Bertrand equilibria and sharing rules

Steffen Hoernig

Nova SBE Working Paper Series from Universidade Nova de Lisboa, Nova School of Business and Economics

Abstract: We analyze how sharing rules affect Nash equilibria in Bertrand games, where the sharing of profits at ties is a decisive assumption. Necessary conditions for either positive or zero equilibrium profits are derived. Zero profit equilibria are shown to exist under weak conditions if the sharing rule is sign-preserving. For Bertrand markets we define the class of expectation sharing rules, where profits at ties are derived from some distribution of quantities. In this class the winner-take-all sharing rule is the only one that is always sign-preserving, while for each pair of demand and cost functions there may be many others.

Keywords: Bertrand games; sharing rule; tie-breaking rule; sign-preserving sharing rules; expectation sharing rules (search for similar items in EconPapers)
JEL-codes: C72 D43 L13 (search for similar items in EconPapers)
Pages: 42 pages
Date: 2005
New Economics Papers: this item is included in nep-gth, nep-ind and nep-mic
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Working Paper: Bertrand Equilibria and Sharing Rules (2005)
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Persistent link: https://EconPapers.repec.org/RePEc:unl:unlfep:wp468

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