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Contemporary applications of machine learning in two-team e-sports and the superior expressivity of multi-agent generative adversarial networks raise important and overlooked theoretical questions regarding optimization in two-team games.…
We study optimal execution in markets with transient price impact in a competitive setting with $N$ traders. Motivated by prior negative results on the existence of pure Nash equilibria, we consider randomized strategies for the traders and…
This paper studies a class of network games with linear-quadratic payoffs and externalities exerted through a strictly concave interaction function. This class of game is motivated by the diminishing marginal effects with peer influences.…
McLennan and Tourky (2010) showed that "imitation games" provide a new view of the computation of Nash equilibria of bimatrix games with the Lemke-Howson algorithm. In an imitation game, the payoff matrix of one of the players is the…
The distributed task allocation problem, as one of the most interesting distributed optimization challenges, has received considerable research attention recently. Previous works mainly focused on the task allocation problem in a population…
In this paper, we study the problem of multiple stochastic agents interacting in a dynamic game scenario with continuous state and action spaces. We define a new notion of stochastic Nash equilibrium for boundedly rational agents, which we…
Balancing safety, efficiency, and operational costs in highway driving poses a challenging decision-making problem for heavy-duty vehicles. A central difficulty is that conventional scalar reward formulations, obtained by aggregating these…
Combinatorial optimization algorithms for graph problems are usually designed afresh for each new problem with careful attention by an expert to the problem structure. In this work, we develop a new framework to solve any combinatorial…
We design a computational approach to find equilibria in a class of Nash games possessing a hierarchical structure. By using tools from mixed-integer optimization and the characterization of variational equilibria in terms of the…
This study investigates an adaptive pricing scheme aimed at achieving an efficient state in a traffic congestion game characterized by a diverse population of road users. While the planner possesses knowledge of players' preferences, their…
We propose a novel decision making framework for forming potential collaboration among otherwise competing agents in subsurface systems. The agents can be, e.g., groundwater, CO$_2$, or hydrogen injectors and extractors with conflicting…
Matrix games constitute a fundamental problem of game theory and describe a situation of two players with completely conflicting interests. We show how methods from statistical mechanics can be used to investigate the statistical properties…
How can we design mechanisms to promote efficient use of shared resources? Here, we answer this question in relation to the well-studied class of atomic congestion games, used to model a variety of problems, including traffic routing.…
The goal in this paper is to approximate the Price of Stability (PoS) in stochastic Nash games using stochastic approximation (SA) schemes. PoS is amongst the most popular metrics in game theory and provides an avenue for estimating the…
This paper proposes an asymmetric perturbation technique for solving bilinear saddle-point optimization problems, commonly arising in minimax problems, game theory, and constrained optimization. Perturbing payoffs or values is known to be…
In dynamic games with shared constraints, Generalized Nash Equilibria (GNE) are often computed using the normalized solution concept, which assumes identical Lagrange multipliers for shared constraints across all players. While widely used,…
When a centrally operated ride-hailing company considers to enter a market already served by another company, it has to make a strategic decision about how to distribute its fleet among different regions in the area. This decision will be…
Current fault-tolerant quantum compilers allocate error budgets uniformly during resource estimation, causing suboptimal physical resource overhead. We optimize this allocation using a potential game formulation, where Nash Equilibrium…
We propose a new hierarchical approach to understand the complexity of the open problem of computing a Nash equilibrium in a bimatrix game. Specifically, we investigate a hierarchy of bimatrix games $(A,B)$ which results from restricting…
We present multilinear and mixed-integer multilinear programs to find a Nash equilibrium in multi-player noncooperative games. We compare the formulations to common algorithms in Gambit, and conclude that a multilinear feasibility program…