DP4972 Bertrand Equilibria and Sharing Rules

Author(s): Steffen Hoernig
Publication Date: March 2005
Keyword(s): Bertrand games, expectation sharing rules, sharing rule, sign-preserving sharing rules, tie-breaking rule
JEL(s): C72, D43, L13
Programme Areas: Industrial Organization
Link to this Page: www.cepr.org/active/publications/discussion_papers/dp.php?dpno=4972

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.