Related papers: The YY game
We illustrate how one can use basic combinatorial theory and computer programming technique (Python) to analyze the combinatorial game: Mahjong. The results confirm some folklore concerning the game, and expose some unexpected results.…
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…
Duparc introduced a two-player game for a function $f$ between zero-dimensional Polish spaces in which Player II has a winning strategy iff $f$ is of Baire class 1. We generalize this result by defining a game for an arbitrary function $f :…
Inspired by asynchronous cooperative Parrondo's games we introduce two new types of games in which all players simultaneously play game A or game B or a combination of these two games. These two types of games differ in the way a…
We introduce a search game for two players played on a "scenario" consisting of a ground set together with a collection of feasible partitions. This general setting allows us to obtain new characterisations of many width parameters such as…
Motivated by the sequence form formulation of Koller et al. (GEB'96), this paper defines {\em bilinear games}, and proposes efficient algorithms for its rank based subclasses. Bilinear games are two-player non-cooperative single-shot games…
This work contains the mathematical exploration of a few prototypical games in which central concepts from statistics and probability theory naturally emerge. The first two kinds of games are termed Fisher and Bayesian games, which are…
In this paper, we examine a class of $\alpha$-potential stochastic differential games with random coefficients via the backward stochastic differential equations (BSDEs) approach. Specifically, we show that the first and second order linear…
Evolutionary game theory is a powerful mathematical framework to study how intelligent individuals adjust their strategies in collective interactions. It has been widely believed that it is impossible to unilaterally control players'…
We consider a setting in which a principal gets to choose which game from some given set is played by a group of agents. The principal would like to choose a game that favors one of the players, the social preferences of the players, or the…
Graph Pebbling is a well-studied single-player game on graphs. We introduce the game of Blocking Pebbles which adapts Graph Pebbling into a two-player strategy game in order to examine it within the context of Combinatorial Game Theory.…
Modern board games are a rich source of interesting and new challenges for combinatorial problems. The game Nmbr9 is a solitaire style puzzle game using polyominoes. The rules of the game are simple to explain, but modelling the game…
We develop a theory of combinatorial games that is appropriate for describing positions in Hex and other monotone set coloring games. We consider two natural conditions on such games: a game is monotone if all moves available to both…
We create a new two-player game on the Sperner Triangle based on Sperner's lemma. Our game has simple rules and several desirable properties. First, the game is always certain to have a winner. Second, like many other interesting games such…
We consider some well-known families of two-player, zero-sum, perfect information games that can be viewed as special cases of Shapley's stochastic games. We show that the following tasks are polynomial time equivalent: - Solving simple…
Matching games is a novel matching model introduced by Garrido-Lucero and Laraki, in which agents' utilities are endogenously determined as the outcome of a strategic game they play simultaneously with the matching process. Matching games…
We study bipartite correlations in Bell-type games. We show that in a setup where the information carriers are allowed to locally deform the manifold on which the game is played, stronger correlations may be obtained than those maximally…
Stochastic games are an important class of problems that generalize Markov decision processes to game theoretic scenarios. We consider finite state two-player zero-sum stochastic games over an infinite time horizon with discounted rewards.…
We study unique games and estimate some of their values. We prove that if a unique game has a quantum-assisted value close to 1, then it must have a perfect deterministic strategy. We introduce a family of unique games based on groups that…
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…