Bertrand Competition with Subcontracting

We investigate how the possibility of subsequently subcontracting production to each other influences rivals' initial competition for a contract or a market as a two-stage game. In its first stage, the two firms engage in price competition to supply a contract or a market. In the second stage, the firms may subcontract production to each other. It is supposed that the firms produce the identical product with the same strictly convex cost function. The incentive for subcontracting comes from the strictly convex production costs. A firm is obliged to supply the entire quantity demanded at its quoted price. Our analysis discloses that if the winner of the game's first stage determines the terms of the subcontract in its second stage, there exists a unique, subgame perfect Nash equilibrium (SPNE) in pure strategies in which the firms bid the same price in the first stage and both receive zero profits. On the other hand, if the loser of the game's first stage sets the terms of the subcontract in the second stage, there exists a unique SPNE in pure strategies in which the firms bid the same price in the first stage and both receive positive profits. The presence of the possibility of subcontracting supports a unique SPNE in pure strategies, even though no actual subcontracting may occur. The SPNE price is below the socially-optimal price in the first case and is above it in the second case. We also consider other modes of sharing the gains from subcontracting between the two firms, such as the Nash bargaining solution.