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We focus on the design of algorithms for finding equilibria in 2-player zero-sum games. Although it is well known that such problems can be solved by a single linear program, there has been a surge of interest in recent years for simpler…
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 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…
Fully-discrete approximations of the Allen-Cahn equation are considered. In particular, we consider schemes of arbitrary order based on a discontinuous Galerkin (in time) approach combined with standard conforming finite elements (in…
We define a class of zero-sum games with combinatorial structure, where the best response problem of one player is to maximize a submodular function. For example, this class includes security games played on networks, as well as the problem…
Variational inequalities are a formalism that includes games, minimization, saddle point, and equilibrium problems as special cases. Methods for variational inequalities are therefore universal approaches for many applied tasks, including…
Statistical solutions are time-parameterized probability measures on spaces of integrable functions, that have been proposed recently as a framework for global solutions and uncertainty quantification for multi-dimensional hyperbolic system…
We present an algorithm to approximate the solutions to variational problems where set of admissible functions consists of convex functions. The main motivator behind this numerical method is estimating solutions to Adverse Selection…
A zero-sum differential game with controlled jump-diffusion driven state is considered, and studied using a combination of dynamic programming and viscosity solution techniques. We prove, under certain conditions, that the value of the game…
We analyze a two-player, nonzero-sum Dynkin game of stopping with incomplete information. We assume that each player observes his own Brownian motion, which is not only independent of the other player's Brownian motion but also not…
In this paper, we formulate a two-player zero-sum game under dynamic constraints defined by hybrid dynamical equations. The game consists of a min-max problem involving a cost functional that depends on the actions and resulting solutions…
Implementation is a common problem with feedback laws with distributed delays. This paper focuses on a specific aspect of the implementation problem for predictor-based feedback laws: the problem of the approximation of the predictor…
We address payoff-based decentralized learning in infinite-horizon zero-sum Markov games. In this setting, each player makes decisions based solely on received rewards, without observing the opponent's strategy or actions nor sharing…
Probabilistic guarantees of safety and performance are important in constrained dynamical systems with stochastic uncertainty. We consider the stochastic reachability problem, which maximizes the probability that the state remains within…
The sequence form, owing to its compact and holistic strategy representation, has demonstrated significant efficiency in computing normal-form perfect equilibria for two-player extensive-form games with perfect recall. Nevertheless, the…
This paper considers a variational inequality (VI) problem arising from a game among multiple agents, where each agent aims to minimize its own cost function subject to its constrained set represented as the intersection of a (possibly…
This work proposes a novel distributed approach for computing a Nash equilibrium in convex games with merely monotone and restricted strongly monotone pseudo-gradients. By leveraging the idea of the centralized operator extrapolation method…
Complementarity problems and variational inequalities arise in a wide variety of areas, including machine learning, planning, game theory, and physical simulation. In all of these areas, to handle large-scale problem instances, we need fast…
We study a general smallest intersecting ball problem and its soft-margin variant in high-dimensional Euclidean spaces for input objects that are compact and convex. These two problems link and unify a series of fundamental problems in…
Nash equilibria provide a principled framework for modeling interactions in multi-agent decision-making and control. However, many equilibrium-seeking methods implicitly assume that each agent has access to the other agents' objectives and…