Endogenous bargaining power in dynamic principal-agent models with wealth-dependent limited liability

Abstract

In standard dynamic principal-agent models, bargaining power is treated as a primitive (or parameter) that remains constant. This dissertation demonstrates that bargaining power is instead an endogenously determined equilibrium phenomenon under circumstances in which the agent’s limited liability constraint on accumulated wealth is binding. Once the limited liability constraint binds, the Pareto frontier becomes nonlinear; there are no longer separate instruments to achieve redistributive objectives other than by adjusting the incentive slope, and changing the incentive slope alters both the aggregate amount of surplus created and how surplus will be distributed. The lack of separability between efficiency and distributional objectives renders the actual bargaining power enjoyed by one party of a contract a strictly increasing function of the total amount of wealth accumulated by that party within the binding regime, but restores the exogenous bargaining weight assigned to each party of the contract once the limited liability constraint is relaxed. The wealth process defined by this system is geometrically ergodic, with a single invariant distribution that assigns approximately 65.9% of stationary mass to the binding regime at the baseline calibration. The structural drift that determines bargaining power over time is based solely upon model primitives and provides microeconomic foundations for reduced-form specifications such as that presented by Di Giannatale et al. (2025), and defines the mechanism through which wealth accumulation leads to persistence in differences in contractual surplus share ownership among contracting parties.