Related papers: An experimental analysis of Lemke-Howson algorithm
Aiming to provide a new class of game dynamics with good long-term rationality properties, we derive a second-order inertial system that builds on the widely studied "heavy ball with friction" optimization method. By exploiting a well-known…
In this letter, we study dynamic game optimal control with imperfect state observations and introduce an iterative method to find a local Nash equilibrium. The algorithm consists of an iterative procedure combining a backward recursion…
We consider quadratic, nonmonotone generalized Nash equilibrium problems with symmetric interactions among the agents. Albeit this class of games is known to admit a potential function, its formal expression can be unavailable in several…
We study the complexity of computing a uniform Nash equilibrium on a non-win-lose bimatrix game. It is known that such a problem is NP-complete even if a bimatrix game is win-lose (Bonifaci et al., 2008). Fortunately, if a win-lose bimatrix…
In this paper, we study a distributed continuous-time design for aggregative games with coupled constraints in order to seek the generalized Nash equilibrium by a group of agents via simple local information exchange. To solve the problem,…
In this paper, we propose a method for solving a PPAD-complete problem [Papadimitriou, 1994]. Given is the payoff matrix $C$ of a symmetric bimatrix game $(C, C^T)$ and our goal is to compute a Nash equilibrium of $(C, C^T)$. In this paper,…
Fictitious play has recently emerged as the most accurate scalable algorithm for approximating Nash equilibrium strategies in multiplayer games. We show that the degree of equilibrium approximation error of fictitious play can be…
In this work, we study the sample complexity of obtaining a Nash equilibrium (NE) estimate in two-player zero-sum matrix games with noisy feedback. Specifically, we propose a novel algorithm that repeatedly solves linear programs (LPs) to…
This paper proposes a novel approach for local convergence to Nash equilibrium in quadratic noncooperative games based on a distributed Lie-bracket extremum seeking control scheme. This is the first instance of noncooperative games being…
In this paper, we study the distributed generalized Nash equilibrium seeking problem of non-cooperative games in dynamic environments. Each player in the game aims to minimize its own time-varying cost function subject to a local action…
We consider a multi-player stochastic differential game with linear McKean-Vlasov dynamics and quadratic cost functional depending on the variance and mean of the state and control actions of the players in open-loop form. Finite and…
Designing efficient algorithms to find Nash equilibrium (NE) refinements in sequential games is of paramount importance in practice. Indeed, it is well known that the NE has several weaknesses, since it may prescribe to play sub-optimal…
In recent years, randomized algorithms have established themselves as fundamental tools in computational linear algebra, with applications in scientific computing, machine learning, and quantum information science. Many randomized matrix…
We consider multi-agent decision making where each agent optimizes its convex cost function subject to individual and coupling constraints. The constraint sets are compact convex subsets of a Euclidean space. To learn Nash equilibria, we…
In large-scale games, approximating the opponent's strategy space with a small portfolio of representative strategies is a common and powerful technique. However, the construction of these portfolios often relies on domain-specific…
To optimally select a generalized Nash equilibrium, in this paper, we propose a semi-decentralized algorithm based on a double-layer Tikhonov regularization method. Technically, we extend the Tikhonov method for equilibrium selection in…
Modern random access mechanisms combine packet repetitions with multi-user detection mechanisms at the receiver to maximize the throughput and reliability in massive Internet of Things (IoT) scenarios. However, optimizing the access policy,…
Autonomous racing extends beyond the challenge of controlling a racecar at its physical limits. Professional racers employ strategic maneuvers to outwit other competing opponents to secure victory. While modern control algorithms can…
In this paper, we consider the problem of finding a Nash equilibrium in a multi-player game over generally connected networks. This model differs from a conventional setting in that players have partial information on the actions of their…
We develop provably efficient reinforcement learning algorithms for two-player zero-sum finite-horizon Markov games with simultaneous moves. To incorporate function approximation, we consider a family of Markov games where the reward…