Related papers: Universal Algorithms for Parity Games and Nested F…

Data mining and knowledge discovery are two important growing research fields in the last two decades due to the abundance of data collected from various sources. The exponentially growing volumes of generated data urge the development of…

In cooperative game theory, the primary focus is the equitable allocation of payoffs or costs among agents. However, in the practical applications of cooperative games, accurately representing games is challenging. In such cases, using an…

We introduce the notions of w-lower semicontinuous and almost w-lower semicontinuous correspondence with respect to a given set and prove a new fixed-point theorem. We also introduce the notion of correspondence with e-LSCS-property. As…

The goal of this paper is to develop a generic framework for converting modern optimization algorithms into mechanisms where inputs come from self-interested agents. We focus on aggregating preferences from $n$ players in a context without…

Two-player graph games have found numerous applications, most notably in the synthesis of reactive systems from temporal specifications, but also in verification. The relevance of infinite-state systems in these areas has lead to…

In a two-player zero-sum graph game, the players move a token throughout a graph to produce an infinite play, which determines the winner of the game. Bidding games are graph games in which in each turn, an auction (bidding) determines…

Self-play via online learning is one of the premier ways to solve large-scale two-player zero-sum games, both in theory and practice. Particularly popular algorithms include optimistic multiplicative weights update (OMWU) and optimistic…

Many recent practical and theoretical breakthroughs focus on adversarial team multi-player games (ATMGs) in ex ante correlation scenarios. In this setting, team members are allowed to coordinate their strategies only before the game starts.…

In mean-payoff games, the objective of the protagonist is to ensure that the limit average of an infinite sequence of numeric weights is nonnegative. In energy games, the objective is to ensure that the running sum of weights is always…

Optimistic Gradient Descent Ascent (OGDA) and Optimistic Multiplicative Weights Update (OMWU) for saddle-point optimization have received growing attention due to their favorable last-iterate convergence. However, their behaviors for simple…

Nash equilibrium is a central concept in game theory. Several Nash solvers exist, yet none scale to normal-form games with many actions and many players, especially those with payoff tensors too big to be stored in memory. In this work, we…

The design of fixed point algorithms is at the heart of monotone operator theory, convex analysis, and of many modern optimization problems arising in machine learning and control. This tutorial reviews recent advances in understanding the…

Two-player games on graphs is central in many problems in formal verification and program analysis such as synthesis and verification of open systems. In this work we consider solving recursive game graphs (or pushdown game graphs) that can…

Parities have become a standard benchmark for evaluating learning algorithms. Recent works show that regular neural networks trained by gradient descent can efficiently learn degree $k$ parities on uniform inputs for constant $k$, but fail…

Motivated by a connection with the factorization of multivariate polynomials, we study integral convex polytopes and their integral decompositions in the sense of the Minkowski sum. We first show that deciding decomposability of integral…

This paper is an exposition of algorithms for finding one or all equilibria of a bimatrix game (a two-player game in strategic form) in the style of a chapter in a graduate textbook. Using labeled "best-response polytopes", we present the…

This paper investigates the distributed fixed point finding problem for a global operator over a directed and unbalanced multi-agent network, where the global operator is quasinonexpansive and only partially accessible to each individual…

Definable zero-sum stochastic games involve a finite number of states and action sets, reward and transition functions that are definable in an o-minimal structure. Prominent examples of such games are finite, semi-algebraic or globally…

We settle a long-standing open question in algorithmic game theory. We prove that Bimatrix, the problem of finding a Nash equilibrium in a two-player game, is complete for the complexity class PPAD Polynomial Parity Argument, Directed…

We introduce several methods of decomposition for two player normal form games. Viewing the set of all games as a vector space, we exhibit explicit orthonormal bases for the subspaces of potential games, zero-sum games, and their orthogonal…