Existence of Equilibrium Mechanisms in Generalized Principal-Agent Problems with Interacting Teams

TL;DR

This paper investigates the existence of equilibrium mechanisms in multi-principal, multi-team incentive problems with strategic spillovers, introducing a novel approach to establish equilibrium conditions.

Contribution

It develops general conditions for equilibrium existence in complex multi-principal settings using a new method involving outcome distribution tracking.

Findings

Established conditions for equilibrium existence in multi-principal incentive games.

Introduced a novel approach tracking outcome distributions and deviations.

Provided a foundation for analyzing multi-team mechanism design problems.

Abstract

We study incentive design when multiple principals simultaneously design mechanisms for their respective teams in environments with strategic spillovers. In this environment, each principal's set of incentive-compatible mechanisms--those that satisfy their own agents' incentive compatibility constraints--depends on the mechanisms offered by the other teams. Following a classic example by Myerson (1982), such games may lack equilibrium due to discontinuities in the correspondence of incentive-compatible mechanisms. We establish general conditions for equilibrium existence by introducing a novel approach that involves tracking both the outcome distributions along the truthful-obedient path and the sets of outcome distributions achievable through unilateral deviations, thereby providing a foundation for analyzing a wide range of multi-principal mechanism design with team production and agency problems.