DP4972 Bertrand Equilibria and Sharing Rules
|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.