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

Nobuo Matsubayashi; Masashi Umezawa; Yasushi Masuda; Hisakazu Nishino

doi:10.15807/jorsj.47.25

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

Nobuo Matsubayashi, Masashi Umezawa, Yasushi Masuda, Hisakazu Nishino

Department of Industrial and Systems Engineering

Research output: Contribution to journal › Article › peer-review

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
Pages (from-to)	25-37
Number of pages	13
Journal	Journal of the Operations Research Society of Japan
Volume	47
Issue number	1
DOIs	https://doi.org/10.15807/jorsj.47.25
Publication status	Published - 2004 Mar

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

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10.15807/jorsj.47.25

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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

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

Abstract

Keywords

ASJC Scopus subject areas

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