Rank Uncertainty in Organizations

Abstract

A principal incentivizes a team of agents to work by privately offering them bonuses contingent on team success. We study the principal’s optimal incentive scheme that implements work as a unique equilibrium. This scheme leverages rank uncertainty to address strategic uncertainty. Each agent is informed only of a ranking distribution and his own bonus, the latter making work dominant provided that higher-rank agents work. If agents are symmetric, their bonuses are identical. Thus, discrimination is strictly suboptimal, in sharp contrast with the case of public contracts (Winter 2004). We characterize how agents’ ranking and compensation vary with asymmetric effort costs. (JEL D23, D62, D81, D82, D86)

Implementation via Information Design in Binary‐Action Supermodular Games

“…This interpretation of our results provides a new perspective on contracting with externalities (Segal (2003) and Winter (2004)), where agents make decisions about whether to participate or not in the presence of strategic complementarities 24 . In fact, the recent studies by Halac, Lipnowski, and Rappoport (2021) and Moriya and Yamashita (2020), who considered the optimal joint design of transfers and information and showed how the “divide‐and‐conquer” incentive schemes (Segal (2003)) in the model of Winter (2004) can be improved upon by introducing higher order payoff uncertainty, can be understood from this viewpoint. In particular, the optimization problem of Halac, Lipnowski, and Rappoport (2021) can be equivalently rewritten as a problem with the constraint that “all participating” is limit S‐ (hence fully) implementable, which is characterized by our sequential obedience condition—a stochastic version of “divide‐and‐conquer.” In Morris, Oyama, and Takahashi (2022b), we formally describe the above solution method.…”

“…In fact, the recent studies by Halac, Lipnowski, and Rappoport (2021) and Moriya and Yamashita (2020), who considered the optimal joint design of transfers and information and showed how the “divide‐and‐conquer” incentive schemes (Segal (2003)) in the model of Winter (2004) can be improved upon by introducing higher order payoff uncertainty, can be understood from this viewpoint. In particular, the optimization problem of Halac, Lipnowski, and Rappoport (2021) can be equivalently rewritten as a problem with the constraint that “all participating” is limit S‐ (hence fully) implementable, which is characterized by our sequential obedience condition—a stochastic version of “divide‐and‐conquer.” In Morris, Oyama, and Takahashi (2022b), we formally describe the above solution method. By appealing also to the fact that their model has a potential, we obtain additional insights over Halac, Lipnowski, and Rappoport (2021).…”

“…In particular, the optimization problem of Halac, Lipnowski, and Rappoport (2021) can be equivalently rewritten as a problem with the constraint that “all participating” is limit S‐ (hence fully) implementable, which is characterized by our sequential obedience condition—a stochastic version of “divide‐and‐conquer.” In Morris, Oyama, and Takahashi (2022b), we formally describe the above solution method. By appealing also to the fact that their model has a potential, we obtain additional insights over Halac, Lipnowski, and Rappoport (2021). 25…”

“…1717 This condition has appeared in Oyama and Takahashi (2020) and also played an important role in Halac, Lipnowski, and Rappoport (2021). See also Gershkov and Szentes (2009) for an earlier study where a similar condition is found (but in a different, voting situation). …”

Exploiting social influence in networks

“…The unique implementation approach was pioneered by Segal (1999, 2003), who develops a general contracting model, and Winter (2004), who explores incentives provision in organizations. Babaioff, Feldman, Nisan, and Winter (2012), Bernstein and Winter (2012), Halac, Kremer, and Winter (2020), and Halac, Lipnowski, and Rappoport (2021) are prominent papers in this vein. We contribute to this literature by incorporating local externalities captured by a social network.…”