Related papers: Toward Quantum Combinatorial Games
We study variations of classical combinatorial games on two finite heaps of tokens, a.k.a. \emph{subtraction games}. Given non-negative integers $p_1,q_1, p_2,q_2$, where $p_1q_2 > q_1p_2$, $p_1>0$ and $q_2>0$, two players alternate in…
This paper consider the possibility of using some quantum tools in decision making strategies. In particular, we consider here a dynamical open quantum system helping two players, $\G_1$ and $\G_2$, to take their decisions in a specific…
We study a combinatorial game derived from a problem in the German National Mathematics Competition. In this game, two players take turns removing numbers from a finite set of natural numbers, aiming to satisfy a certain divisibility…
A game-theoretic setting provides a mathematical basis for analysis of strategic interaction among competing agents and provides insights into both classical and quantum decision theory and questions of strategic choice. An outstanding…
Positional games are a mathematical class of two-player games comprising Tic-tac-toe and its generalizations. We propose a novel encoding of these games into Quantified Boolean Formulas (QBFs) such that a game instance admits a winning…
In this work we propose a quantum version of a generalized Monty Hall game, that is, one in which the parameters of the game are left free, and not fixed on its regular values. The developed quantum scheme is then used to study the expected…
Poset games have been the object of mathematical study for over a century, but little has been written on the computational complexity of determining important properties of these games. In this introduction we develop the fundamentals of…
We consider an application of the mathematical formalism of quantum mechanics (QM) outside physics, namely, to game theory. We present a simple game between macroscopic players, say Alice and Bob (or in a more complex form - Alice, Bob and…
We propose an interpretation of the infinite sum of combinatorial games. In such an interpretation, plays involve infinite runs, but without loops. The notion of a run is quite natural, but different possibilities arises for the notion of…
A class of discrete Bidding Combinatorial Games that generalize alternating normal play was introduced by Kant, Larsson, Rai, and Upasany (2022). The major questions concerning optimal outcomes were resolved. By generalizing standard game…
An approach towards quantum games is proposed that uses the unusual probabilities involved in EPR-type experiments directly in two-player games.
The theory of combinatorial game (like board games) and the theory of social games (where one looks for Nash equilibria) are normally considered as two separate theories. Here we shall see what comes out of combining the ideas. The central…
The game of nim, with its simple rules, its elegant solution and its historical importance is the quintessence of a combinatorial game, which is why it led to so many generalizations and modifications. We present a modification with a new…
The study of the combinatorial game Nim and its variants is rich and varied, but little is known of the game Nim with a Pass. It is Nim, but once per game a player is permitted to skip their turn but this can only be done if a nonempty pile…
We present a two-party protocol for quantum gambling, a new task closely related to coin tossing. The protocol allows two remote parties to play a gambling game, such that in a certain limit it becomes a fair game. No unconditionally secure…
The challenge of programming classical computers to play traditional, competitive games against human players has helped to advance classical hardware and software. Quantum computers have the potential to play games in a unique way:…
Quantum Tiq-Taq-Toe is a well-known benchmark and playground for both quantum computing and machine learning. Despite its popularity, no reinforcement learning (RL) methods have been applied to Quantum Tiq-Taq-Toe. Although there has been…
We give a concise and self-contained introduction to the theory of Quantum Games by reviewing the seminal works of Meyer, Eisert-Wilkens-Lewenstein, Marinatto-Weber and Landsburg, which initiated the study of this field. By generalizing…
We build new quantum games, similar to the spin flip game, where as a novelty the players perform measurements on a quantum system associated to a continuous time search algorithm. The measurements collapse the wave function into one of the…
Quantum generalizations of conventional games broaden the range of available strategies, which can help improve outcomes for the participants. With many players, such quantum games can involve entanglement among many states which is…