Related papers: The solution to an open problem for a caching game
The payoff in the Chow-Robbins coin-tossing game is the proportion of heads when you stop. Knowing when to stop to maximize expectation was addressed by Chow and Robbins(1965), who proved there exist integers ${k_n}$ such that it is optimal…
The cup game on $n$ cups is a multi-step game with two players, a filler and an emptier. At each step, the filler distributes $1$ unit of water among the cups, and then the emptier selects a single cup to remove (up to) $1$ unit of water…
A two-player one-round binary game consists of two cooperative players who each replies by one bit to a message that he receives privately; they win the game if both questions and answers satisfy some predetermined property. A game is…
Zeckendorf proved that every positive integer $n$ can be written uniquely as the sum of non-adjacent Fibonacci numbers. We use this decomposition to construct a two-player game. Given a fixed integer $n$ and an initial decomposition of $n=n…
We consider a zero-sum continuous time stopping game in which the pay-off is revealed in the maximum of the two stopping times instead of the minimum, which is the case in Dynkin games.
We start with the well-known game below: Two players hold a sheet of paper to their forehead on which a positive integer is written. The numbers are consecutive and each player can only see the number of the other one. In each time step,…
Several variations of hat guessing games have been popularly discussed in recreational mathematics. In a typical hat guessing game, after initially coordinating a strategy, each of $n$ players is assigned a hat from a given color set.…
We consider a variant of the game of Cops and Robbers, called Containment, in which cops move from edge to adjacent edge, the robber moves from vertex to adjacent vertex (but cannot move along an edge occupied by a cop). The cops win by…
Stackelberg equilibrium is a solution concept in two-player games where the leader has commitment rights over the follower. In recent years, it has become a cornerstone of many security applications, including airport patrolling and…
Graph Exploration problems ask a searcher to explore an unknown environment. The environment is modeled as a graph, where the searcher needs to visit each vertex beginning at some vertex. Treasure Hunt problems are a variation of Graph…
A large class of Positional Games are defined on the complete graph on $n$ vertices. The players, Maker and Breaker, take the edges of the graph in turns, and Maker wins iff his subgraph has a given -- usually monotone -- property. Here we…
We propose and study a model of strategic network design and exploration where the hider, subject to a budget constraint restricting the number of links, chooses a connected network and the location of an object. Meanwhile, the seeker, not…
Consider the following Maker-Breaker game. Fix a finite subset $S\subset\mathbb{N}$ of the naturals. The players Maker and Breaker take turns choosing previously unclaimed natural numbers. Maker wins by eventually building a homothetic copy…
The numbers game is a one-player game played on a finite simple graph with certain ``amplitudes'' assigned to its edges and with an initial assignment of real numbers to its nodes. The moves of the game successively transform the numbers at…
We consider the problem of a particular kind of quantum correlation that arises in some two-party games. In these games, one player is presented with a question they must answer, yielding an outcome of either 'win' or 'lose'. Molina and…
The game of Cops and Robber is traditionally played on a finite graph. The purpose of this note is to introduce and analyze the game that is played on an arbitrary geodesic space. The game is defined in such a way that it preserves the…
Given a fixed graph $H$ and a positive integer $n$, a Picker-Chooser $H$-game is a biased game played on the edge set of $K_n$ in which Picker is trying to force many copies of $H$ and Chooser is trying to prevent him from doing so. In this…
We introduce a new family of one-player games, involving the movement of coins from one configuration to another. Moves are restricted so that a coin can be placed only in a position that is adjacent to at least two other coins. The goal of…
Over the years, researchers have studied the complexity of several decision versions of Nash equilibrium in (symmetric) two-player games (bimatrix games). To the best of our knowledge, the last remaining open problem of this sort is the…
A decade ago, Gerhard Woeginger posed an open problem that became well-known as "Woeginger's Hiking Problem": Consider a group of $n$ people that want to go hiking; everyone expresses preferences over the size of their hiking group in the…