Related papers: Matroid isomorphism games
Combinatorial games lead to several interesting, clean problems in algorithms and complexity theory, many of which remain open. The purpose of this paper is to provide an overview of the area to encourage further research. In particular, we…
We introduce the notion of a quasi-matroidal class of ordered simplicial complexes: an approximation to the idea of a matroid cryptomorphism in the landscape of ordered simplicial complexes. A quasi-matroidal class contains pure shifted…
The characterization of second-order type isomorphisms is a purely syntactical problem that we propose to study under the enlightenment of game semantics. We study this question in the case of second-order λ$\mu$-calculus, which can be…
We present a systematic investigation of the quantum games, constructed using a novel repeated game protocol, when played repeatedly ad infinitum. We focus on establishing that such repeated games -- by virtue of inherent quantum-mechanical…
We pursue the possible connections between classical games and quantum computation. The Parrondo game is one in which a random combination of two losing games produces a winning game. We introduce novel realizations of this Parrondo effect…
The aim of the paper is to examine the notion of simple Kantian equilibrium in $2 \times 2$ symmetric games and their quantum counterparts. We focus on finding the Kantian equilibrium strategies in the general form of the games. As a…
We study how strategic interaction can arise from controlled quantum dynamics rather than being imposed as an external mathematical structure. We introduce a class of interaction-defined quantum games in which players are represented by…
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…
Validation of a presumably universal theory, such as quantum mechanics, requires a quantum mechanical description of systems that carry out theoretical calculations and experiments. The description of quantum computers is under active…
We propose a simple yet rich model to extend the notions of Nash equilibria and correlated equilibria of strategic games to the quantum setting, in which we then study the relations between classical and quantum equilibria. Unlike the…
In quantum information, nonlocal games are particularly useful for differentiating classical, quantum, and non-signalling correlations. An example of differentiation is given by the principle of no-collapse of communication complexity,…
A protocol for considering decoherence in quantum games is presented. Results for two-player, two-strategy quantum games subject to decoherence are derived and some specific examples are given. Decoherence in other types of quantum games is…
Using the representation introduced in \cite{frame}, an artificial game in quantum strategy space is proposed and studied. Although it has well-known classical correspondence, which has classical mixture strategy Nash Equilibrium states,…
Equilibrium solution concepts of normal-form games, such as Nash equilibria, correlated equilibria, and coarse correlated equilibria, describe the joint strategy profiles from which no player has incentive to unilaterally deviate. They are…
We define homological matrices, construct examples of one-dimension restricted homological quantum field theories, and show a relationship between the two theories.
Candogan et al. (2011) provide an orthogonal direct-sum decomposition of finite games into potential, harmonic and nonstrategic components. In this paper we study the issue of decomposing games that are strategically equivalent from a…
Game theory is a well established branch of mathematics whose formalism has a vast range of applications from the social sciences, biology, to economics. Motivated by quantum information science, there has been a leap in the formulation of…
We study optimal and nearly-optimal quantum strategies for non-local XOR games. First, we prove the following general result: for every non-local XOR game, there exists a set of relations with the properties: (1) a quantum strategy is…
The notions of symmetry and anonymity in strategic games have been formalized in different ways in the literature. We propose a combinatorial framework to analyze these notions, using group actions. Then, the same framework is used to…
We show that the C*-algebras associated with synchronous games give rise to certain quantum families of maps between the input and output sets of the game. In particular situations (e.g. for graph endomorphism games) these quantum families…