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

Nobuo Matsubayashi, Masashi Umezawa, Yasushi Masuda, Hisakazu Nishino

Research output: Contribution to journalArticle

2 Citations (Scopus)

### 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 25-37 13 Journal of the Operations Research Society of Japan 47 1 Published - 2004 Mar

### Fingerprint

Nash equilibrium
Node
Duopoly
Polynomials
Existence of equilibrium
Demand function
Profit function

### 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

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

In: Journal of the Operations Research Society of Japan, Vol. 47, No. 1, 03.2004, p. 25-37.

Research output: Contribution to journalArticle

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