Endogenous Choice of the Timing of Setting Incentive Parameters and the Strategic Contracts in a Managerial Mixed Duopoly with a Welfare-Based Delegation Contract and a Sales Delegation Contract

This study explores the game in which both the timing of setting the welfare-based incentive parameter of a public firm with a welfare-maximizing owner and the sales incentive parameter of a private firm and the contents of their strategic contracts in a managerial mixed duopoly with a welfare-based delegation a la (Nakamura in Int Rev Econ Financ 35:262-277, 2015) and a sales delegation are endogenously determined by their owners. We show two market structures: (1) the market structure in which the owner of the public (private) firm with a quantity contract is the leader (follower) in the determination of the incentive parameters and (2) the market structure in which the owner of the public (private) firm with a quantity (price) contract is the follower (leader) in the determination of the incentive parameters. The equilibrium market structures and highest social welfare are achieved in market structure (1). Therefore, in a managerial mixed duopoly with a welfare-based delegation and a sales delegation, it is not as necessary for the relevant authority including the government to regulate the free determination of both the timing of setting the welfare-based incentive parameter of the public firm and the sales incentive parameter of the private firm and the contents of their strategic contracts by their owners. The payoffs of the owners of both the public firm and the private firm stay relatively low in market structure (2), another equilibrium market structure. Finally, we confirm the robustness of the results on the equilibrium market structures against the change in the cost functions of both the public firm and the private firm from their constant marginal costs to their increasing marginal costs on the basis of the quadratic cost functions with their quantities.