Related papers: Parity Games: Zielonka's Algorithm in Quasi-Polyno…
This paper provides effective methods for the polyhedral formulation of impartial finite combinatorial games as lattice games. Given a rational strategy for a lattice game, a polynomial time algorithm is presented to decide (i) whether a…
Traditionally, there are several polynomial algorithms for linear programming including the ellipsoid method, the interior point method and other variants. Recently, Chubanov [Chubanov, 2015] proposed a projection and rescaling algorithm,…
We present efficient algorithms for computing optimal or approximately optimal strategies in a zero-sum game for which Player I has n pure strategies and Player II has an arbitrary number of pure strategies. We assume that for any given…
We describe how to approximate, in quasi-polynomial time, the largest independent set of polygons, in a given set of polygons. Our algorithm works by extending the result of Adamaszek and Wiese \cite{aw-asmwi-13, aw-qmwis-14} to polygons of…
We introduce perfect half space games, in which the goal of Player 2 is to make the sums of encountered multi-dimensional weights diverge in a direction which is consistent with a chosen sequence of perfect half spaces (chosen dynamically…
We develop value iteration-based algorithms to solve in a unified manner different classes of combinatorial zero-sum games with mean-payoff type rewards. These algorithms rely on an oracle, evaluating the dynamic programming operator up to…
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 study polynomial-time approximation algorithms for (edge/vertex) Sparsest Cut and Small Set Expansion in terms of $k$, the number of edges or vertices cut in the optimal solution. Our main results are $\mathcal{O}(\text{polylog}\,…
In this paper, we present a polynomial-time algorithm that approximates sufficiently high-value Max 2-CSPs on sufficiently dense graphs to within $O(N^{\varepsilon})$ approximation ratio for any constant $\varepsilon > 0$. Using this…
An extensive literature in economics and social science addresses contests, in which players compete to outperform each other on some measurable criterion, often referred to as a player's score, or output. Players incur costs that are an…
This article analyses the simple projection method proposed by Izuchukwu et al. [8, Algorithm 3.2] for solving variational inequality problems by incorporating momentum terms. A new step size strategy is also introduced, in which the step…
We study the problem of computing an $\epsilon$-approximate Nash equilibrium of a two-player, bilinear game with a bounded payoff matrix $A \in \mathbb{R}^{m \times n}$, when the players' strategies are constrained to lie in simple sets. We…
The Nash equilibrium is an important benchmark for behaviour in systems of strategic autonomous agents. Polymatrix games are a succinct and expressive representation of multiplayer games that model pairwise interactions between players. The…
Stochastic games are a classical model in game theory in which two opponents interact and the environment changes in response to the players' behavior. The central solution concepts for these games are the discounted values and the value,…
Many analysis and verifications tasks, such as static program analyses and model-checking for temporal logics reduce to the solution of systems of equations over suitable lattices. Inspired by recent work on lattice-theoretic progress…
We investigate the computation of equilibria in extensive-form games where ex ante correlation is possible, focusing on correlated equilibria requiring the least amount of communication between the players and the mediator. Motivated by the…
Temporal graphs are a popular modelling mechanism for dynamic complex systems that extend ordinary graphs with discrete time. Simply put, time progresses one unit per step and the availability of edges can change with time. We consider the…
Continuous games are multiplayer games in which strategy sets are compact and utility functions are continuous. These games typically have a highly complicated structure of Nash equilibria, and numerical methods for the equilibrium…
We conjecture that PPAD has a PCP-like complete problem, seeking a near equilibrium in which all but very few players have very little incentive to deviate. We show that, if one assumes that this problem requires exponential time, several…
Combinatorial games lead to several interesting, clean problems in algorithms and complexity theory, many of which remain open. The purpose of this paper is to provide an overview of the area to encourage further research. In particular, we…