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We explore static noise in a discrete quantum random walk over a homogeneous cyclic graph, focusing on spectral and dynamical properties. Using a three-parameter unitary coin, we control the spectral structure of the noiseless step operator…

We study the existence of mixed-strategy equilibria in concurrent games played on graphs. While existence is guaranteed with safety objectives for each player, Nash equilibria need not exist when players are given arbitrary terminal-reward…

Multistage robust optimization problems can be interpreted as two-person zero-sum games between two players. We exploit this game-like nature and utilize a game tree search in order to solve quantified integer programs (QIPs). In this…

A game-theoretic model is proposed to study the cross-layer problem of joint power and rate control with quality of service (QoS) constraints in multiple-access networks. In the proposed game, each user seeks to choose its transmit power…

We study the query complexity of approximate notions of Nash equilibrium in games with a large number of players $n$. Our main result states that for $n$-player binary-action games and for constant $\varepsilon$, the query complexity of an…

Towards characterizing the optimization landscape of games, this paper analyzes the stability of gradient-based dynamics near fixed points of two-player continuous games. We introduce the quadratic numerical range as a method to…

Quantum information processing faces a significant hurdle: noise. Different noise sources induce varying errors in quantum operations depending on the underlying dynamics. To gain a deeper understanding of these error mechanisms, we…

We study the foundations of empirical equilibrium, a refinement of Nash equilibrium that is based on a non-parametric characterization of empirical distributions of behavior in games (Velez and Brown,2020b arXiv:1907.12408). The refinement…

We show a simple method for constructing an infinite family of graph formation games with link bias so that the resulting games admits, as a \textit{pairwise stable} solution, a graph with an arbitrarily specified degree distribution.…

In this paper we study the problem of exact recovery of the pure-strategy Nash equilibria (PSNE) set of a graphical game from noisy observations of joint actions of the players alone. We consider sparse linear influence games --- a…

Quantum effects are known to provide an advantage in particle transfer across networks. In order to achieve this advantage, requirements on both a graph type and a quantum system coherence must be found. Here we show that the process of…

The Kelly or proportional allocation mechanism is a simple and efficient auction-based scheme that distributes an infinitely divisible resource proportionally to the agents bids. When agents are aware of the allocation rule, their…

We study binary coordination games over graphs under log-linear learning when neighbor actions are conveyed through explicit noisy communication links. Each edge is modeled as either a binary symmetric channel (BSC) or a binary erasure…

We study the role of local effects and finite size effects in reaching coordination and in equilibrium selection in different types of two-player coordination games. We investigate three update rules -- the replicator dynamics (RD), the…

Game theory is playing more and more important roles in understanding complex systems and in investigating intelligent machines with various uncertainties. As a starting point, we consider the classical two-player zero-sum linear-quadratic…

We consider a class of two-player dynamic stochastic nonzero-sum games where the state transition and observation equations are linear, and the primitive random variables are Gaussian. Each controller acquires possibly different dynamic…

We propose a scheme to distribute graph states over quantum networks in the presence of noise in the channels and in the operations. The protocol can be implemented efficiently for large graph sates of arbitrary (complex) topology. We…

In a scenario where data-storage qubits are kept in isolation as far as possible, with minimal measurements and controls, noise mitigation can still be done using additional noise probes, with corrections applied only when needed. Motivated…

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 introduce a two-player nonlocal game, called the $(G,H)$-isomorphism game, where classical players can win with certainty if and only if the graphs $G$ and $H$ are isomorphic. We then define the notions of quantum and non-signalling…