Related papers: Noncommutative Nullstellens\"atze and Perfect Game…

By results of Dantzig (1951) and Adler (2013), computing the optimal solutions of a linear program is equivalent to finding optimal strategies in zero-sum bimatrix games. Dantzig's original result was incomplete, in the sense that the…

Many recent AI architectures are inspired by zero-sum games, however, the behavior of their dynamics is still not well understood. Inspired by this, we study standard gradient descent ascent (GDA) dynamics in a specific class of non-convex…

This article extends the classical Real Nullstellensatz to matrices of polynomials in a free $\ast$-algebra $\RR\axs$ with $x=(x_1, \ldots, x_n)$. This result is a generalization of a result of Cimpri\vc, Helton, McCullough, and the author.…

This article takes up the challenge of extending the classical Real Nullstellensatz of Dubois and Risler to left ideals in a *-algebra A. After introducing the notions of non-commutative zero sets and real ideals, we develop three themes…

First, we consider the problem of deciding whether a nonlocal game admits a perfect entangled strategy that uses projective measurements on a maximally entangled shared state. Via a polynomial-time Karp reduction, we show that independent…

Coordination games with explicit spatial or relational structure are of interest to economists, ecologists, sociologists, and others studying emergent global properties in collective behavior. When assemblies of individuals seek to…

The geometric form of Hilbert's Nullstellensatz may be understood as a property of "geometric saturation" in algebraically closed fields. We conceptualise this property in the language of first order logic, following previous approaches and…

Two-player (antagonistic) games on (possibly stochastic) graphs are a prevalent model in theoretical computer science, notably as a framework for reactive synthesis. Optimal strategies may require randomisation when dealing with inherently…

We give an operator-algebraic formulation of robust self-testing in terms of states on C*-algebras. We show that a quantum correlation p is a robust self-test only if among all (abstract) states, there is a unique one achieving p. We show…

We investigate quantum and nonsignaling generalizations of perfect matchings in graphs using nonlocal games. Specifically, we introduce nonlocal games that test for $L$-perfect matchings in bipartite graphs, perfect matchings in general…

We introduce and study the class of semidefinite games, which generalizes bimatrix games and finite $N$-person games, by replacing the simplex of the mixed strategies for each player by a slice of the positive semidefinite cone in the space…

In classical game theory, optimal strategies are determined for games with complete information; this requires knowledge of the opponent's goals. We analyze games when a player is mistaken about their opponents goals. For definitiveness, we…

Optimization under uncertainty is a fundamental problem in learning and decision-making, particularly in multi-agent systems. Previously, Feldman, Kalai, and Tennenholtz [2010] demonstrated the ability to efficiently compete in repeated…

Optimal behavior in (competitive) situation is traditionally determined with the help of utility functions that measure the payoff of different actions. Given an ordering on the space of revenues (payoffs), the classical axiomatic approach…

We study new classes of games, called zero-sum equivalent games and zero-sum equivalent potential games, and prove decomposition theorems involving these classes of games. We say that two games are "strategically equivalent" if, for every…

This paper introduces a new solution concept for non-cooperative games in normal form with no ties and pure strategies: the Perfectly Transparent Equilibrium. The players are rational in all possible worlds and know each other's strategies…

We consider zero-sum stochastic games with perfect information and finitely many states and actions. The payoff is computed by a function which associates to each infinite sequence of states and actions a real number. We prove that if the…

This paper presents new families of algorithms for the repeated play of two-agent (near) zero-sum games and two-agent zero-sum stochastic games. For example, the family includes fictitious play and its variants as members. Commonly, the…

The article introduces a notion of a stochastic game with failure states and proposes two logical systems with modality "coalition has a strategy to transition to a non-failure state with a given probability while achieving a given goal."…

Preordered semialgebras and semirings are two kinds of algebraic structures occurring in real algebraic geometry frequently and usually play important roles therein. They have many interesting and promising applications in the fields of…