Related papers: Solving Monotone Variational Inequalities with Bes…
Generating payoff matrices of normal-form games at random, we calculate the frequency of games with a unique pure strategy Nash equilibrium in the ensemble of $n$-player, $m$-strategy games. These are perfectly predictable as they must…
We consider a class of hierarchical noncooperative $N$-player games where the $i$th player solves a parametrized stochastic mathematical program with equilibrium constraints (MPEC) with the caveat that the implicit form of the $i$th…
Game-theoretic models are effective tools for modeling multi-agent interactions, especially when robots need to coordinate with humans. However, applying these models requires inferring their specifications from observed behaviors -- a…
Variational inequalities are a universal optimization paradigm that incorporate classical minimization and saddle point problems. Nowadays more and more tasks require to consider stochastic formulations of optimization problems. In this…
Adaptive momentum methods have recently attracted a lot of attention for training of deep neural networks. They use an exponential moving average of past gradients of the objective function to update both search directions and learning…
In this paper, we study multi-agent network games subject to affine time-varying coupling constraints and a time-varying communication network. We focus on the class of games adopting proximal dynamics and study their convergence to a…
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…
We study a class of semi-discrete variational problems that arise in economic matching and game theory, where agents with continuous attributes are matched to a finite set of outcomes with a one dimensional structure. Such problems appear…
We consider two-player normal form games where each player has the same finite strategy set. The payoffs of each player are assumed to be i.i.d. random variables with a continuous distribution. We show that, with high probability, the…
Variational inequalities (VIs) are a broad class of optimization problems encompassing machine learning problems ranging from standard convex minimization to more complex scenarios like min-max optimization and computing the equilibria of…
We study generalized games with full row rank equality constraints and we provide a strikingly simple proof of strong monotonicity of the associated KKT operator. This allows us to show linear convergence to a variational equilibrium of the…
We investigate a portfolio selection problem involving multi competitive agents, each exhibiting mean-variance preferences. Unlike classical models, each agent's utility is determined by their relative wealth compared to the average wealth…
Game theory has emerged as a powerful framework for modeling a large range of multi-agent scenarios. Many algorithmic solutions require discrete, finite games with payoffs that have a closed-form specification. In contrast, many real-world…
We study the convergence of best-response dynamics in Tullock contests with convex cost functions (these games always have a unique pure-strategy Nash equilibrium). We show that best-response dynamics rapidly converges to the equilibrium…
We consider multi-agent decision making where each agent's cost function depends on all agents' strategies. We propose a distributed algorithm to learn a Nash equilibrium, whereby each agent uses only obtained values of her cost function at…
Smooth game optimization has recently attracted great interest in machine learning as it generalizes the single-objective optimization paradigm. However, game dynamics is more complex due to the interaction between different players and is…
In finite games mixed Nash equilibria always exist, but pure equilibria may fail to exist. To assess the relevance of this nonexistence, we consider games where the payoffs are drawn at random. In particular, we focus on games where a large…
If a game has a unique Nash equilibrium, then this equilibrium is arguably the solution of the game from the refinement's literature point of view. However, it might be that for almost all initial conditions, all strategies in the support…
The distributed computation of equilibria and optima has seen growing interest in a broad collection of networked problems. We consider the computation of equilibria of convex stochastic Nash games characterized by a possibly nonconvex…
We consider seeking a Nash equilibrium (NE) of a monotone game, played by dynamic agents which are modeled as a class of lower-triangular nonlinear uncertain dynamics with external disturbances. We establish a general framework that…