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This paper proposes a multiscale method for solving the numerical solution of mean field games which accelerates the convergence and addresses the problem of determining the initial guess. Starting from an approximate solution at the…
After the social learning models were proposed, finding the solutions of the games becomes a well-defined mathematical question. However, almost all papers on the games and their applications are based on solutions built upon either an…
We analyze the quantum penny flip game using geometric algebra and so determine all possible unitary transformations which enable the player Q to implement a winning strategy. Geometric algebra provides a clear visual picture of the quantum…
Computational aspects of solution notions such as Nash equilibrium have been extensively studied, including settings where the ultimate goal is to find an equilibrium that possesses some additional properties. Furthermore, in order to…
In the paper it is proven that the two-players turn-based stochastic game "Risk or Safety" has a unique solution. Both players need to play the same strategy if they want to maximize their winning chances. An analytical method based on the…
In an investigation of the applications of Combinatorial Game Theory to chess, we construct novel mutual Zugzwang positions, explain an otherwise mysterious pawn endgame from "A Guide to Chess Endings" (Euwe and Hooper), show positions…
Quantum game theory is a recently developing field of physical research. In this paper, we investigate quantum games in a systematic way. With the famous instance of the Prisoner's Dilemma, we present the fascinating properties of quantum…
Examining games from a fresh perspective we present the idea of game-inspired and game-based algorithms, dubbed "gamorithms".
In this paper, we study the problem of learning the set of pure strategy Nash equilibria and the exact structure of a continuous-action graphical game with quadratic payoffs by observing a small set of perturbed equilibria. A…
We study the complexity of a particular class of board games, which we call `slide and merge' games. Namely, we consider 2048 and Threes, which are among the most popular games of their type. In both games, the player is required to slide…
General methods for the construction of magic squares of any order have been searched for centuries. There have been several standard strategies for this purpose, such as the knight movement, or the construction of bordered magic squares,…
A common format for sports contests involves pairwise matches between two teams, with the #1 player of team A matched against the #1 player of team B, the #2 player of team A against the #2 player of team B, and so on. This paper addresses…
We develop a generic computational model that can be used effectively for establishing the existence of winning strategies for concrete finite combinatorial games. Our modelling is (equational) logic-based involving advanced techniques from…
In this paper, we study the subset-sum problem by using a quantum heuristic approach similar to the verification circuit of quantum Arthur-Merlin games. Under described certain assumptions, we show that the exact solution of the subset sum…
Tablut is a complete-knowledge, deterministic, and asymmetric board game, which has not been solved nor properly studied yet. In this work, its rules and characteristics are presented, then a study on its complexity is reported. An upper…
In this paper we correct an analysis of the two-player perfect-information game Dukego given in Berlekamp, Conway, and Guy's Winning Ways for your Mathematical Plays (Chapter 19). In particular, we characterize the board dimensions that are…
This paper presents a general approach for measuring distances between board games within the Ludii general game system. These distances are calculated using a previously published set of general board game concepts, each of which…
We study an iteration approach to solve the coupled algebraic Riccati equations when they appear in general two player closed-loop type Nash differential games over an infinite time horizon. Also, we propose an effective algorithm for…
We introduce the concept of Conversion/Preference Games, or CP games for short. CP games generalize the standard notion of strategic games. First we exemplify the use of CP games. Second we formally introduce and define the CP-games…
A quantum logic gate of particular interest to both electrical engineers and game theorists is the quantum multiplexer. This shared interest is due to the facts that an arbitrary quantum logic gate may be expressed, up to arbitrary…