Economic Theory

, Volume 31, Issue 3, pp 573–585 | Cite as

Bertrand Games and Sharing Rules

Research Article

Abstract

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.

Keywords

Bertrand games Sharing rule Tie-decreasing sharing rule Coalition monotonicity 

JEL Classification Numbers

C72 D43 L13 

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Copyright information

© Springer-Verlag 2006

Authors and Affiliations

  1. 1.School of EconomicsUniversidade Nova de LisboaLisboaPortugal
  2. 2.CEPRLondonUK

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