### Abstract

This paper studies a spatial duopoly model where customers are located at nodes and the demand functions are given for each node. For any fixed location of two firms, we analyze Bertrand-Nash equilibrium and derive a necessary and sufficient condition for the existence of equilibrium. We present an algorithm to compute all equilibria, provided profit functions have a finite number of peaks. The algorithm terminates within polynomial time if the number of peaks is polynomial in the numben of nodes.

Original language | English |
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Pages (from-to) | 25-37 |

Number of pages | 13 |

Journal | Journal of the Operations Research Society of Japan |

Volume | 47 |

Issue number | 1 |

Publication status | Published - 2004 Mar |

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### Keywords

- Bertrand-Nash equilibrium
- Discrete model
- Game theory
- Hotelling's duopoly model
- Polynomial time algorithm
- Spatial competition

### ASJC Scopus subject areas

- Decision Sciences(all)
- Management Science and Operations Research

### Cite this

*Journal of the Operations Research Society of Japan*,

*47*(1), 25-37.

**Evaluating all bertrand-nash equilibria in a discrete spatial duopoly model.** / Matsubayashi, Nobuo; Umezawa, Masashi; Masuda, Yasushi; Nishino, Hisakazu.

Research output: Contribution to journal › Article

*Journal of the Operations Research Society of Japan*, vol. 47, no. 1, pp. 25-37.

}

TY - JOUR

T1 - Evaluating all bertrand-nash equilibria in a discrete spatial duopoly model

AU - Matsubayashi, Nobuo

AU - Umezawa, Masashi

AU - Masuda, Yasushi

AU - Nishino, Hisakazu

PY - 2004/3

Y1 - 2004/3

N2 - This paper studies a spatial duopoly model where customers are located at nodes and the demand functions are given for each node. For any fixed location of two firms, we analyze Bertrand-Nash equilibrium and derive a necessary and sufficient condition for the existence of equilibrium. We present an algorithm to compute all equilibria, provided profit functions have a finite number of peaks. The algorithm terminates within polynomial time if the number of peaks is polynomial in the numben of nodes.

AB - This paper studies a spatial duopoly model where customers are located at nodes and the demand functions are given for each node. For any fixed location of two firms, we analyze Bertrand-Nash equilibrium and derive a necessary and sufficient condition for the existence of equilibrium. We present an algorithm to compute all equilibria, provided profit functions have a finite number of peaks. The algorithm terminates within polynomial time if the number of peaks is polynomial in the numben of nodes.

KW - Bertrand-Nash equilibrium

KW - Discrete model

KW - Game theory

KW - Hotelling's duopoly model

KW - Polynomial time algorithm

KW - Spatial competition

UR - http://www.scopus.com/inward/record.url?scp=3242747554&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=3242747554&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:3242747554

VL - 47

SP - 25

EP - 37

JO - Journal of the Operations Research Society of Japan

JF - Journal of the Operations Research Society of Japan

SN - 0453-4514

IS - 1

ER -