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

Nobuo Matsubayashi, Masashi Umezawa, Yasushi Masuda, Hisakazu Nishino

Research output: Contribution to journalArticlepeer-review

2 Citations (Scopus)


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 languageEnglish
Pages (from-to)25-37
Number of pages13
JournalJournal of the Operations Research Society of Japan
Issue number1
Publication statusPublished - 2004 Mar


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

ASJC Scopus subject areas

  • General Decision Sciences
  • Management Science and Operations Research


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