Related papers: Testing Randomness by Matching Pennies
A zero-one matrix $A$ contains another zero-one matrix $P$ if some submatrix of $A$ can be transformed to $P$ by changing some ones to zeros. $A$ avoids $P$ if $A$ does not contain $P$. The Pattern Avoidance Game is played by two players.…
Consider the following one-player game played on an initially empty graph with $n$ vertices. At each stage a randomly selected new edge is added and the player must immediately color the edge with one of $r$ available colors. Her objective…
In 2010, Bre\v{s}ar, Klav\v{z}ar and Rall introduced the optimization variant of the graph domination game and the game domination number, which was proved PSPACE-hard by Bre\v{s}ar et al. in 2016. In 2024, Leo Versteegen obtained the…
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…
Team captains Alice and Bob divide up $2m$ footballers, each reduced to a real-valued score, into two teams of $m$ footballers each. On each turn, one captain plays picker, and the other chooser: the picker names a footballer yet to be…
In a $(1:b)$ Maker-Breaker game, a primary question is to find the maximal value of $b$ that allows Maker to win the game (that is, the critical bias $b^*$). Erd\H{o}s conjectured that the critical bias for many Maker-Breaker games played…
In set theory without the axiom of regularity, we consider a game in which two players choose in turn an element of a given set, an element of this element, etc.; a player wins if its adversary cannot make any next move. Sets that are…
Consider concurrent, infinite duration, two-player win/lose games played on graphs. If the winning condition satisfies some simple requirement, the existence of Player 1 winning (finite-memory) strategies is equivalent to the existence of…
In a two-player game, two cooperating but non communicating players, Alice and Bob, receive inputs taken from a probability distribution. Each of them produces an output and they win the game if they satisfy some predicate on their…
Quantum gambling --- a secure remote two-party protocol which has no classical counterpart --- is demonstrated through optical approach. A photon is prepared by Alice in a superposition state of two potential paths. Then one path leads to…
We study a variation of the minority game. There are N agents. Each has to choose between one of two alternatives everyday, and there is reward to each member of the smaller group. The agents cannot communicate with each other, but try to…
Games often incorporate random elements in the form of dice or shuffled card decks. This randomness is a key contributor to the player experience and the variety of game situations encountered. There is a tension between a level of…
We examine a two-person game we call Will-Testing in which the strategy space for both players is a real number. It has no equilibrium. When an infinitely large set of players plays this in all possible pairings, there is an equilibrium for…
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…
We study concurrent graph games where n players cooperate against an opponent to reach a set of target states. Unlike traditional settings, we study distributed randomisation: team players do not share a source of randomness, and their…
We study variants of a stochastic game inspired by backgammon where players may propose to double the stake, with the game state dictated by a one-dimensional random walk. Our variants allow for different numbers of proposals and different…
We present a computer assisted proof for a result concerning a three player betting game, introduced by Angel and Holmes. The three players start with initial capital $x, y, z > 0$ respectively. At each step of this game two players are…
We study the following game. Three players start with initial capitals of $s_{1},s_{2},s_{3}$ dollars; in each round player $P_{m}$ is selected with probability $\frac{1}{3}$; then \emph{he} selects player $P_{n}$ and they play a game in…
On March 16, 2024, Daniel Litt, in an X-post, proposed the following brainteaser: "Flip a fair coin 100 times. It gives a sequence of heads (H) and tails (T). For each HH in the sequence of flips, Alice gets a point; for each HT, Bob does,…
Richman games are zero-sum games, where in each turn players bid in order to determine who will play next [Lazarus et al.'99]. We extend the theory to impartial general-sum two player games called \emph{bidding games}, showing the existence…