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Is litigation a serious search for truth or simply a game of skill or luck? Although the process of litigation has been modeled as a Prisoner's Dilemma, as a War of Attrition, as a Game of Chicken and even as a simple coin toss, no one has…
Go has long been considered as a testbed for artificial intelligence. By introducing certain quantum features, such as superposition and collapse of wavefunction, we experimentally demonstrate a quantum version of Go by using correlated…
Peg solitaire is an old puzzle with a 300 year history. We consider two ways a computer can be utilized to find interesting peg solitaire puzzles. It is common for a peg solitaire puzzle to begin from a symmetric board position, we have…
In this paper we provide a case study of the use of relatively sophisticated mathematics and algorithms to redefine and adapt a simple traditional game/puzzle to exploit the computational power of smart devices. The focus here is not so…
Recent development in quantum computation and quantum information theory allows to extend the scope of game theory for the quantum world. The authors have recently proposed a quantum description of financial market in terms of quantum game…
Quark Wars is an all-new, adventure style game. We recommended playing it outdoors. Quark Wars is modeled upon the outdoor game called Hungarian Number War, with notable influence from Star Wars, the American epic space saga. The players…
Abalone is a 2-player board game with perfect information. The game is played on a 5x5x5 hexagonal grid and ends when a player pushes 6 of their opponents' pieces off the board. Abalone is similar to games like chess and Go in that all…
In this lecture I will talk about three mathematical puzzles involving mathematics and computation that have preoccupied me over the years. The first puzzle is to understand the amazing success of the simplex algorithm for linear…
We will describe a combinatorial game that models the problem of resolution of singularities of algebraic varieties over a field of characteristic zero. By giving a winning strategy for this game, we give another proof of the existence of…
We analysed quantum version of the game battle of sexes using a general initial quantum state. For a particular choice of initial entangled quantum state it is shown that the classical dilemma of the battle of sexes can be resolved and a…
Markov chains are an important example for a course on stochastic processes because simple board games can be used to illustrate the fundamental concepts. For example, a looping board game (like Monopoly) consists of all recurrent states,…
We solve the classical "Game of Pure Strategy" using linear programming. We notice an intricate even-odd behavior in the results of our computations, that seems to encourage odd or maximal bids.
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…
In this research article, we survey existing quantum physics-related games and, based on this survey, propose a definition for the concept of quantum games. We define a quantum game as any type of rule-based game that either employs the…
People have made remarkable progress in game AIs, especially in domain of perfect information game. However, trick-taking poker game, as a popular form of imperfect information game, has been regarded as a challenge for a long time. Since…
We introduce and analyze the Walker-Breaker game, a variant of Maker-Breaker games where Maker is constrained to choose edges of a walk or path in a given graph G, with the goal of visiting as many vertices of the underlying graph as…
Main papers on quantum games are written by physicists for physicists, and the inevitable exploitation of physics jargon may create difficulties for mathematicians or economists. Our goal here is to make clear the physical content and to…
Our paper explores the game theoretic value of the 7-in-a-row game. We reduce the problem to solving a finite board game, which we target using Proof Number Search. We present a number of heuristic improvements to Proof Number Search and…
We propose a quantum-like description of markets and economics. The approach has roots in the recently developed quantum game theory.
Quantum games have proposed a new point of view for the solution of the classical problems and dilemmas in game theory. Certain quantization relationships can be proposed with the objective that a game can be generalized into a quantum…