Related papers: Four Games on Boolean Algebras
We give an elementary proof that in a Borel family of games, the set of games for which player II has a winning strategy is Baire measurable, universally measurable, and completely Ramsey in the case where $X = [\mathbb{N}]^{\aleph_0}$.
Throughout this abstract let U be a fixed p-point ultrafilter and let I be the dual ideal. Grigorieff forcing is P(U)={p:omega to 2|dom(p) is an element of I} ordered by reverse inclusion. It is well known that Grigorieff forcing is proper.…
We propose a new model of provenance, based on a game-theoretic approach to query evaluation. First, we study games G in their own right, and ask how to explain that a position x in G is won, lost, or drawn. The resulting notion of game…
We provide two methodologies in the area of computation theory to solve optimal strategies for board games such as Xi Gua Qi and Go. From experimental results, we find relevance to graph theory, matrix representation, and mathematical…
Tumbleweed is a popular two-player perfect-information new territorial game played at the prestigious Mind Sport Olympiad. We define a generalized version of the game, where the board size is arbitrary and so is the possible number of…
We study a game where two players take turns selecting points of a convex geometry until the convex closure of the jointly selected points contains all the points of a given winning set. The winner of the game is the last player able to…
The \emph{graph grabbing game} is a two-player game on a weighted connected graph in which two players, Alice and Bob, alternatively remove non-cut vertices one by one to gain the weights on them. Alice wins the game if she gains at least…
The Maker-Breaker domination game is played on a graph $G$ by Dominator and Staller who alternate turns selecting an unplayed vertex of $G$. The goal of Dominator is that the vertices he selected during the game form a dominating set while…
We introduce Boolean Observation Games, a subclass of multi-player finite strategic games with incomplete information and qualitative objectives. In Boolean observation games, each player is associated with a finite set of propositional…
In this short note we consider a variation of the connectivity Waiter-Client game $WC(n,q,\mathcal{A})$ played on an $n$-vertex graph $G$ which consists of $q+1$ disjoint spanning trees. In this game in each round Waiter offers Client $q+1$…
For suitable groups G we will show that one can add a Boolean algebra B by forcing in such a way that Aut(B) is almost isomorphic to G. In particular, we will give a positive answer to the following question due to J.Roitman: Is…
We study two positional games played on hypergraphs, whose edges may be interpreted as winning sets. Two players take turns picking a previously unpicked vertex of the hypergraph. We say a player fills an edge if that player has picked all…
The Maker-Breaker domination game is played on a graph $G$ by two players, called Dominator and Staller. They alternately select an unplayed vertex in $G$. Dominator wins the game if he forms a dominating set while Staller wins the game if…
We study alternating good-for-games (GFG) automata, i.e., alternating automata where both conjunctive and disjunctive choices can be resolved in an online manner, without knowledge of the suffix of the input word still to be read. We show…
Behavioural equivalences can be characterized via bisimulation, modal logics, and spoiler-duplicator games. In this paper we work in the general setting of coalgebra and focus on generic algorithms for computing the winning strategies of…
Players are arranged on a regular lattice and coded with a specific strategy for a pre-defined game. Each player sums their payoffs from playing the game with each of their neighbors, and then adopts the strategy of the most successful…
We characterize all the pairs of complementary non-homogenous Beatty sequences $(A_n)_{n\ge 0}$ and $(B_n)_{n\ge 0}$ for which there exists an invariant game having exactly $\{(A_n,B_n)\mid n\ge 0\}\cup \{(B_n,A_n)\mid n\ge 0\}$ as set of…
We provide a criterion for determining the winner in two-player win-lose alternating-move games on trees, in terms of the Hausdorff dimension of the target set. We focus our study on special cases, including the Gale-Stewart game on the…
We unify and consolidate various results about non-signall-ing games, a subclass of non-local two-player one-round games, by introducing and studying several new families of games and establishing general theorems about them, which extend a…
Game theory is usually considered applied mathematics, but a few game-theoretic results, such as Borel determinacy, were developed by mathematicians for mathematics in a broad sense. These results usually state determinacy, i.e. the…