Discussion paper

DP4972 Bertrand Equilibria and Sharing Rules

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.

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Citation

Hoernig, S (2005), ‘DP4972 Bertrand Equilibria and Sharing Rules‘, CEPR Discussion Paper No. 4972. CEPR Press, Paris & London. https://cepr.org/publications/dp4972