scholarly journals On the equivalence between non-factorizable mixed-strategy classical games and quantum games

2016 ◽  
Vol 3 (1) ◽  
pp. 150477 ◽  
Author(s):  
Azhar Iqbal ◽  
James M. Chappell ◽  
Derek Abbott
Keyword(s):  
Decision Theory ◽  
Mixed Strategy ◽  
Strategic Interaction ◽  
Quantum Game ◽  
Mathematical Basis ◽  
Quantum Games ◽  
Mathematical Question ◽  
Game Theoretic ◽  
Classical Game ◽  
Quantum Decision Theory

A game-theoretic setting provides a mathematical basis for analysis of strategic interaction among competing agents and provides insights into both classical and quantum decision theory and questions of strategic choice. An outstanding mathematical question is to understand the conditions under which a classical game-theoretic setting can be transformed to a quantum game, and under which conditions there is an equivalence. In this paper, we consider quantum games as those that allow non-factorizable probabilities. We discuss two approaches for obtaining a non-factorizable game and study the outcome of such games. We demonstrate how the standard version of a quantum game can be analysed as a non-factorizable game and determine the limitations of our approach.

scholarly journals Strong Isomorphism in Eisert-Wilkens-Lewenstein Type Quantum Games

2016 ◽  
Vol 2016 ◽  
pp. 1-8 ◽  
Author(s):  
Piotr Frąckiewicz
Keyword(s):  
Quantum Game ◽  
Quantum Games ◽  
New Criterion ◽  
Game Isomorphism ◽  
Classical Game ◽  
Game Scheme

The aim of this paper is to bring together the notions of quantum game and game isomorphism. The work is intended as an attempt to introduce a new criterion for quantum game schemes. The generally accepted requirement forces a quantum scheme to generate the classical game in a particular case. Now, given a quantum game scheme and two isomorphic classical games, we additionally require the resulting quantum games to be isomorphic as well. We are concerned with the Eisert-Wilkens-Lewenstein quantum game scheme and the strong isomorphism between games in strategic form.

scholarly journals Quantum Mean-Field Games with the Observations of Counting Type

Games ◽  
2021 ◽  
Vol 12 (1) ◽  
pp. 7
Author(s):  
Vassili N. Kolokoltsov
Keyword(s):  
Game Theory ◽  
Nash Equilibrium ◽  
Open Problem ◽  
Existence And Uniqueness ◽  
Existence Of Solutions ◽  
Mean Field ◽  
Mean Field Games ◽  
Quantum Game ◽  
Quantum Games ◽  
Interesting Open Problem

Quantum games and mean-field games (MFG) represent two important new branches of game theory. In a recent paper the author developed quantum MFGs merging these two branches. These quantum MFGs were based on the theory of continuous quantum observations and filtering of diffusive type. In the present paper we develop the analogous quantum MFG theory based on continuous quantum observations and filtering of counting type. However, proving existence and uniqueness of the solutions for resulting limiting forward-backward system based on jump-type processes on manifolds seems to be more complicated than for diffusions. In this paper we only prove that if a solution exists, then it gives an ϵ-Nash equilibrium for the corresponding N-player quantum game. The existence of solutions is suggested as an interesting open problem.

Quantum Game of Dual-channel Supply Chain under Free-riding Behavior

2021 ◽  
Vol 1 (1) ◽  
pp. 3-17
Author(s):  
Yu-Chung Chang ◽  
Keyword(s):  
Game Theory ◽  
Decision Making ◽  
Quantum Entanglement ◽  
Free Riding ◽  
Selling Price ◽  
Quantum Game ◽  
Optimal Price ◽  
Dual Channel ◽  
Dual Channel Supply Chain ◽  
Classical Game

Based on the perspective of the quantum game, this paper explores when the online direct sales channel takes the free-riding behavior after the retail channel provides high-quality experience and services and how the dual-channel supply chain establishes a commodity pricing strategy. The retailer’s selling price follows a decreasing function of the free-riding behavior coefficient. while the online direct selling price does an increasing function of the free-riding behavior coefficient. Under centralized decision-making, there is no quantum entanglement, so the quantum game solution is consistent with the classical game solution. Under decentralized decision-making, the optimal price and profit of the quantum game are higher than those of the classical game when the quantum entanglement degree is greater than zero. When the quantum entanglement tends to be infinite, the optimal price of the quantum game finally remains in convergence. The quantum game theory is a more optimal decision-making method than the classical game theory.

scholarly journals Model of information deterrence between states based on the theory of reflexive games

2020 ◽  
Author(s):  
V. A. Savchenko ◽  
◽  
T. M. Dzyuba
Keyword(s):  
State Level ◽  
Soviet Period ◽  
Theoretic Approach ◽  
State Behavior ◽  
Proposed Model ◽  
Game Theoretic ◽  
Pragmatic Aspects ◽  
Classical Game ◽  
Game Theoretic Approach ◽  
Post Soviet Period

The article considers the approach to modeling the processes of information counteraction and information deterrence at the state level. The shortcomings of the game-theoretic approach to the development of formalized models of information counteraction are identified. The concept of formalization of interstate information deterrence on the basis of the theory of reflexive management of V. Lefevre is offered. Unlike classical game theory, this approach takes into account the possible irrationality of human (state) behavior in combination with moral-motivational and pragmatic aspects of choice. The adequacy of the proposed model is confirmed by the analysis of examples of information confrontation between Ukraine and Russia in the post-Soviet period.

Strategic Interaction and the Statistical Analysis of International Conflict

1999 ◽  
Vol 93 (2) ◽  
pp. 279-297 ◽  
Author(s):  
Curtis S. Signorino
Keyword(s):  
International Conflict ◽  
Empirical Support ◽  
Interaction Model ◽  
Strategic Interaction ◽  
Monte Carlo Analysis ◽  
Discrete Choice Models ◽  
Theoretic Model ◽  
Game Theoretic ◽  
International Interaction ◽  
True Values

Although strategic interaction is at the heart of most international relations theory, it has largely been missing from much empirical analysis in the field. Typical applications of logit and probit to theories of international conflict generally do not capture the structure of the strategic interdependence implied by those theories. I demonstrate how to derive statistical discrete choice models of international conflict that directly incorporate the theorized strategic interaction. I show this for a simple crisis interaction model and then use Monte Carlo analysis to show that logit provides estimates with incorrect substantive interpretations as well as fitted values that can be far from the true values. Finally, I reanalyze a well-known game-theoretic model of war, Bueno de Mesquita and Lalman's (1992) international interaction game. My results indicate that there is at best modest empirical support for their model.

Quantum decision corrections for the neuroeconomics of irrational movement control and goal attainment

2021 ◽  
Vol 44 ◽  
Author(s):  
Kevin B. Clark
Keyword(s):  
Decision Theory ◽  
Optimal Foraging ◽  
Propositional Logic ◽  
Goal Attainment ◽  
Movement Control ◽  
Subjective Utility ◽  
Quantum Decision Theory

Abstract Quantum decision theory corrects categorical and propositional logic pathologies common to classic statistical goal-oriented reasoning, such as rational neuroeconomics-based optimal foraging. Within this ecosalient framework, motivation, perception, learning, deliberation, brain computation, and conjunctive risk-order errors may be understood for subjective utility judgments underlying either rational or irrational canonical decisions-actions used to choose, procure, and consume rewarding nutrition with variable fitness.

scholarly journals Process estimation in qubit systems: a quantum decision theory approach

2019 ◽  
Vol 18 (7) ◽  
Author(s):  
Ivan Maffeis ◽  
Seid Koudia ◽  
Abdelhakim Gharbi ◽  
Matteo G. A. Paris
Keyword(s):  
Decision Theory ◽  
Theory Approach ◽  
Quantum Decision Theory
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