Bertrand Equilibria and Sharing Rules

Steffen Hoernig

No 4972, CEPR Discussion Papers from C.E.P.R. Discussion Papers

Abstract: We analyse 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-takes-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)
Date: 2005-03
New Economics Papers: this item is included in nep-gth
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Citations: View citations in EconPapers (1)

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