John Wu. Correlated Equilibrium of Bertrand Competition. In Christos H. Papadimitriou, Shuzhong Zhang, editors, Internet and Network Economics, 4th International Workshop, WINE 2008, Shanghai, China, December 17-20, 2008. Proceedings. Volume 5385 of Lecture Notes in Computer Science, pages 166-177, Springer, 2008.
This paper explores the relation between equilibrium coarsenings and equilibrium refinements via Bertrand competition example and similar situations, it shows that the typical equilibrium coarsening — a unique correlated equilibrium — is equivalent to the unique Nash equilibrium itself, is also equivalent to the equilibrium refinement, for the standard n-firms Bertrand competition model with linear demand and symmetric, linear costs in the most special and simplest case, and compares some wonderful and remarkable differences of the existence, uniqueness, stability, connectivity, and strategic property of Nash equilibrium and correlated equilibrium between Cournot and Bertrand model. We also propose some open questions.
Keywords: equilibrium coarsenings - equilibrium refinements - strategic correlativity principle - positive correlated equilibrium - negative correlated equilibrium - duality gap