Strategic delegation and second mover advantage in duopoly

We consider a duopoly in which each firm has one owner and one manager playing a multi-stage delegation game. The decision of each firm consists of two stages. In the first stage, the owner offers his manager a contract based on profits and sales. In the second stage, the manager chooses its output or price. Several possible sequential games will be analysed, depending on the sequence of the strategic variables. In the first scenario in which firm 1 makes a contract decision and a producing decision sequentially, and firm 2 follows in the same fashion, we show that any delegation equilibrium in which both owners commit their managers to profit-maximising behaviour disappears. In the second scenario in which the firms first enter into the contract stage and then Stackelberg competition follows in the second stage, sales-based delegation occurs. If firms compete in quantities, second mover advantage appears if firms make simultaneous delegation contracts, while first mover advantage is recovered if they make sequential contracts. If firms compete in prices, the results are reversed