Related papers: The space complexity of mirror games
We study two-player general sum repeated finite games where the rewards of each player are generated from an unknown distribution. Our aim is to find the egalitarian bargaining solution (EBS) for the repeated game, which can lead to much…
We study the following combinatorial game played by two players, Alice and Bob, which generalizes the Pizza game considered by Brown, Winkler and others. Given a connected graph G with nonnegative weights assigned to its vertices, the…
In a recently introduced coset guessing game, Alice plays against Bob and Charlie, aiming to meet a joint winning condition. Bob and Charlie can only communicate before the game starts to devise a joint strategy. The game we consider begins…
Introducing the simplest of all No-Signalling Games: the RGB Game where two verifiers interrogate two provers, Alice and Bob, far enough from each other that communication between them is too slow to be possible. Each prover may be…
Here, we present the quantum version of a very famous statistical decision problem, whose classical version is counter-intuitive to many. The Monty Hall game can be phrased as a two person game between Alice and Bob. In their pioneering…
We study a guessing game where Alice holds a discrete random variable $X$, and Bob tries to sequentially guess its value. Before the game begins, Bob can obtain side-information about $X$ by asking an oracle, Carole, any binary question of…
Wireless secret sharing is crucial to information security in the era of Internet of Things. One method is to utilize the effect of the randomness of the wireless channel in the data link layer to generate the common secret between two…
In 2024, Daniel Litt posed a simple coinflip game pitting Alice's "Heads-Heads" vs Bob's "Heads-Tails": who is more likely to win if they score 1 point per occurrence of their substring in a sequence of n fair coinflips? This attracted over…
Zeckendorf proved that every positive integer $n$ can be written uniquely as the sum of non-adjacent Fibonacci numbers; a similar result holds for other positive linear recurrence sequences. These legal decompositions can be used to…
In Problem #1542 of Mathematics Magazine, Grossman and Turett define the Cantor game. In his 2007 Mathematics Magazine article about the Cantor game, Matt Baker proves several results and poses three challenging questions about it: Do there…
A single-player game of Memory is played with $n$ distinct pairs of cards, with the cards in each pair bearing identical pictures. The cards are laid face-down. A move consists of revealing two cards, chosen adaptively. If these cards…
In this paper, we consider the problem of guessing a sequence subject to a distortion constraint. Specifically, we assume the following game between Alice and Bob: Alice has a sequence $\bx$ of length $n$. Bob wishes to guess $\bx$, yet he…
We show a parallel repetition theorem for the entangled value $\omega^*(G)$ of any two-player one-round game $G$ where the questions $(x,y) \in \mathcal{X}\times\mathcal{Y}$ to Alice and Bob are drawn from a product distribution on…
We consider turn-based stochastic two-player games with a combination of a parity condition that must hold surely, that is in all possible outcomes, and of a parity condition that must hold almost-surely, that is with probability 1. The…
In this work, we consider "decision" variants of a monogamy-of-entanglement game by Tomamichel, Fehr, Kaniewski, and Wehner [New Journal of Physics '13]. In its original "search" variant, Alice prepares a (possibly entangled) state on…
The multiplication game is a two-person game in which each player chooses a positive integer without knowledge of the other player's number. The two numbers are then multiplied together and the first digit of the product determines the…
This paper is concerned with the death-birth updating process. This model is an example of a spatial game in which players located on the~$d$-dimensional integer lattice are characterized by one of two possible strategies and update their…
Let $a$, $b$, and $n$ be integers with $0<a<b<n$. In a certain two-player probabilistic chip-collecting game, Alice tosses a coin to determine whether she collects $a$ chips or $b$ chips. If Alice collects $a$ chips, then Bob collects $b$…
Pointer-chasing is a central problem in two-party communication complexity: given input size $n$ and a parameter $k$, the two players Alice and Bob are given functions $N_A, N_B: [n] \rightarrow [n]$, respectively, and their goal is to…
In this paper, we study algorithms for special cases of energy games, a class of turn-based games on graphs that show up in the quantitative analysis of reactive systems. In an energy game, the vertices of a weighted directed graph belong…