codes

- Economics and Econometrics
- Applied Mathematics

### Cita questo

**Stackelberg equilibrium with multiple firms and setup costs.** / Tesoriere, Antonio.

Risultato della ricerca: Article

*Journal of Mathematical Economics*, vol. 73, pagg. 86-102.

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TY - JOUR

T1 - Stackelberg equilibrium with multiple firms and setup costs

AU - Tesoriere, Antonio

PY - 2017

Y1 - 2017

N2 - I provide conditions that guarantee that a Stackelberg game with a setup cost and an integer number of identical leaders and followers has an equilibrium in pure strategies. The main feature of the game is that when the marginal follower leaves the market the price jumps up, so that a leader’s payoff is neither continuous nor quasiconcave. To show existence I check that a leader’s value function satisfies the following single crossing condition: When the other leaders produce more the leader never accommodates entry of more followers. If demand is strictly logconcave, and if marginal costs are both non decreasing and not flatter than average costs, then a Stackelberg equilibrium exists. Besides showing existence I characterize the equilibrium set and provide a number of results that contribute to the applied literature. As the number of leaders increases, leaders produce more and eventually they deter entry. Leaders produce more than the Cournot best reply, but they may underinvest in entry deterrence. As the number of followers increases, leaders become more aggressive. When this number is large, if leaders can produce the limit quantity and at the same time have market power, then they deter entry.

AB - I provide conditions that guarantee that a Stackelberg game with a setup cost and an integer number of identical leaders and followers has an equilibrium in pure strategies. The main feature of the game is that when the marginal follower leaves the market the price jumps up, so that a leader’s payoff is neither continuous nor quasiconcave. To show existence I check that a leader’s value function satisfies the following single crossing condition: When the other leaders produce more the leader never accommodates entry of more followers. If demand is strictly logconcave, and if marginal costs are both non decreasing and not flatter than average costs, then a Stackelberg equilibrium exists. Besides showing existence I characterize the equilibrium set and provide a number of results that contribute to the applied literature. As the number of leaders increases, leaders produce more and eventually they deter entry. Leaders produce more than the Cournot best reply, but they may underinvest in entry deterrence. As the number of followers increases, leaders become more aggressive. When this number is large, if leaders can produce the limit quantity and at the same time have market power, then they deter entry.

UR - http://hdl.handle.net/10447/243204

M3 - Article

VL - 73

SP - 86

EP - 102

JO - Journal of Mathematical Economics

JF - Journal of Mathematical Economics

SN - 0304-4068

ER -