Merger Incentives and Inverse Matrices from Bertrand Competition

This paper first inverts a general class of matrices for solving Bertrand equilibria from arbitrary coalition structures in linear Bertand oligopolies. It then studies merger incentives and obtains two main results; 1) for any asymmetric costs, mergers of any size are profitable; 2) a merger will reduce outsiders' profits when there are large cost savings or cost asymmetry. The second result is in sharp constrast to Cournot competition where mergers always increase outsiders' profits. This striking new feature not only supports the belief that Bertrand competition is more general than Cournot competition, but will also open up a new line of arguments in future attempts to block merger proposals