nep-cta New Economics Papers
on Contract Theory and Applications
Issue of 2023‒04‒10
four papers chosen by
Guillem Roig
University of Melbourne

  1. Distributionally Robust Principal-Agent Problems and Optimality of Contract Menus By Peter Zhang
  2. Optimal Insurance: Dual Utility, Random losses and Adverse Selection By Alex Gershkov; Benny Moldovanu; Philipp Strack; Mengxi Zhang
  3. Reform for Sale: a Common Agency Model with Moral Hazard Frictions By Lefebvre, Perrin; Martimort, David
  4. Delegation, Capture and Endogenous Information Structures By Lefebvre, Perrin; Martimort, David

  1. By: Peter Zhang
    Abstract: We propose a distributionally robust principal-agent formulation, which generalizes some common variants of worst-case and Bayesian principal-agent problems. With this formulation, we first construct a theoretical framework to certify whether any surjective contract menu is optimal, and quantify its sub-optimality. The framework and its proofs rely on a novel construction and comparison of several related optimization problems. Roughly speaking, our framework transforms the question of contract menu optimality into the study of duality gaps. We then operationalize the framework to study the optimality of simple -- affine and linear -- contract menus. By our framework, the optimality gap of a contract menu is broken down into an adjustability gap and an information rent. We show that, with strong geometric intuition, these simple contract menus tend to be close to optimal when the social value of production is convex in production cost and the conversion ratio is large at the agent's highest effort level. We also provide succinct and closed-form expressions to quantify the optimality gap when the social value function is concave. With this systematic analysis, our results shed light on the technical root of a higher-level question -- why are there more positive results in the literature in terms of a simple menu's optimality in a \emph{robust} (worst-case) setting rather than in a \emph{stochastic} (Bayesian) setting? Our results demonstrate that the answer relates to two facts: the sum of quasi-concave functions is not quasi-concave in general; the maximization operator and the expectation operator do not commute in general. Overall, our study is among the first to cross-pollinate the contract theory and optimization literature.
    Date: 2023–03
  2. By: Alex Gershkov; Benny Moldovanu; Philipp Strack; Mengxi Zhang
    Abstract: We study a generalization of the classical monopoly insurance problem under adverse selection (see Stiglitz [1977]) where we allow for a random distribution of losses, possibly correlated with the agent’s risk parameter that is private information. Our model explains patterns of observed customer behavior and predicts insurance contracts most often observed in practice: these consist of menus of several deductible-premium pairs, or menus of insurance with coverage limits-premium pairs. The main departure from the classical insurance literature is obtained here by endowing the agents with risk-averse preferences that can be represented by a dual utility functional (Yaari [1987]).
    Keywords: digital platforms, Big Tech, market definition, multi-markets approach, German Competition Act, 19a designations, competition law
    JEL: K21
    Date: 2023–03
  3. By: Lefebvre, Perrin; Martimort, David
    Abstract: Lobbying competition is viewed as a delegated common agency game under moral hazard. Several interest groups try to influence a policy-maker who exerts effort to increase the probability that a reform be implemented. With no restriction on the space of contribution schedules, all equilibria perfectly reflect the principals’ preferences over alternatives. As a result, lobbying competition reaches efficiency. Unfortunately, such equilibria require that the policy-maker pays an interest group when the latter is hurt by the reform. When payments remain non-negative, inducing effort requires leaving a moral hazard rent to the decision-maker. Contributions schedules no longer reflect the principals preferences, and the unique equilibrium is inefficient. Free-riding across congruent groups arises and the set of groups active at equilibrium is endogenously derived. Allocative efficiency and redistribution of the aggregate surplus are linked altogether and both depend on the set of active principals, as well as on the groups size.
    Keywords: Pluralistic Politics; Lobbying; Common Agency; Moral Hazard
    JEL: D72 D82 H10
    Date: 2023–03–10
  4. By: Lefebvre, Perrin; Martimort, David
    Abstract: A substantial literature has been devoted to analyzing how legislators delegate regulatory power to a more knowledgeable agency. Yet, much less attention has been paid to understand how this delegation process is shaped by the environment in which this agency operates, and more specifically by the actions of interest groups. We propose a model of regula-tory capture to assess how the distribution of information across interest groups and agencies impacts optimal delegation. Whether an interest group and his agency share information or not determines the scope for capture and how much discretion should be left to this agency in response. Whether asymmetric information reduces or increases discretion depends on the biases of the group and the agency vis-`a-vis Congress. Groups that are more aligned with Congress collect politically relevant information, while more extreme groups remain poorly informed. The information structure that endogenously emerges increases discretion under broad circumstances.
    Keywords: Pluralistic Politics; Lobbying; Common Agency; Moral Hazard
    JEL: D82 D86 H10
    Date: 2023–03–10

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