Related papers: A New Variation of Hat Guessing Games
We consider two-player games played on finite colored graphs where the goal is the construction of an infinite path with one of the following frequency-related properties: (i) all colors occur with the same asymptotic frequency, (ii) there…
We build new quantum games, similar to the spin flip game, where as a novelty the players perform measurements on a quantum system associated to a continuous time search algorithm. The measurements collapse the wave function into one of the…
A major open problem in the area of infinite-duration games is to characterize winning conditions that are determined in finite-memory strategies. Infinite-duration games are usually studied over edge-colored graphs, with winning conditions…
In his list of open problems, Martin Erickson described a certain game: "Two players alternately put queens on an n x n chess board so that each new queen is not in range of any queen already on the board (the color of the queens is…
This paper studies the game of guessing riffle-shuffled cards with complete feedback. A deck of $n$ cards labelled 1 to $n$ is riffle-shuffled once and placed on a table. A player tries to guess the cards from top and is given complete…
Minority game is a model of heterogeneous players who think inductively. In this game, each player chooses one out of two alternatives every turn and those who end up in the minority side wins. It is instructive to extend the minority game…
This paper is on developing some computer-assisted proof methods involving non-classical inequalities for Shannon entropy. Two areas of the applications of information inequalities are studied: Secret sharing schemes and hat guessing games.…
We consider a two-player search game on a tree $T$. One vertex (unknown to the players) is randomly selected as the target. The players alternately guess vertices. If a guess $v$ is not the target, then both players are informed in which…
We consider the following two-player game, parametrised by positive integers $n$ and $k$. The game is played between Painter and Builder, alternately taking turns, with Painter moving first. The game starts with the empty graph on $n$…
In a game where both contestants have perfect information, there is a strict limit on how perfect that information can be. By contrast, when one player is deprived of all information, the limit on the other player's information disappears,…
This paper introduces a new solution concept for non-cooperative games in normal form with no ties and pure strategies: the Perfectly Transparent Equilibrium. The players are rational in all possible worlds and know each other's strategies…
We introduce the game of Cat Herding, where an omnipresent herder slowly cuts down a graph until an evasive cat player has nowhere to go. The number of cuts made is the score of a game, and we study the score under optimal play. In this…
In a $(1:b)$ biased Maker-Breaker game, how good a strategy is for a player can be measured by the bias range for which its rival can win, choosing an appropriate counterstrategy. Bednarska and {\L}uczak proved that, in the $H$-subgraph…
Coding theory revolves around the incorporation of redundancy into transmitted symbols, computation tasks, and stored data to guard against adversarial manipulation. However, error correction in coding theory is contingent upon a strict…
This contribution deals with a two-level discrete decision problem, a so-called Stackelberg strategic game: A Subset Sum setting is addressed with a set $N$ of items with given integer weights. One distinguished player, the leader, may…
One of the most popular lottery games worldwide is the so-called ``lotto k/N''. It considers N numbers 1,2,...,N from which k are drawn randomly, without replacement. A player selects k or more numbers and the first prize is shared amongst…
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…
The Stackelberg equilibrium solution concept describes optimal strategies to commit to: Player 1 (termed the leader) publicly commits to a strategy and Player 2 (termed the follower) plays a best response to this strategy (ties are broken…
In this paper, we study the notion of admissibility for randomised strategies in concurrent games. Intuitively, an admissible strategy is one where the player plays `as well as possible', because there is no other strategy that dominates…
We introduce games with probabilistic uncertainty, a natural model for controller synthesis in which the controller observes the state of the system through imprecise sensors that provide correct information about the current state with a…