Leadership Under Multitasking

Abstract: We study multitasking problems a la Holmstrom and Milgrom (1991) where an agent engages in both a contractible and a non-contractible tasks which are substitutes. In our model, there are two agents and there is asymmetric information about the value of the non-contractible task between the agents. The agents play a signaling game: after observing an informed agent's action (called a leader), an uninformed agent (called a follower) can choose their own action. In contrast to the previous literature, we show that a principal may provide the leader with a higher incentive to the contractible task in order for the agents to work more in the non-contractible task. Intuitively, the leader's action works akin to the literature on leading by example a la Hermalin (1998) in that the leader's higher effort in the non-contractible task enhances the credibility of the signal about the value of this task. In this case, the higher incentive for the leader to the contractible task makes it easier for the leader to send a credible signal. We provide the conditions for this result and discuss its economic implications.