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Related papers: Parallel Repetition for $3$-Player XOR Games

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The domatic number of a graph is the maximum number of pairwise disjoint dominating sets admitted by the graph. We introduce a game based around this graph invariant. The domatic number game is played on a graph $G$ by two players, Alice…

Combinatorics · Mathematics 2025-08-15 Bert L. Hartnell , Douglas F. Rall

We give an explicit family of XOR games with O(n)-bit questions requiring 2^n ebits to play near-optimally. More generally we introduce a new technique for proving lower bounds on the amount of entanglement required by an XOR game: we show…

Quantum Physics · Physics 2015-05-19 William Slofstra

We study a competitive optimization version of $\alpha'(G)$, the maximum size of a matching in a graph $G$. Players alternate adding edges of $G$ to a matching until it becomes a maximal matching. One player (Max) wants that matching to be…

Combinatorics · Mathematics 2015-08-06 Daniel W. Cranston , William B. Kinnersley , Suil O. , Douglas B. West

Dull, weak and nested solitaire games are important classes of parity games, capturing, among others, alternation-free mu-calculus and ECTL* model checking problems. These classes can be solved in polynomial time using dedicated algorithms.…

Logic in Computer Science · Computer Science 2013-07-18 Maciej Gazda , Tim A. C. Willemse

In this work we show a barrier towards proving a randomness-efficient parallel repetition, a promising avenue for achieving many tight inapproximability results. Feige and Kilian (STOC'95) proved an impossibility result for…

Computational Complexity · Computer Science 2016-07-26 Dana Moshkovitz , Govind Ramnarayan , Henry Yuen

We introduce two-player games which build words over infinite alphabets, and we study the problem of checking the existence of winning strategies. These games are played by two players, who take turns in choosing valuations for variables…

Logic in Computer Science · Computer Science 2023-06-22 Diego Figueira , Anirban Majumdar , M. Praveen

We consider game-theoretically secure distributed protocols for coalition games that approximate the Shapley value with small multiplicative error. Since all known existing approximation algorithms for the Shapley value are randomized, it…

Computer Science and Game Theory · Computer Science 2024-12-30 T-H. Hubert Chan , Qipeng Kuang , Quan Xue

In the graph sharing game, two players share a connected graph $G$ with non-negative weights assigned to the vertices, claiming and collecting the vertices of $G$ one by one, while keeping the set of all claimed vertices connected through…

Combinatorics · Mathematics 2017-04-21 Adam Gągol , Piotr Micek , Bartosz Walczak

The classical (parallel) black pebbling game is a useful abstraction which allows us to analyze the resources (space, space-time, cumulative space) necessary to evaluate a function $f$ with a static data-dependency graph $G$. Of particular…

Quantum Physics · Physics 2022-10-13 Jeremiah Blocki , Blake Holman , Seunghoon Lee

We show that given an explicit description of a multiplayer game, with a classical verifier and a constant number of players, it is QMA-hard, under randomized reductions, to distinguish between the cases when the players have a strategy…

Quantum Physics · Physics 2019-02-12 Anand Natarajan , Thomas Vidick

In this paper, we analyze linear-quadratic stochastic differential games with a continuum of players interacting through graphon aggregates, each state being subject to idiosyncratic Brownian shocks. The major technical issue is the joint…

Probability · Mathematics 2021-05-27 Alexander Aurell , Rene Carmona , Mathieu Lauriere

This paper studies two-player zero-sum repeated Bayesian games in which every player has a private type that is unknown to the other player, and the initial probability of the type of every player is publicly known. The types of players are…

Computer Science and Game Theory · Computer Science 2017-11-08 Lichun Li , Cedric Langbort , Jeff Shamma

We consider multi-player graph games with partial-observation and parity objective. While the decision problem for three-player games with a coalition of the first and second players against the third player is undecidable, we present a…

Logic in Computer Science · Computer Science 2014-04-23 Krishnendu Chatterjee , Laurent Doyen

Recent results showed it was possible to determine if a modest size 3XOR game has a perfect quantum strategy. We build on these and give an explicit polynomial time algorithm which constructs such a perfect strategy or refutes its…

Quantum Physics · Physics 2022-09-13 Adam Bene Watts , J. William Helton , Zehong Zhao

We show the equivalence between the existence of winning strategies for $G_{\delta \sigma}$ (also called $\Sigma^{0}_{3}$) games in Cantor or Baire space, and the existence of functions generalized-recursive in a higher type-2 functional.…

Logic · Mathematics 2015-10-01 P. D. Welch

We analyze optimal, and approximately optimal, quantum strategies for a variety of non-local XOR games. Building upon previous arguments due to Ostrev in 2016, which characterized approximately optimal, and optimal, strategies that players…

Quantum Physics · Physics 2024-08-08 Pete Rigas

The non-local game scenario provides a powerful framework to study the limitations of classical and quantum correlations, by studying the upper bounds of the winning probabilities those correlations offer in cooperation games where…

Quantum Physics · Physics 2020-07-07 Ricardo Faleiro

In 1901, Bouton proved that a winning strategy of the game of Nim is given by the bitwise XOR, called the nim-sum. But, why does such a weird binary operation work? Led by this question, this paper introduces a categorical reinterpretation…

Combinatorics · Mathematics 2025-11-17 Ryuya Hora

We consider quantum XOR games, defined in [11], from the perspective of unitary correlations defined in [7]. We show that Connes' embedding problem has a positive answer if and only if every quantum XOR game has entanglement bias equal to…

Operator Algebras · Mathematics 2018-01-11 Samuel J. Harris

Covering spaces of graphs have long been useful for studying expanders (as "graph lifts") and unique games (as the "label-extended graph"). In this paper we advocate for the thesis that there is a much deeper relationship between…

Computational Complexity · Computer Science 2018-03-20 Joshua A. Grochow , Jamie Tucker-Foltz