Related papers: Gradient Methods for Solving Stackelberg Games
This contribution deals with a two-level discrete decision problem, a so-called Stackelberg strategic game: A Subset Sum setting is addressed with a set $N$ of items with given integer weights. One distinguished player, the leader, may…
Stochastic optimal control and games have a wide range of applications, from finance and economics to social sciences, robotics, and energy management. Many real-world applications involve complex models that have driven the development of…
Stackelberg games (SGs) constitute the most fundamental and acclaimed models of strategic interactions involving some form of commitment. Moreover, they form the basis of more elaborate models of this kind, such as, e.g., Bayesian…
We study Stackelberg games where a principal repeatedly interacts with a non-myopic long-lived agent, without knowing the agent's payoff function. Although learning in Stackelberg games is well-understood when the agent is myopic, dealing…
Min-max formulations have attracted great attention in the ML community due to the rise of deep generative models and adversarial methods, while understanding the dynamics of gradient algorithms for solving such formulations has remained a…
In this paper, we introduce a generalization of the standard Stackelberg Games (SGs) framework: Calibrated Stackelberg Games (CSGs). In CSGs, a principal repeatedly interacts with an agent who (contrary to standard SGs) does not have direct…
We introduce the framework of LLM-Stackelberg games, a class of sequential decision-making models that integrate large language models (LLMs) into strategic interactions between a leader and a follower. Departing from classical Stackelberg…
We propose a single-level numerical approach to solve Stackelberg mean field game (MFG) problems. In Stackelberg MFG, an infinite population of agents play a non-cooperative game and choose their controls to optimize their individual…
Inverse game theory is utilized to infer the cost functions of all players based on game outcomes. However, existing inverse game theory methods do not consider the learner as an active participant in the game, which could significantly…
In a Stackelberg congestion game (SCG), a leader aims to maximize their own gain by anticipating and manipulating the equilibrium state at which the followers settle by playing a congestion game. Often formulated as bilevel programs,…
Stackelberg games are a classic example of bilevel optimization problems, which are often encountered in game theory and economics. These are complex problems with a hierarchical structure, where one optimization task is nested within the…
Stackelberg games originate where there are market leaders and followers, and the actions of leaders influence the behavior of the followers. Mathematical modelling of such games results in what's called a Bilevel Optimization problem.…
We propose the concept of a Lagrangian game to solve constrained Markov games. Such games model scenarios where agents face cost constraints in addition to their individual rewards, that depend on both agent joint actions and the evolving…
We formulate a general framework for competitive gradient-based learning that encompasses a wide breadth of multi-agent learning algorithms, and analyze the limiting behavior of competitive gradient-based learning algorithms using dynamical…
Optimizing strategic decisions (a.k.a. computing equilibrium) is key to the success of many non-cooperative multi-agent applications. However, in many real-world situations, we may face the exact opposite of this game-theoretic problem --…
Stackelberg equilibria arise naturally in a range of popular learning problems, such as in security games or indirect mechanism design, and have received increasing attention in the reinforcement learning literature. We present a general…
Bilevel optimization has been recently applied to many machine learning tasks. However, their applications have been restricted to the supervised learning setting, where static objective functions with benign structures are considered. But…
Artificially intelligent agents are increasingly being integrated into human decision-making: from large language model (LLM) assistants to autonomous vehicles. These systems often optimize their individual objective, leading to conflicts,…
This paper investigates the convergence of learning dynamics in Stackelberg games. In the class of games we consider, there is a hierarchical game being played between a leader and a follower with continuous action spaces. We establish a…
Playing repeated matrix games (RMG) while maximizing the cumulative returns is a basic method to evaluate multi-agent learning (MAL) algorithms. Previous work has shown that $UCB$, $M3$, $S$ or $Exp3$ algorithms have good behaviours on…