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Combinatorial games are two-player games of pure strategy where the players, usually called Left and Right, move alternately. In this paper, we introduce Cheating Robot games. These arise from simultaneous-play combinatorial games where one…
In a variant of communication tasks, players cooperate in choosing their local strategies to compute a given task later, working separately. Utilizing quantum bits for communication and sharing entanglement between parties is a recognized…
We consider the following communication problem: Alice and Bob each have some valuation functions $v_1(\cdot)$ and $v_2(\cdot)$ over subsets of $m$ items, and their goal is to partition the items into $S, \bar{S}$ in a way that maximizes…
In the Conditional Disclosure of Secrets (CDS) problem, Alice and Bob hold inputs $x\in \mathcal{X}$ and $y\in \mathcal{Y}$ and share a secret. Let $f:\mathcal{X}\times\mathcal{Y}\to\{0,1\}$ be a function such that the secret is revealed to…
Combinatorial optimization is a fundamental problem found in many fields. In many real life situations, the constraints and the objective function forming the optimization problem are naturally distributed amongst different sites in some…
At the end, the house always wins! This simple truth holds for all public games of chance. Nevertheless, since lotteries have existed, people have tried everything to give luck a helping hand. This article compares objective scientific…
The strategies adopted by individuals to select relevant information to pass on are central to understanding problem solving by groups. Here we use agent-based simulations to revisit a cooperative problem-solving scenario where the task is…
Distributed consensus protocols reach agreement among $n$ players in the presence of $f$ adversaries; different protocols support different values of $f$. Existing works study this problem for different adversary types (captured by threat…
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…
In this paper we study a cooperative card game called Hanabi from the viewpoint of algorithmic combinatorial game theory. In Hanabi, each card has one among $c$ colors and a number between $1$ and $n$. The aim is to make, for each color, a…
Batch codes, introduced by Ishai, Kushilevitz, Ostrovsky and Sahai in [1], are methods for solving the following data storage problem: n data items are to be stored in m servers in such a way that any k of the n items can be retrieved by…
Suppose Alice and Bob receive strings $X=(X_1,...,X_n)$ and $Y=(Y_1,...,Y_n)$ each uniformly random in $[s]^n$ but so that $X$ and $Y$ are correlated . For each symbol $i$, we have that $Y_i = X_i$ with probability $1-\eps$ and otherwise…
Finding the clique of maximum cardinality in an arbitrary graph is an NP-Hard problem that has many applications, which has motivated studies to solve it exactly despite its difficulty. The great majority of algorithms proposed in the…
Document exchange and error correcting codes are two fundamental problems regarding communications. In the first problem, Alice and Bob each holds a string, and the goal is for Alice to send a short sketch to Bob, so that Bob can recover…
Suppose that a transmitter Alice potentially wishes to communicate with a receiver Bob over an adversarially jammed binary channel. An active adversary James eavesdrops on their communication over a binary symmetric channel (BSC(q)), and…
We propose a cryptographic scheme that is deterministic: Alice sends single photons to Bob, and each and every photon detected supplies one key bit -- no photon is wasted. This is in marked contrast to other schemes in which a random…
In a recent work (Ghazi et al., SODA 2016), the authors with Komargodski and Kothari initiated the study of communication with contextual uncertainty, a setup aiming to understand how efficient communication is possible when the…
We consider a card guessing strategy for a stack of cards with two different types of cards, say $m_1$ cards of type red (heart or diamond) and $m_2$ cards of type black (clubs or spades). Given a deck of $M=m_1+m_2$ cards, we propose a…
Conditional disclosure of secrets (CDS) is the problem of disclosing as efficiently as possible, one secret from Alice and Bob to Carol if and only if the inputs at Alice and Bob satisfy some function $f$. The information theoretic capacity…
Two parties, Alice and Bob, wish to distill a binary secret key out of a list of correlated variables that they share after running a quantum key distribution protocol based on continuous-spectrum quantum carriers. We present a novel…