Related papers: Interactive games and representation theory. II. A…
Reducible representations of CAR and CCR are applied to second quantization of Dirac and Maxwell fields. The resulting field operators are indeed operators and not operator-valued distributions. Examples show that the formalism may lead to…
Modeling the purposeful behavior of imperfect agents from a small number of observations is a challenging task. When restricted to the single-agent decision-theoretic setting, inverse optimal control techniques assume that observed behavior…
In the real world, agents or entities are in a continuous state of interactions. These inter- actions lead to various types of complexity dynamics. One key difficulty in the study of complex agent interactions is the difficulty of modeling…
Modeling the purposeful behavior of imperfect agents from a small number of observations is a challenging task. When restricted to the single-agent decision-theoretic setting, inverse optimal control techniques assume that observed behavior…
Recently the concept of quantum information has been introduced into game theory. Here we present the first study of quantum games with more than two players. We discover that such games can possess a new form of equilibrium strategy, one…
We review both theoretical and experimental developments in the area of quantum games since the inception of the subject circa 1999. We will also offer a narrative on the controversy that surrounded the subject in its early days, and how…
Recent development in quantum computation and quantum information theory allows to extend the scope of game theory for the quantum world. The paper presents the history and basic ideas of quantum game theory. Description of Giffen paradoxes…
Since the quantum field theory treats a system of particles, there must be a distribution which is associated with the system of particles. It means that a meaningful quantity is adjoined in the system of particles. It seems that these…
The convexification numerical method with the rigorously established global convergence property is constructed for a problem for the Mean Field Games System of the second order. This is the problem of the retrospective analysis of a game…
These lecture notes attempt a mathematical treatment of game theory akin to mathematical physics. A game instance is defined as a sequence of states of an underlying system. This viewpoint unifies classical mathematical models for 2-person…
Traffic scenarios are inherently interactive. Multiple decision-makers predict the actions of others and choose strategies that maximize their rewards. We view these interactions from the perspective of game theory which introduces various…
The paper is devoted to integral quantization, a procedure based on operator-valued measure and resolution of the identity. We insist on covariance properties in the important case where group representation theory is involved. We also…
An approach towards quantum games is proposed that uses the unusual probabilities involved in EPR-type experiments directly in two-player games.
Infinite-state games are a commonly used model for the synthesis of reactive systems with unbounded data domains. Symbolic methods for solving such games need to be able to construct intricate arguments to establish the existence of winning…
Some problems related to an algebraic approach to quantum statistics are discussed. Generalized quantum statistics is described as a result of interactions. The Fock space representation is discussed. The problem of existence of…
Evolutionary game theory has been a successful tool to combine classical game theory with learning-dynamical descriptions in multiagent systems. Provided some symmetric structures of interacting players, many studies have been focused on…
I give an analysis of the simplest non-commutative quantum game, which is a gambling game much like Heads or Tails. The quantum gamespace displays strategies which are not interpretable through direct-product strategies of the two players.…
Effects of quantum and classical correlations on game theory are studied to clarify the new aspects brought into game theory by the quantum mechanical toolbox. In this study, we compare quantum correlation represented by a maximally…
It is shown how the theory of the fields can be constructed in a consistent way in quantized spaces. All constructions are connected with unitary irreducible representations of real forms of six dimensional rotation algebras O(1,5), O(2,4),…
An interrelationship between Game Theory and Control Theory is seeked. In this respect two aspects of this relationship are brought up. To establish the direct relationship Control Based Games and to establish the inverse relationship Game…