Two New Conditions Supporting the First-Order Approach to Multisignal Principal-Agent Problems

Abstract

This paper presents simple new multi-signal generalizations of the two classic methods used to justify the first-order approach to moral hazard principal-agent problems, and compares these two approaches with each other. The paper first discusses limitations of previous generalizations. It then uses a state-space formulation to obtain a new multi-signal generalization of the Jewitt (1988) conditions. Next, using the Mirrlees formulation, the paper obtains new multi-signal generalizations of the CDFC approach of Rogerson (1985) and Sinclair-Desgagné (1994). Vector calculus methods are used to derive easy-to-check local conditions for our generalization of the CDFC. Finally, we argue that the Jewitt conditions may generalize more flexibly than the CDFC to the multi-signal case. This is because, with many signals, the principal can become very well informed about the agent's action and, even in the one-signal case, the CDFC must fail when the signal becomes very accurate.

Player Strength and Effort in Contests

“…In particular, we assume that output is stochastic and that, for a given level of effort, the distribution of output of stronger players dominates that of weaker ones. Heterogeneity with respect to players' output in the contest has been assumed in other contest models as well (e.g., Bastani, Giebe, andGürtler 2022 andKirkegaard 2023a), where some models use the state-space formulation (as we do in the current paper) and others the Mirrlees formulation (see Conlon 2009). One of the most closely related papers is Bastani, Giebe, and Gürtler (2022), who consider two-player contests with a single prize, in which the equilibrium is symmetric and both players exert the same effort.…”