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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…
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…
Regret minimization is a general approach to online optimization which plays a crucial role in many algorithms for approximating Nash equilibria in two-player zero-sum games. The literature mainly focuses on solving individual games in…
Recent literature on online learning has focused on developing adaptive algorithms that take advantage of a regularity of the sequence of observations, yet retain worst-case performance guarantees. A complementary direction is to develop…
In this paper, we consider the contextual variant of the MNL-Bandit problem. More specifically, we consider a dynamic set optimization problem, where a decision-maker offers a subset (assortment) of products to a consumer and observes the…
We introduce an online learning algorithm in the bandit feedback model that, once adopted by all agents of a congestion game, results in game-dynamics that converge to an $\epsilon$-approximate Nash Equilibrium in a polynomial number of…
Decentralized online learning for seeking generalized Nash equilibrium (GNE) of noncooperative games in dynamic environments is studied in this paper. Each player aims at selfishly minimizing its own time-varying cost function subject to…
In this paper, we consider the problem of resource congestion control for competing online learning agents. On the basis of non-cooperative game as the model for the interaction between the agents, and the noisy online mirror ascent as the…
We address learning Nash equilibria in convex games under the payoff information setting. We consider the case in which the game pseudo-gradient is monotone but not necessarily strictly monotone. This relaxation of strict monotonicity…
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…
We study the discrete Bertrand pricing game with a non-increasing demand function. The game has $n \ge 2$ players who simultaneously choose prices from the set $\{1/k, 2/k, \ldots, 1\}$, where $k\in\mathbb{N}$. The player who sets the…
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…
In this paper, we examine the Nash equilibrium convergence properties of no-regret learning in general N-player games. For concreteness, we focus on the archetypal follow the regularized leader (FTRL) family of algorithms, and we consider…
The framework of multi-agent learning explores the dynamics of how individual agent strategies evolve in response to the evolving strategies of other agents. Of particular interest is whether or not agent strategies converge to well known…
We study the repeated congestion game, in which multiple populations of players share resources, and make, at each iteration, a decentralized decision on which resources to utilize. We investigate the following question: given a model of…
We study a repeated game between a supplier and a retailer who want to maximize their respective profits without full knowledge of the problem parameters. After characterizing the uniqueness of the Stackelberg equilibrium of the stage game…
Learning to bid in repeated first-price auctions is a fundamental problem at the interface of game theory and machine learning, which has seen a recent surge in interest due to the transition of display advertising to first-price auctions.…
Competitive non-cooperative online decision-making agents whose actions increase congestion of scarce resources constitute a model for widespread modern large-scale applications. To ensure sustainable resource behavior, we introduce a novel…
This paper presents a new framework for analyzing and designing no-regret algorithms for dynamic (possibly adversarial) systems. The proposed framework generalizes the popular online convex optimization framework and extends it to its…
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…