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1. Sequential optimal contracting in continuous time

   https://doi.org/10.3934/fmf.2025001  

   Alvarez, Guillermo Alonso; Bayraktar, Erhan; Ekren, Ibrahim; Huang, Liwei (January 2025, Frontiers of Mathematical Finance)

   This paper studies a principal-agent problem in continuous time with multiple lump-sum payments (contracts) paid at different deterministic times. We reduce the non-zero-sum Stackelberg game between the principal and agent to a standard stochastic optimal control problem. We apply our result to a benchmark model to investigate how different inputs (payment frequencies, payment distribution, discounting factors, agent's reservation utility) affect the principal's value and agent's optimal compensations. 

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2. Simple Delegated Choice

   Khobadahksh, A; Pountourakis, E; Taggart, S (January 2024, LivingOnTrack)

   Woodruff, D (Ed.)

   This paper studies delegation in a model of discrete choice. In the delegation problem, an uninformed principal must consult an informed agent to make a decision. Both the agent and principal have preferences over the decided-upon action which vary based on the state of the world, and which may not be aligned. The principal may commit to a mechanism, which maps reports of the agent to actions. When this mechanism is deterministic, it can take the form of a menu of actions, from which the agent simply chooses upon observing the state. In this case, the principal is said to have delegated the choice of action to the agent. We consider a setting where the decision being delegated is a choice of a utility-maximizing action from a set of several options. We assume the shared portion of the agent's and principal's utilities is drawn from a distribution known to the principal, and that utility misalignment takes the form of a known bias for or against each action. We provide tight approximation analyses for simple threshold policies under three increasingly general sets of assumptions. With independently-distributed utilities, we prove a 3-approximation. When the agent has an outside option the principal cannot rule out, the constant-approximation fails, but we prove a log ρ/ log log ρ-approximation, where ρ is the ratio of the maximum value to the optimal utility. We also give a weaker but tight bound that holds for correlated values, and complement our upper bounds with hardness results. One special case of our model is utility-based assortment optimization, for which our results are new. 

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3. Simple Delegated Choice

   Khodabakhsh, Ali; Pountourakis, Emmanouil; Taggart, Samuel (January 2024, Society for Industrial and Applied Mathematics)

   This paper studies delegation in a model of discrete choice. In the delegation problem, an uninformed principal must consult an informed agent to make a decision. Both the agent and principal have preferences over the decided-upon action which vary based on the state of the world, and which may not be aligned. The principal may commit to a mechanism, which maps reports of the agent to actions. When this mechanism is deterministic, it can take the form of a menu of actions, from which the agent simply chooses upon observing the state. In this case, the principal is said to have delegated the choice of action to the agent. We consider a setting where the decision being delegated is a choice of a utility-maximizing action from a set of several options. We assume the shared portion of the agent's and principal's utilities is drawn from a distribution known to the principal, and that utility misalignment takes the form of a known bias for or against each action. We provide tight approximation analyses for simple threshold policies under three increasingly general sets of assumptions. With independently-distributed utilities, we prove a 3-approximation. When the agent has an outside option the principal cannot rule out, the constant-approximation fails, but we prove a log ρ/ log log ρ-approximation, where ρ is the ratio of the maximum value to the optimal utility. We also give a weaker but tight bound that holds for correlated values, and complement our upper bounds with hardness results. One special case of our model is utility-based assortment optimization, for which our results are new. 

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4. Optimal Signaling Mechanisms in Unobservable Queues with Strategic Customers

   https://doi.org/10.1145/3033274.3085135  

   Lingenbrink, David; Iyer, Krishnamurthy (June 2017, Proceedings of the 2017 ACM Conference on Economics and Computation (EC))

   We study the problem of optimal information sharing in the context of a service system. In particular, we consider an unobservable single server queue offering a service at a fixed price to a Poisson arrival of delay-sensitive customers. The service provider can observe the queue, and may share information about the state of the queue with each arriving customer. The customers are Bayesian and strategic, and incorporate any information provided by the service provider into their prior beliefs about the queue length before making the decision whether to join the queue or leave without obtaining service. We pose the following question: which signaling mechanism and what price should the service provider select to maximize her revenue? We formulate this problem as an instance of Bayesian persuasion in dynamic settings. The underlying dynamics make the problem more difficult because, in contrast to static settings, the signaling mechanism adopted by the service provider affects the customers' prior beliefs about the queue (given by the steady state distribution of the queue length in equilibrium). The core contribution of this work is in characterizing the structure of the optimal signaling mechanism. We summarize our main results as follows. (1) Structural characterization: Using a revelation-principle style argument, we find that it suffices to consider signaling mechanisms where the service provider sends a binary signal of "join" or "leave", and under which the equilibrium strategy of a customer is to follow the service provider's recommended action. (2) Optimality of threshold policies: For a given fixed price for service, we use the structural characterization to show that the optimal signaling mechanism can be obtained as a solution to a linear program with a countable number of variables and constraints. Under some mild technical conditions on the waiting costs, we establish that there exists an optimal signaling mechanism with a threshold structure, where service provider sends the "join" signal if the queue length is below a threshold, and "leave" otherwise. (In addition, at the threshold, the service provider randomizes.) For the special case of linear waiting costs, we derive an analytical expression for the optimal threshold i terms of the two branches of the Lambert-W function. (3) Revenue comparison: Finally, we show that with the optimal choice of the fixed price and using the corresponding optimal signaling mechanism, the service provider can achieve the same revenue as with the optimal state-dependent pricing mechanism in a fully-observable queue. This implies that in settings where state-dependent pricing is not feasible, the service provider can effectively use optimal signaling (with the optimal fixed price) to achieve the same revenue. 

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5. Delegated Search Approximates Efficient Search

   https://doi.org/10.1145/3219166.3219205  

   Kleinberg, Jon; Kleinberg, Robert (June 2018, Proceedings of the 2018 ACM Conference on Economics and Computation)

   There are many settings in which a principal performs a task by delegating it to an agent, who searches over possible solutions and proposes one to the principal. This describes many aspects of the workflow within organizations, as well as many of the activities undertaken by regulatory bodies, who often obtain relevant information from the parties being regulated through a process of delegation. A fundamental tension underlying delegation is the fact that the agent's interests will typically differ -- potentially significantly -- from the interests of the principal, and as a result the agent may propose solutions based on their own incentives that are inefficient for the principal. A basic problem, therefore, is to design mechanisms by which the principal can constrain the set of proposals they are willing to accept from the agent, to ensure a certain level of quality for the principal from the proposed solution. In this work, we investigate how much the principal loses -- quantitatively, in terms of the objective they are trying to optimize -- when they delegate to an agent. We develop a methodology for bounding this loss of efficiency, and show that in a very general model of delegation, there is a family of mechanisms achieving a universal bound on the ratio between the quality of the solution obtained through delegation and the quality the principal could obtain in an idealized benchmark where they searched for a solution themself. Moreover, it is possible to achieve such bounds through mechanisms with a natural threshold structure, which are thus structurally simpler than the optimal mechanisms typically considered in the literature on delegation. At the heart of our framework is an unexpected connection between delegation and the analysis of prophet inequalities, which we leverage to provide bounds on the behavior of our delegation mechanisms. 

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