Truthful Equilibria in Generalized Common Agency Models

💡 Research Summary

The paper expands the classic common‑agency framework—where multiple principals interact with a single agent—into a more realistic setting that captures networked principals, multidimensional agent actions, and noisy public signals. The authors introduce a “generalized common‑agency model” consisting of (i) a graph‑structured network of principals whose payoff functions may exhibit externalities toward each other, (ii) an agent whose private type θ determines preferences over a vector of actions a∈ℝ^k, and (iii) a common signal s = g(a,θ,ε) observed by all principals but not the agent’s exact action or type. Each principal i offers a contract R_i(s), which can be any measurable function of the signal; the paper focuses on linear contracts R_i(s)=α_i·s+β_i because they admit tractable analysis and are widely used in practice.

The central concept is a “truthful equilibrium”: a Bayesian Nash equilibrium in which the agent reports his type truthfully (or, equivalently, chooses actions that make the reported type equal to the true type) and all principals maximize expected utility given the contract functions. To guarantee the existence of such an equilibrium, the authors impose two classic regularity conditions: (1) a single‑crossing property of each principal’s utility with respect to the agent’s action and type, ensuring that higher types always prefer higher actions in a consistent direction, and (2) monotonicity of the contract, i.e., non‑decreasing compensation with respect to the signal (α_i ≥ 0). Under these assumptions, together with continuity of the prior distribution over types and compactness of the type space, they prove via a fixed‑point argument that a truthful Bayesian Nash equilibrium always exists.

A second major result characterizes when the truthful equilibrium is unique and Pareto‑efficient. When the public signal is fully observed by all principals and contracts are restricted to the linear form, the authors derive explicit formulas for the optimal contract parameters: α_i = E