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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. Calibrated Stackelberg Games: Learning Optimal Commitments Against Calibrated Agents

   Haghtalab, Nika; Podimata, Chara; Yang, Kunhe (December 2023, Advances in Neural Information Processing Systems 36 (NeurIPS 2023))

   In this paper, we introduce a generalization of the standard Stackelberg Games (SGs) framework: Calibrated Stackelberg Games. In CSGs, a principal repeatedly interacts with an agent who (contrary to standard SGs) does not have direct access to the principal's action but instead best responds to calibrated forecasts about it. CSG is a powerful modeling tool that goes beyond assuming that agents use ad hoc and highly specified algorithms for interacting in strategic settings to infer the principal's actions and thus more robustly addresses real-life applications that SGs were originally intended to capture. Along with CSGs, we also introduce a stronger notion of calibration, termed adaptive calibration, that provides fine-grained any-time calibration guarantees against adversarial sequences. We give a general approach for obtaining adaptive calibration algorithms and specialize them for finite CSGs. In our main technical result, we show that in CSGs, the principal can achieve utility that converges to the optimum Stackelberg value of the game both in finite and continuous settings and that no higher utility is achievable. Two prominent and immediate applications of our results are the settings of learning in Stackelberg Security Games and strategic classification, both against calibrated agents. 

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3. Incentive Mechanisms for Strategic Classification and Regression Problems

   https://doi.org/10.1145/3490486.3538300  

   Jin, Kun; Zhang, Xueru; Khalili, Mohammad Mahdi; Naghizadeh, Parinaz; Liu, Mingyan (July 2022, ACM Conference on Economics and Computation (EC))

   We study the design of a class of incentive mechanisms that can effectively prevent cheating in a strategic classification and regression problem. A conventional strategic classification or regression problem is modeled as a Stackelberg game, or a principal-agent problem between the designer of a classifier (the principal) and individuals subject to the classifier's decisions (the agents), potentially from different demographic groups. The former benefits from the accuracy of its decisions, whereas the latter may have an incentive to game the algorithm into making favorable but erroneous decisions. While prior works tend to focus on how to design an algorithm to be more robust to such strategic maneuvering, this study focuses on an alternative, which is to design incentive mechanisms to shape the utilities of the agents and induce effort that genuinely improves their skills, which in turn benefits both parties in the Stackelberg game. Specifically, the principal and the mechanism provider (which could also be the principal itself) move together in the first stage, publishing and committing to a classifier and an incentive mechanism. The agents are (simultaneous) second movers and best respond to the published classifier and incentive mechanism. When an agent's strategic action merely changes its observable features, it hurts the performance of the algorithm. However, if the action leads to improvement in the agent's true label, it not only helps the agent achieve better decision outcomes, but also preserves the performance of the algorithm. We study how a subsidy mechanism can induce improvement actions, positively impact a number of social well-being metrics, such as the overall skill levels of the agents (efficiency) and positive or true positive rate differences between different demographic groups (fairness). 

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4. Leadership Inference for Multi-Agent Interactions

   https://doi.org/10.1109/LRA.2024.3381469  

   Khan, Hamzah I; Fridovich-Keil, David (May 2024, IEEE Robotics and Automation Letters)

   Effectively predicting intent and behavior requires inferring leadership in multi-agent interactions. Dynamic games provide an expressive theoretical framework for modeling these interactions. Employing this framework, we propose a novel method to infer the leader in a two-agent game by observing the agents’ behavior in complex, long-horizon interactions. We make two con- tributions. First, we introduce an iterative algorithm that solves dynamic two-agent Stackelberg games with nonlinear dynamics and nonquadratic costs, and demonstrate that it consistently converges in repeated trials. Second, we propose the Stackelberg Leadership Filter (SLF), an online method for identifying the leading agent in interactive scenarios based on observations of the game interactions. We validate the leadership filter’s efficacy on simulated driving scenarios to demonstrate that the SLF can draw conclusions about leadership that match right-of-way expectations. 

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5. 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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