Related papers: The Ungar Games

For a poset $P$, an Ungar move sends $P$ to $P\setminus T$, where $T$ is some subset of maximal elements of $P$. With these Ungar moves, Defant, Kravitz, and Williams define the Ungar games, where two players alternate making nontrivial…

In 2023, Defant and Li introduced the Ungar move, which sends an element $v$ of a finite meet-semilattice $L$ to the meet of some subset of the elements covered by $v$. More recently, Defant, Kravitz, and Williams introduced the Ungar game…

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…

Partially-ordered set games, also called poset games, are a class of two-player combinatorial games. The playing field consists of a set of elements, some of which are greater than other elements. Two players take turns removing an element…

A general position set of a graph $G$ is a set of vertices $S$ in $G$ such that no three vertices from $S$ lie on a common shortest path. In this paper we introduce and study the general position achievement game. The game is played on a…

Euclid is a well known two-player impartial combinatorial game. A position in Euclid is a pair of positive integers and the players move alternately by subtracting a positive integer multiple of one of the integers from the other integer…

M\"uller games form a well-established class of games for model checking and verification. These games are played on directed graphs $\mathcal G$ where Player 0 and Player 1 play by generating an infinite path through the graph. The winner…

In the domination game studied here, Dominator and Staller alternately choose a vertex of a graph $G$ and take it into a set $D$. The number of vertices dominated by the set $D$ must increase in each single turn and the game ends when $D$…

Strategy iteration is a technique frequently used for two-player games in order to determine the winner or compute payoffs, but to the best of our knowledge no general framework for strategy iteration has been considered. Inspired by…

We introduce two new iteration games: the game G, which is a strengthening of the weak iteration game, and the game G+, which is somewhat stronger than G but weaker than the full iteration game of length omega_1. For a countable M…

We study a combinatorial game derived from a problem in the German National Mathematics Competition. In this game, two players take turns removing numbers from a finite set of natural numbers, aiming to satisfy a certain divisibility…

There are many combinatorial games in which a move can terminate the game, such as a checkmate in chess. These moves give rise to diverse situations that fall outside the scope of the classical normal play structure. To analyze these games,…

Positional games are a well-studied class of combinatorial game. In their usual form, two players take turns to play moves in a set (`the board'), and certain subsets are designated as `winning': the first person to occupy such a set wins…

The domination game is played on a graph $G$ by two players, named Dominator and Staller. They alternatively select vertices of $G$ such that each chosen vertex enlarges the set of vertices dominated before the move on it. Dominator's goal…

We consider a matching problem, which is meaningful in team competitions, as well as in information theory, recommender systems, and assignment problems. In the competitions which we study, each competitor in a team order plays a match with…

Infinite games where several players seek to coordinate under imperfect information are deemed to be undecidable, unless the information is hierarchically ordered among the players. We identify a class of games for which joint winning…

We study two impartial games introduced by Anderson and Harary and further developed by Barnes. Both games are played by two players who alternately select previously unselected elements of a finite group. The first player who builds a…

Motivated by the success of domination games and by a variation of the coloring game called the indicated coloring game, we introduce a version of domination games called the indicated domination game. It is played on an arbitrary graph $G$…

A finite impartial game is a two-player game in which the players take turns making moves and the game ends after finitely many moves. In this paper, we study a class of finite impartial games introduced by H.~Lenstra, which we call coin…

We investigate the following version of the well-known R\'enyi-Ulam game. Two players - the Questioner and the Responder - play against each other. The Responder thinks of a number from the set $\{1,\ldots,n\}$, and the Questioner has to…