Related papers: A dynamic that evolves toward a Nash equilibrium
In this paper, we study the dynamic behavior of Hedge, a well-known algorithm in theoretical machine learning and algorithmic game theory. The empirical average (arithmetic mean) of the iterates Hedge generates is known to converge to a…
Distributed Nash equilibrium seeking of aggregative games is investigated and a continuous-time algorithm is proposed. The algorithm is designed by virtue of projected gradient play dynamics and distributed average tracking dynamics, and is…
This paper studies the last-iterate convergence properties of the exponential weights algorithm with constant learning rates. We consider a repeated interaction in discrete time, where each player uses an exponential weights algorithm…
Motivated by applications to data networks where fast convergence is essential, we analyze the problem of learning in generic N-person games that admit a Nash equilibrium in pure strategies. Specifically, we consider a scenario where…
We introduce a new class of population games that we call monotropic; these are games characterized by the presence of a unique globally neutrally stable Nash equilibrium. Monotropic games generalize strictly concave potential games and…
This work proposes a novel distributed approach for computing a Nash equilibrium in convex games with restricted strongly monotone pseudo-gradients. By leveraging the idea of the centralized operator extrapolation method presented in [4] to…
We use techniques from the statistical mechanics of disordered systems to analyse the properties of Nash equilibria of bimatrix games with large random payoff matrices. By means of an annealed bound, we calculate their number and analyse…
This paper introduces a new method to achieve stable convergence to Nash equilibrium in duopoly noncooperative games. Inspired by the recent fixed-time Nash Equilibrium seeking (NES) as well as prescribed-time extremum seeking (ES) and…
We consider a class of Wasserstein distributionally robust Nash equilibrium problems, where agents construct heterogeneous data-driven Wasserstein ambiguity sets using private samples and radii, in line with their individual risk-averse…
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 introduce a new hypothesis testing-based learning dynamics in which players update their strategies by combining hypothesis testing with utility-driven exploration. In this dynamics, each player forms beliefs about opponents' strategies…
We consider the basic problem of approximating Nash equilibria in noncooperative games. For monotone games, we design continuous time flows which converge in an averaged sense to Nash equilibria. We also study mean field equilibria, which…
We consider the problem of computing mixed Nash equilibria of two-player zero-sum games with continuous sets of pure strategies and with first-order access to the payoff function. This problem arises for example in game-theory-inspired…
Our work focuses on extra gradient learning algorithms for finding Nash equilibria in bilinear zero-sum games. The proposed method, which can be formally considered as a variant of Optimistic Mirror Descent…
This paper presents a new distributed algorithm that leverages heavy-ball momentum and a consensus-based gradient method to find a Nash equilibrium (NE) in a class of non-cooperative convex games with unconstrained action sets. In this…
We study the connection between the evolutionary replicator dynamics and the number of Nash equilibria in large random bi-matrix games. Using techniques of disordered systems theory we compute the statistical properties of both, the fixed…
We consider evolutionary dynamics for population games in which players have a continuum of strategies at their disposal. Models in this setting amount to infinite-dimensional differential equations evolving on the manifold of probability…
Dynamic nonzero sum games are widely used to model multi agent decision making in control, economics, and related fields. Classical methods for computing Nash equilibria, especially in linear quadratic settings, rely on strong structural…
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…
We show that, by using multiplicative weights in a game-theoretic thought experiment (and an important convexity result on the composition of multiplicative weights with the relative entropy function), a symmetric bimatrix game (that is, a…