arXiv subjects

Anna Maddux

Publications and source records attributed to Anna Maddux.

4 recordsLinked to original sources

arXiv2026

Finite-time convergence to an $ε$-efficient Nash equilibrium in potential games

This paper investigates the convergence time of log-linear learning to an $ε$-efficient Nash equilibrium in potential games, where an efficient Nash equilibrium is defined as the maximizer of the potential function. Previous literature provides asymptotic convergence rates to efficient Nash equilibria, and existing finite-time rates are limited to potential games with further assumptions such as the interchangeability of players. We prove the first finite-time convergence to an $ε$-efficient Nash equilibrium in general potential games. Our bounds depend polynomially on $1/ε$, an improvement over previous bounds for subclasses of potential games that are exponential in $1/ε$. We then strengthen our convergence result in two directions: first, we show that a variant of log-linear learning requiring a constant factor less feedback on the utility per round enjoys a similar convergence time; second, we demonstrate the robustness of our convergence guarantee if log-linear learning is subject to small perturbations such as alterations in the learning rule or noise-corrupted utilities.

cs.MA↗

arXiv2025

No-Regret Learning in Stackelberg Games with an Application to Electric Ride-Hailing

We consider the problem of efficiently learning to play single-leader multi-follower Stackelberg games when the leader lacks knowledge of the lower-level game. Such games arise in hierarchical decision-making problems involving self-interested agents. For example, in electric ride-hailing markets, a central authority aims to learn optimal charging prices to shape fleet distributions and charging patterns of ride-hailing companies. Existing works typically apply gradient-based methods to find the leader's optimal strategy. Such methods are impractical as they require that the followers share private utility information with the leader. Instead, we treat the lower-level game as a black box, assuming only that the followers' interactions approximate a Nash equilibrium while the leader observes the realized cost of the resulting approximation. Under kernel-based regularity assumptions on the leader's cost function, we develop a no-regret algorithm that converges to an $ε$-Stackelberg equilibrium in $O(\sqrt{T})$ rounds. Finally, we validate our approach through a numerical case study on optimal pricing in electric ride-hailing markets.

eess.SY↗

arXiv2025

Eliciting Truthful Feedback for Preference-Based Learning via the VCG Mechanism

We study resource allocation problems in which a central planner allocates resources among strategic agents with private cost functions in order to minimize a social cost, defined as an aggregate of the agents' costs. This setting poses two main challenges: (i) the agents' cost functions may be unknown to them or difficult to specify explicitly, and (ii) agents may misreport their costs strategically. To address these challenges, we propose an algorithm that combines preference-based learning with Vickrey-Clarke-Groves (VCG) payments to incentivize truthful reporting. Our algorithm selects informative preference queries via D-optimal design, estimates cost parameters through maximum likelihood, and computes VCG allocations and payments based on these estimates. In a one-shot setting, we prove that the mechanism is approximately truthful, individually rational, and efficient up to an error of $\tilde{\mathcal O}(K^{-1/2})$ for $K$ preference queries per agent. In an online setting, these guarantees hold asymptotically with sublinear regret at a rate of $\tilde{\mathcal O}(T^{2/3})$ after $T$ rounds. Finally, we validate our approach through a numerical case study on demand response in local electricity markets.

cs.GT↗

arXiv2025

On the characterization of constrained correlated equilibria in Markov games

Markov games with coupling constraints model constrained dynamical decision-making involving self-interested agents, where the feasibility of an individual agent's strategy depends on the joint strategies of the others. Such games arise in numerous real-world applications involving safety requirements and budget caps, for example, in environmental management, electricity markets, and transportation systems. In unconstrained dynamical decision-making, the correlated equilibrium has emerged as a desired solution concept, due to its computational tractability and amenability to learning algorithms. Understanding how coupling constraints shape correlated equilibria is a crucial step towards computing solutions in constrained Markov games. In this paper, we formalize and characterize the notion of constrained correlated equilibria for Markov games, defined as feasible joint policies where any unilateral deviation is either unprofitable or infeasible.

cs.GT↗