Related papers: Quantum information approach to normal representat…
We present a robust framework with computational algorithms to support decision makers in sequential games. Our framework includes methods to solve games with complete information, assess the robustness of such solutions and, finally,…
The strategic Go game, known for the tedious mathematical complexities, has been used as a theme in many fiction, movies, and books. Here, we introduce the Go game and provide a new version of quantum Go in which the boxes are initially in…
A game in which one player makes unitary transformations of a simple system, and another seeks to confound the resulting state by a randomly chosen action is analyzed carefully. It is shown that the second player can reduce any system to a…
The relationships between game theory and quantum mechanics let us propose certain quantization relationships through which we could describe and understand not only quantum but also classical, evolutionary and the biological systems that…
Normal-form proper equilibrium, introduced by Myerson as a refinement of normal-form perfect equilibrium, occupies a distinctive position in the equilibrium analysis of extensive-form games because its more stringent perturbation structure…
This is a reply to the paper by S.C.Benjamin, quant-ph/0008127.
In the flavour of categorical quantum mechanics, we extend nonlocal games to allow quantum questions and answers, using quantum sets (special symmetric dagger Frobenius algebras) and the quantum functions of Musto, Reutter, and Verdon…
We prove the existence of (one-way) communication tasks with a subconstant versus superconstant asymptotic gap, which we call "doubly infinite," between their quantum information and communication complexities. We do so by studying the…
Normal-form games (NFGs) are the fundamental model of strategic interaction. We study their representation using neural networks. We describe the inherent equivariance of NFGs -- any permutation of strategies describes an equivalent game --…
We introduce a framework for translating game descriptions in natural language into extensive-form representations in game theory, leveraging Large Language Models (LLMs) and in-context learning. Given the varying levels of strategic…
Game theory is appropriate for studying cyber conflict because it allows for an intelligent and goal-driven adversary. Applications of game theory have led to a number of results regarding optimal attack and defense strategies. However, the…
Heifetz, Meier, and Schipper (2013) introduced dynamic game with unawareness consisting of a partially ordered set of games in extensive form. Here, we study the normal form of dynamic games with unawareness. The generalized normal form…
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…
Quantum game theory, whatever opinions may be held due to its abstract physical formalism, have already found various applications even outside the orthodox physics domain. In this paper we introduce the concept of a quantum auction, its…
We study mean field games and corresponding $N$-player games in continuous time over a finite time horizon where the position of each agent belongs to a finite state space. As opposed to previous works on finite state mean field games, we…
Two-player (antagonistic) games on (possibly stochastic) graphs are a prevalent model in theoretical computer science, notably as a framework for reactive synthesis. Optimal strategies may require randomisation when dealing with inherently…
We propose a new viewpoint on variational mean-field games with diffusion and quadratic Hamiltonian. We show the equivalence of such mean-field games with a relative entropy minimization at the level of probabilities on curves. We also…
In this paper, we explore the historical development of playable quantum physics related games (\textit{\textbf{quantum games}}). For the purpose of this examination, we have collected over 260 quantum games ranging from commercial games,…
We investigate a multi-player and multi-choice quantum game. We start from two-player and two-choice game and the result is better than its classical version. Then we extend it to N-player and N-choice cases. In the quantum domain, we…
Game theory provides a mathematical framework for analysing strategic situations involving at least two players. Normal-form games model situations where the players simultaneously pick their moves. In this thesis we explore the strategic…