Related papers: Game Semantics for Higher-Order Unitary Quantum Co…
We extend the open games framework for compositional game theory to encompass also mixed strategies, making essential use of the discrete probability distribution monad. We show that the resulting games form a symmetric monoidal category,…
Game semantics aim at describing the interactive behaviour of proofs by interpreting formulas as games on which proofs induce strategies. In this article, we introduce a game semantics for a fragment of first order propositional logic. One…
We present a game semantics for intuitionistic type theory. Specifically, we propose categories with families of a new variant of games and strategies for both extensional and intensional variants of the type theory with dependent function,…
We propose a quantum-like description of markets and economics. The approach has roots in the recently developed quantum game theory.
Categorical quantum mechanics, which examines quantum theory via dagger-compact closed categories, gives satisfying high-level explanations to the quantum information procedures such as Bell-type entanglement or complementary observables…
We present a quantum approach to a signaling game; a special kind of extensive games of incomplete information. Our model is based on quantum schemes for games in strategic form where players perform unitary operators on their own qubits of…
Game semantics describe the interactive behavior of proofs by interpreting formulas as games on which proofs induce strategies. Such a semantics is introduced here for capturing dependencies induced by quantifications in first-order…
A framework for discussing relationships between different types of games is proposed. Within the framework, quantum simultaneous games, finite quantum simultaneous games, quantum sequential games, and finite quantum sequential games are…
The present paper introduces a novel notion of `(effective) computability', called viability, of strategies in game semantics in an intrinsic (i.e., without recourse to the standard Church-Turing computability), non-inductive and…
Compositional Game Theory is a new, recently introduced model of economic games based upon the computer science idea of compositionality. In it, complex and irregular games can be built up from smaller and simpler games, and the equilibria…
The framework of graded semantics uses graded monads to capture behavioural equivalences of varying granularity, for example as found on the linear-time/branching-time spectrum, over general system types. We describe a generic…
We define a notion of morphisms between open games, exploiting a surprising connection between lenses in computer science and compositional game theory. This extends the more intuitively obvious definition of globular morphisms as mappings…
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…
We continue the analysis of quantum-like description of markets and economics. The approach has roots in the recently developed quantum game theory and quantum computing. The present paper is devoted to quantum bargaining games which are a…
The categories of open learners (due to Fong, Spivak and Tuy\'eras) and open games (due to the present author, Ghani, Winschel and Zahn) bear a very striking and unexpected similarity. The purpose of this short note is to prove that there…
Parity games are combinatorial representations of closed Boolean mu-terms. By adding to them draw positions, they have been organized by Arnold and one of the authors into a mu-calculus. As done by Berwanger et al. for the propositional…
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,…
This paper generalises the treatment of compositional game theory as introduced by Ghani et al. in 2018, where games are modelled as morphisms of a symmetric monoidal category. From an economic modelling perspective, the notion of a game in…
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…
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…