We derive Bertrand and Cournot equilibria in a differentiated duopoly in which each firm hires a manager to undertake research and development (R&D) and production decisions. We show that manager overconfidence and over-investment occur in each market competition. Furthermore, the Cournot game induces a higher level of overconfidence and more R&D investments than Bertrand game. However, if R&D spillovers are strong, the price is lower, and output is more abundant in Bertrand than in Cournot game. Furthermore, Cournot and Bertrand models with overconfident managers induce low prices, massive productions, and are more efficient if R&D productivity is low and spillovers are strong. We also show that if firms can only make two types of binding contracts with shareholders, it is a dominant strategy for each firm to choose the delegation contract.
Tondji, Jean-Baptiste, Delegation, Overconfidence, and Welfare in a Differentiated Duopoly (March 16, 2020). Available at SSRN: https://ssrn.com/abstract=3555348 or http://dx.doi.org/10.2139/ssrn.3555348