Session: Mechanism and Pricing Designs in Stochastic Decision Making
Chair: Frédy Pokou
Cluster:
Talk 1: Incentive Design in Nonsmooth Games
Speaker: Frédy Pokou
Abstract: Considering the growing trend towards integrated human-in-the-loop systems, incorporating irrational behaviors into game-theoretic models that allow to closely reflect human-beings attitudes towards risk is of high relevance. Ultimately, understanding how agents with different risk preferences interact can better inform the mechanism designer and provide guidelines on how to effectively steer agents towards improved collective and individual outcomes. To this end, we study non-cooperative stochastic games, where agents display irrational behaviors in response to underlying risk factors. Our formulation incorporates Prospect Theory (PT), a behavioral model used to describe agents’ risk attitude. We show that the resulting nonconvex nonsmooth game admits equilibria and we quantify the suboptimality induced by irrational behaviors. Then, we extend our PT-based game to an incentive-design problem formulated as a decision-dependent learning game, enabling us to cope with the multiplicity of solutions of the lower-level problem. In this setting, we provide a distributed algorithm with provable convergence, allowing the incentives to adapt dynamically to the information received in a feedback-loop approach. The results are applied to a local energy community involving strategic end users exposed to two-part tariffs.
Talk 2: Distributionally Fair Two-stage Stochastic Programming by Bilevel Optimization
Speaker: Yutian He
Abstract: Two-stage stochastic programming (TSSP) is a fundamental framework for decision-making under uncertainty, where a first-stage decision is made before uncertainty is realized, followed by scenario-dependent second-stage decisions. While most TSSP literature focuses on cost minimization, fairness considerations in decision-making have largely been overlooked. Recently, Ye et al (2025) studied a one-stage stochastic program subject to a distributional fairness constraint, but similar development under the two-stage setting is still unavailable. In this work, we propose two models of TSSP under distributional fairness constraints: one where the first- and second-stage decision-makers collaborate to ensure fairness, and another where only the first-stage decision-maker wants to ensure fairness, while the second-stage decision-maker only aims at minimizing the cost. To solve these models, we approximate the expectations by sample average and then reformulate them as mixed integer nonlinear programs. For large instances, we further develop an alternating minimization method to efficiently solve our problems, providing faster solutions.
Talk 3: Robust Bilevel Optimization with Wait-and-See Follower: A Column-and-Constraint Generation Approach
Speaker: Henri Lefebvre
Abstract: Bilevel optimization is a classical framework for modeling hierarchical decision-making processes. Typically, it is assumed that all input parameters for both the leader and the follower are known when the leader makes a decision. However, in many real-world applications, the leader must decide without fully anticipating the follower's response due to uncertainties in the follower's problem. In this talk, we address robust bilevel optimization problems in which the follower adopts a ``wait-and-see'' approach. Thus, the leader decides without knowledge of the explicit realization of the uncertainty, then the uncertainty realizes in a worst-case manner, and afterward the follower's decisions are made. For this challenging problem class, we discuss mathematical properties and present a corresponding solution approach based on column-and-constraint generation. The convergence of the proposed algorithm is discussed along with its practical implementation including numerical results. We finally outline potential research directions.
