Session: Mechanism and Pricing Designs in Stochastic Decision Making
Chair: Helene Le Cadre
Cluster: nan
Talk 1: Incentive Design in Nonsmooth Games
Speaker: Helene Le Cadre
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: Competitive Demand Learning: A Non-cooperative Pricing Algorithm with Coordinated Price Experimentation
Speaker: Yu-Ching Lee
Abstract: We consider a periodical equilibrium pricing problem for multiple firms over a planning horizon of $T$ periods. At each period, firms set their selling prices and receive stochastic demand from consumers. Firms do not know their underlying demand curve, but they wish to determine the selling prices to maximize total revenue under competition. Hence, they have to do some price experiments such that the observed demand data are informative to make price decisions. However, uncoordinated price updating can render the demand information gathered by price experimentation less informative or inaccurate. We design a nonparametric learning algorithm to facilitate coordinated dynamic pricing, in which competitive firms estimate their demand functions based on observations and adjust their pricing strategies in a prescribed manner. We show that the pricing decisions, determined by estimated demand functions, converge to underlying equilibrium as time progresses. {We obtain a bound of the revenue difference that has an order of $\mathcal{O}(F^2T^{3/4})$ and a regret bound that has an order of $\mathcal{O}(F\sqrt{T})$ with respect to the number of the competitive firms~$F$ and $T$.} We also develop a modified algorithm to handle the situation where some firms may have the knowledge of the demand curve.
