Addressing Strategic Uncertainty with Incentives and Information

Abstract

A principal privately contracts with a set of agents who then simultaneously make a binary decision. Each contract specifies an individual allocation and the information the agent is given about a fundamental state and other agents' contracts. We study the principal's optimal scheme that induces a desired action profile as the unique rationalizable outcome. Our main result reduces this multiagent problem to a two-step procedure where information is designed agent-by-agent: the principal chooses a fundamental-state-contingent distribution over agent rankings and, separately for each agent, the agent's information about the realized ranking and fundamental states. We illustrate with a team-production application.

Implementation via Information Design in Binary‐Action Supermodular Games

“…A similar condition appears in Halac, Lipnowski, and Rappoport (2021, Section V) andHalac, Lipnowski, and Rappoport (2022).…”

“…This condition has appeared inOyama and Takahashi (2020) and also played an important role inHalac, Lipnowski, and Rappoport (2021). See alsoGershkov and Szentes (2009) for an earlier study where a similar condition is found (but in a different, voting situation).18 The latter condition can also be equivalently written as ν k (• θ * ) → ξ as k → ∞.…”

“…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."…”