Related papers: A Note on a Communication Game
The sensitivity conjecture is a longstanding conjecture concerning the relationship between the degree and sensitivity of a Boolean function. In 2015, a communication game was formulated by Justin Gilmer, Michal Kouck\'{y}, and Michael Saks…
One of the major outstanding foundational problems about boolean functions is the sensitivity conjecture, which (in one of its many forms) asserts that the degree of a boolean function (i.e. the minimum degree of a real polynomial that…
This paper considers a game-theoretic formulation of the covert communications problem with finite blocklength, where the transmitter (Alice) can randomly vary her transmit power in different blocks, while the warden (Willie) can randomly…
The Sensitivity Conjecture is a long-standing problem in theoretical computer science that seeks to fit the sensitivity of a Boolean function into a unified framework formed by the other complexity measures of Boolean functions, such as…
We show a communication complexity lower bound for finding a correlated equilibrium of a two-player game. More precisely, we define a two-player $N \times N$ game called the 2-cycle game and show that the randomized communication complexity…
This article uses data from two experimental studies of two-person Prisoner's Dilemma games [1, 2] and compares the data with the theoretic predictions calculated with the use of a quantum game theoretical method. The experimental findings…
So far, the theory of equilibrium selection in the infinitely repeated prisoner's dilemma is insensitive to communication possibilities. To address this issue, we incorporate the assumption that communication reduces -- but does not…
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…
Sensitivity conjecture is a longstanding and fundamental open problem in the area of complexity measures of Boolean functions and decision tree complexity. The conjecture postulates that the maximum sensitivity of a Boolean function is…
We prove communication complexity lower bounds for (possibly mixed) Nash equilibrium in potential games. In particular, we show that finding a Nash equilibrium requires $poly(N)$ communication in two-player $N \times N$ potential games, and…
A communication game consists of distributed parties attempting to jointly complete a task with restricted communication. Such games are useful tools for studying limitations of physical theories. A theory exhibits preparation contextuality…
We reduce the problem of proving a "Boolean Unique Games Conjecture" (with gap 1-delta vs. 1-C*delta, for any C> 1, and sufficiently small delta>0) to the problem of proving a PCP Theorem for a certain non-unique game. In a previous work,…
We provide an interesting two-party parity oblivious communication game whose success probability is solely determined by the Bell expression. The parity-oblivious condition in an operational quantum theory implies the preparation…
A theory is universal contextual if its prediction cannot be reproduced by an ontological model satisfying both preparation and measurement noncontextuality assumptions. In this report, we first generalize the logical proofs of quantum…
We use the example of playing a 2-player game with entangled quantum objects to investigate the effect of quantum correlation. We find that for simple game scenarios it is classical correlation that is the central feature and that these…
The GKS game was formulated by Justin Gilmer, Michal Koucky, and Michael Saks in their research of the sensitivity conjecture. Mario Szegedy invented a protocol for the game with the cost of $O(n^{0.4732})$. Then a protocol with the cost of…
We consider a game in which two separate laboratories collaborate to prepare a quantum system and are then asked to guess the outcome of a measurement performed by a third party in a random basis on that system. Intuitively, by the…
In a vintage paper concerning Parsimonious games, a subset of constant sum homogeneous weighted majority games, Isbell introduced a twin relationship based on transposition properties of the incidence matrices upon minimal winning…
In this thesis we introduce quantum refereed games, which are quantum interactive proof systems with two competing provers. We focus on a restriction of this model that we call "short quantum games" and we prove an upper bound and a lower…
Network congestion games are a well-understood model of multi-agent strategic interactions. Despite their ubiquitous applications, it is not clear whether it is possible to design information structures to ameliorate the overall experience…