Related papers: Solving a Mathematical Problem in Square War: a Go…
We define the Sign Game as a two-player game played on a simple undirected mathematical graph $G$. The players alternate turns, assigning vertices of $G$ either $1$ or $-1$, and edges take on the value of the product of their endvertices.…
We prove that king chasing problem in Chinese Chess is NP-hard when generalized to $n\times n$ boards. `King chasing' is a frequently-used strategy in Chinese Chess, which means that the player has to continuously check the opponent in…
Game theory is an established branch of mathematics that offers a rich set of mathematical tools for multi-person strategic decision making that can be used to model the interactions of decision makers in security problems who compete for…
The following four classes of computational problems are equivalent: solving matrix games, solving linear programs, best $l^{\infty}$ linear approximation, best $l^1$ linear approximation.
The sudoku puzzles have a long history, with variations going back more than a hundred years, but its current and perhaps surprising world-wide prominence goes back to certain initiatives and then puzzle-generating computer programmes from…
This paper identifies a manifold in the space of bimatrix games which contains games that are strategically equivalent to rank-1 games through a positive affine transformation. It also presents an algorithm that can compute, in polynomial…
Games are useful tools for introducing new concepts to students. This paper describes a competitive two-player game for sophomore students in a modern physics survey course or junior/senior students in an introductory quantum mechanics…
In Part I of this two-part paper [1], we proposed a new game, called Chinese restaurant game, to analyze the social learning problem with negative network externality. The best responses of agents in the Chinese restaurant game with…
We quantize prisoners dilemma and chicken game by our generalized quantization scheme to explore the role of quantum discord in quantum games. In order to establish this connection we use Werner-like state as an initial state of the game.…
Parity games play an important role in model checking and synthesis. In their paper, Calude et al. have shown that these games can be solved in quasi-polynomial time. We show that their algorithm can be implemented efficiently: we use their…
In this paper we will look at the book Mathematical Go by Elwyn Berlekamp and David Wolfe \cite{MG}, and argue that the definitions and theories that they use are not the correct ones. We will argue that the new theory of scoring play games…
A $\mathrm{CHSH}_{q}$ game is a generalization of the standard two player $\mathrm{CHSH}$ game, having $q$ different input and output options. In contrast to the binary game, the best classical and quantum winning strategies are not known…
In this paper we solve the three-player-game question. A three-player-game consists of a series of rounds. There are altogether three players. Two players participate in each round, at the end of the round the loser quits and the third…
Parity games have important practical applications in formal verification and synthesis, especially to solve the model-checking problem of the modal mu-calculus. They are also interesting from the theory perspective, because they are widely…
Chess championships are often organised as a Swiss-system tournament, causing great challenges in ranking the participants due to the different strength of schedules and possible circular triads. The paper suggests that pairwise comparison…
This paper examines two different variants of the Ludo game, involving multiple dice and a fixed number of total turns. Within each variant, multiple game lengths (total no. of turns) are considered. To compare the two variants, a set of…
We consider the $n\times n$ game of Phutball. It is shown that, given an arbitrary position of stones on the board, it is a PSPACE-hard problem to determine whether the specified player can win the game, regardless of the opponent's choices…
Variational quantum algorithms (VQAs) offer a promising near-term approach to finding optimal quantum strategies for playing non-local games. These games test quantum correlations beyond classical limits and enable entanglement…
We define a new concept of "mistake" strategies and actions for strategic-form and extensive-form games, analyze the relationship to prior main game-theoretic solution concepts, study algorithms for computation, and explore practicality.…
This document presents the rules of a tactical two-player board game which is inspired by spin glasses. The aim is, while placing bonds and spins, to achieve a majority of the spins facing the chosen direction of each player. The game has…