Bertrand games and sharing rules

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26 Citations (Scopus)


We consider asymmetric Bertrand games with arbitrary payoffs at ties or sharing rules, and identify sufficient conditions for the zero-profit outcome and the existence of Nash equilibria. Subject to some technical conditions on non- tied payoffs the following hold. If the sharing rule is strictly tie-decreasing all players but one receive zero equilibrium payoffs, while everybody does so if non- tied payoffs are symmetric. Mixed (pure) strategy Nash equilibria exist if the sharing rule is (norm) tie-decreasing and coalition-monotone.
Original languageEnglish
Pages (from-to)573-585
JournalEconomic Theory
Issue number3
Publication statusPublished - 1 Jan 2007


  • Bertrand games
  • sharing rule
  • tie-decreasing sharing rule
  • coalition monotonicity


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