Working Paper: CEPR ID: DP4972
Authors: Steffen Hoernig
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; Expectation sharing rules; Sharing rule; Sign preserving sharing rules; Tiebreaking rule
JEL Codes: C72; D43; L13
Edges that are evidenced by causal inference methods are in orange, and the rest are in light blue.
| Cause | Effect |
|---|---|
| sharing rules (D16) | zero profit equilibria (D59) |
| tiedecreasing sharing rules (D30) | zero profit equilibria (D59) |
| non-tiedecreasing sharing rules (C71) | positive profit equilibria (D59) |
| sign-preserving sharing rules (C71) | zero profit Nash equilibria (C72) |