Bertrand Equilibria and Sharing Rules

• Autor(a) principal: Hoernig, Steffen
• Data de Publicação: 2005
• Tipo de documento: Artigo
• Idioma: eng
• Título da fonte: Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
• Texto Completo: http://hdl.handle.net/10362/83199
• topic: Bertrand games; Sharing rule; Tie-breaking rule; Sign-preserving sharing rules; Expectation sharing rules

We analyze 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-take-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.