Related papers: Quantum algorithms for zero-sum games
The framework outlined in [arXiv:2010.13024] provides an approximation algorithm for computing Nash equilibria of normal form games. Since NASH is a well-known PPAD-complete problem, this framework has potential applications to other $PPAD$…
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 present quantum algorithms for solving two problems regarding stochastic processes. The first algorithm prepares the thermal Gibbs state of a quantum system and runs in time almost linear in $\sqrt{N \beta/{\cal Z}}$ and polynomial in…
Game-theoretic approaches and Nash equilibrium have been widely applied across various engineering domains. However, practical challenges such as disturbances, delays, and actuator limitations can hinder the precise execution of Nash…
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…
This paper investigates Nash equilibrium (NE) seeking problems for noncooperative games over multi-players networks with finite bandwidth communication. A distributed quantized algorithm is presented, which consists of local gradient play,…
Computing Nash equilibria for strategic multi-agent systems is challenging for expensive black box systems. Motivated by the ubiquity of games involving exploitation of common resources, this paper considers the above problem for potential…
Nash equilibrium is a key concept in game theory fundamental for elucidating the equilibrium state of strategic interactions, finding applications in diverse fields such as economics, political science, and biology. However, the Nash…
In an $\epsilon$-Nash equilibrium, a player can gain at most $\epsilon$ by unilaterally changing his behaviour. For two-player (bimatrix) games with payoffs in $[0,1]$, the best-known$\epsilon$ achievable in polynomial time is 0.3393. In…
We investigate quantum algorithms for classification, a fundamental problem in machine learning, with provable guarantees. Given $n$ $d$-dimensional data points, the state-of-the-art (and optimal) classical algorithm for training…
We study the problem of finding the Nash equilibrium in a two-player zero-sum Markov game. Due to its formulation as a minimax optimization program, a natural approach to solve the problem is to perform gradient descent/ascent with respect…
We consider two classes of constrained finite state-action stochastic games. First, we consider a two player nonzero sum single controller constrained stochastic game with both average and discounted cost criterion. We consider the same…
We consider an algorithmic framework for two-player non-zero-sum semidefinite games, where each player's strategy is a positive semidefinite matrix with trace one. We formulate the computation of Nash equilibria in such games as…
Nash equilibrium has long been a desired solution concept in multi-player games, especially for those on continuous strategy spaces, which have attracted a rapidly growing amount of interests due to advances in research applications such as…
This paper presents a new primal-dual method for computing an equilibrium of generalized (continuous) Nash game (referred to as generalized Nash equilibrium problem (GNEP)) where each player's feasible strategy set depends on the other…
We explore the power of semidefinite programming (SDP) for finding additive $epsilon$-approximate Nash equilibria in bimatrix games. We introduce an SDP relaxation for a quadratic programming formulation of the Nash equilibrium (NE) problem…
Continuous games are multiplayer games in which strategy sets are compact and utility functions are continuous. These games typically have a highly complicated structure of Nash equilibria, and numerical methods for the equilibrium…
This paper studies the distributed generalized Nash equilibrium seeking problem for aggregative games with coupling constraints, where each player optimizes its strategy depending on its local cost function and the estimated strategy…
The Nash equilibrium is an important benchmark for behaviour in systems of strategic autonomous agents. Polymatrix games are a succinct and expressive representation of multiplayer games that model pairwise interactions between players. The…
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…