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Applications of combinatorial auctions (CA) as market mechanisms are prevalent in practice, yet their Bayesian Nash equilibria (BNE) remain poorly understood. Analytical solutions are known only for a few cases where the problem can be…
In this paper, an energy efficiency (EE) game in a MIMO multiple access channel (MAC) communication system is considered. The existence and the uniqueness of the Nash Equilibrium (NE) is affirmed. A bisection search algorithm is designed to…
We present a new algorithm for computing pure-strategy $\varepsilon$-Bayes-Nash equilibria ($\varepsilon$-BNEs) in combinatorial auctions with continuous value and action spaces. An essential innovation of our algorithm is to separate the…
In the domain of machine learning and game theory, the quest for Nash Equilibrium (NE) in extensive-form games with incomplete information is challenging yet crucial for enhancing AI's decision-making support under varied scenarios.…
Driven by the global decarbonization effort, the rapid integration of renewable energy into the conventional electricity grid presents new challenges and opportunities for the battery energy storage system (BESS) participating in the energy…
This paper provides the first expert sample complexity characterization for learning a Nash equilibrium from expert data in Markov Games. We show that a new quantity named the single policy deviation concentrability coefficient is…
We investigate Nash equilibrium learning in a competitive Markov Game (MG) environment, where multiple agents compete, and multiple Nash equilibria can exist. In particular, for an oligopolistic dynamic pricing environment, exact Nash…
We develop a scheme based on active learning to compute equilibria in a generalized Nash equilibrium problem (GNEP). Specifically, an external observer (or entity), with little knowledge on the multi-agent process at hand, collects sensible…
Save for some special cases, current training methods for Generative Adversarial Networks (GANs) are at best guaranteed to converge to a `local Nash equilibrium` (LNE). Such LNEs, however, can be arbitrarily far from an actual Nash…
It is a common practice in the current literature of electricity markets to use game-theoretic approaches for strategic price bidding. However, they generally rely on the assumption that the strategic bidders have prior knowledge of rival…
We consider the process of bidding by electricity suppliers in a day-ahead market context where each supplier bids a linear non-decreasing function of her generating capacity with the goal of maximizing her individual profit given other…
We introduce the use of generative adversarial learning to compute equilibria in general game-theoretic settings, specifically the generalized Nash equilibrium (GNE) in pseudo-games, and its specific instantiation as the competitive…
The concept of Nash equilibrium (NE), pivotal within game theory, has garnered widespread attention across numerous industries. Recent advancements introduced several quantum Nash solvers aimed at identifying pure strategy NE solutions…
With the growing penetration of renewable energy resource, electricity market prices have exhibited greater volatility. Therefore, it is important for Energy Storage Systems(ESSs) to leverage the multidimensional nature of energy market…
We study online optimization methods for zero-sum games, a fundamental problem in adversarial learning in machine learning, economics, and many other domains. Traditional methods approximate Nash equilibria (NE) using either regret-based…
The nested Extremum Seeking (nES) algorithm is a model-free optimization method that has been shown to converge to a neighborhood of a Nash equilibrium. In this work, we demonstrate that the same nES dynamics can instead be made to converge…
We address the generalized Nash equilibrium seeking problem in a partial-decision information scenario, where each agent can only exchange information with some neighbors, although its cost function possibly depends on the strategies of all…
This paper studies the fundamental problem of learning energy-based model (EBM) in the latent space of the generator model. Learning such prior model typically requires running costly Markov Chain Monte Carlo (MCMC). Instead, we propose to…
In this paper, we investigate the seeking of Nash equilibrium (NE) in a non-cooperative quadratic game where all agents exchange their delayed strategy information with their neighbors. To extend best-response algorithms to the delayed…
This paper addresses the problem of distributed online generalized Nash equilibrium (GNE) learning for multi-cluster games with delayed feedback information. Specifically, each agent in the game is assumed to be informed a sequence of local…