Related papers: Efficiency and formalism of quantum games
We introduce a new unified framework for modelling both decision problems and finite games based on quantifiers and selection functions. We show that the canonical utility maximisation is one special case of a quantifier and that our more…
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…
While fictitious play is guaranteed to converge to Nash equilibrium in certain game classes, such as two-player zero-sum games, it is not guaranteed to converge in non-zero-sum and multiplayer games. We show that fictitious play in fact…
We study turn-based quantitative multiplayer non zero-sum games played on finite graphs with reachability objectives. In such games, each player aims at reaching his own goal set of states as soon as possible. A previous work on this model…
This paper investigates the convergence time of log-linear learning to an $\epsilon$-efficient Nash equilibrium in potential games, where an efficient Nash equilibrium is defined as the maximizer of the potential function. Previous…
We develop a rigorous mathematical framework for quantum game theory applied to static 2x2 games, extending classical concepts to the quantum setting where players may employ arbitrary unitary operations (pure strategies) or probability…
We show that under some general conditions the finite memory determinacy of a class of two-player win/lose games played on finite graphs implies the existence of a Nash equilibrium built from finite memory strategies for the corresponding…
In this paper, we study turn-based quantitative multiplayer non zero-sum games played on finite graphs with both reachability and safety objectives. In this framework a player with a reachability objective aims at reaching his own goal as…
Quantum computers that process information by harnessing the remarkable power of quantum mechanics are increasingly being put to practical use. In the future, their impact will be felt in numerous fields, including in online casino games.…
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…
A quantum financial approach to finite games of strategy is addressed, with an extension of Nash's theorem to the quantum financial setting, allowing for an entanglement of games of strategy with two-period financial allocation problems…
Nash equilibria are crucial for understanding game behavior and systems in economics, physics, biology, and computer science. A significant application arises from the connection between Nash equilibria and optimization problems . However,…
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…
In this paper we review our earlier work on quantum computing and the Nash Equilibrium, in particular, tracing the history of the discovery of new Nash Equilibria and then reviewing the ways in which quantum computing may be expected to…
Games with incomplete information are formulated in a multi-sector probability matrix formalism that can cope with quantum as well as classical strategies. An analysis of classical and quantum strategy in a multi-sector extension of the…
Finite objects and more specifically finite games are formalized using induction, whereas infinite objects are formalized using coinduction. In this article, after an introduction to the concept of coinduction, we revisit on infinite…
In this thesis we introduce quantum refereed games, which are quantum interactive proof systems with two competing provers. We focus on a restriction of this model that we call "short quantum games" and we prove an upper bound and a lower…
We study the asymptotic organization among many optimizing individuals interacting in a suitable "moderate" way. We justify this limiting game by proving that its solution provides approximate Nash equilibria for large but finite player…
The recent theory of sequential games and selection functions by Mar- tin Escardo and Paulo Oliva is extended to games in which players move simultaneously. The Nash existence theorem for mixed-strategy equilibria of finite games is…
We study the extension of classical games to the quantum domain, generated by the addition of one unitary strategy to two classical strategies of each player. The conditions that need to be met by unitary operations to ensure that the…