Related papers: Lipschitz Continuity and Approximate Equilibria
In decision-dependent games, multiple players optimize their decisions under a data distribution that shifts with their joint actions, creating complex dynamics in applications like market pricing. A practical consequence of these dynamics…
Classical objectives in two-player zero-sum games played on graphs often deal with limit behaviors of infinite plays: e.g., mean-payoff and total-payoff in the quantitative setting, or parity in the qualitative one (a canonical way to…
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…
We propose a general class of symmetric games called position-optimization games. Given a probability distribution $Q$ over a set of targets $\mathcal{Y}$, the $n$ players each choose a position in a space $\mathcal{X}$. A player's utility…
The strategy improvement algorithm for mean payoff games and parity games is a local improvement algorithm, just like the simplex algorithm for linear programs. Their similarity has turned out very useful: many lower bounds on running time…
Classical objectives in two-player zero-sum games played on graphs often deal with limit behaviors of infinite plays: e.g., mean-payoff and total-payoff in the quantitative setting, or parity in the qualitative one (a canonical way to…
We establish a priori error bounds for monotone stabilized finite element discretizations of stationary second-order mean field games (MFG) on Lipschitz polytopal domains. Under suitable hypotheses, we prove that the approximation is…
We tackle a fundamental problem in empirical game-theoretic analysis (EGTA), that of learning equilibria of simulation-based games. Such games cannot be described in analytical form; instead, a black-box simulator can be queried to obtain…
Through a stochastic control theoretic approach, we analyze reputation games where a strategic long-lived player acts in a sequential repeated game against a collection of short-lived players. The key assumption in our model is that the…
We show that the shortfall risk of binomial approximations of game (Israeli) options converges to the shortfall risk in the corresponding Black--Scholes market considering Lipschitz continuous path-dependent payoffs for both discrete- and…
We introduce a notion of subgames for stochastic timing games and the related notion of subgame-perfect equilibrium in possibly mixed strategies. While a good notion of subgame-perfect equilibrium for continuous-time games is not available…
Simple stochastic games are turn-based 2.5-player games with a reachability objective. The basic question asks whether one player can ensure reaching a given target with at least a given probability. A natural extension is games with a…
In this paper, we provide an effective characterization of all the subgame-perfect equilibria in infinite duration games played on finite graphs with mean-payoff objectives. To this end, we introduce the notion of requirement, and the…
We prove that, under appropriate conditions, an abstract game with quasi-Leontief payoff functions $u_i : \prod_{j=1}^nX_j\to\mathbb{R}$ has a Nash equilibria. When all the payoff functions are globally quasi-Leontief, the existence and the…
We study nondeterministic strategies in parity games with the aim of computing a most permissive winning strategy. Following earlier work, we measure permissiveness in terms of the average number/weight of transitions blocked by the…
Penalty methods are a well known class of algorithms for constrained optimization. They transform a constrained problem into a sequence of unconstrained \emph{penalized} problems in the hope that approximate solutions of the latter converge…
We prove a rate of convergence for finite element approximations of stationary, second-order mean field games with nondifferentiable Hamiltonians posed in general bounded polytopal Lipschitz domains with strongly monotone running costs. In…
Lipschitz learning is a graph-based semi-supervised learning method where one extends labels from a labeled to an unlabeled data set by solving the infinity Laplace equation on a weighted graph. In this work we prove uniform convergence…
This paper investigates value function approximation in the context of zero-sum Markov games, which can be viewed as a generalization of the Markov decision process (MDP) framework to the two-agent case. We generalize error bounds from MDPs…
We study the problem of computing approximate Nash equilibria of bimatrix games, in a setting where players initially know their own payoffs but not the payoffs of the other player. In order for a solution of reasonable quality to be found,…