scholarly journals On Correlated Equilibria in Marinatto–Weber Type Quantum Games

2020 ◽  
Vol 10 (24) ◽  
pp. 9003
Author(s):  
Piotr Frąckiewicz
Keyword(s):  
Probability Distribution ◽  
Nash Equilibria ◽  
The Other ◽  
Correlated Equilibrium ◽  
Mixed Strategies ◽  
Quantum Game ◽  
Classical Probability ◽  
Quantum Games ◽  
Weber Type ◽  
Correlated Equilibria

Players’ choices in quantum game schemes are often correlated by a quantum state. This enables players to obtain payoffs that may not be achievable when classical pure or mixed strategies are used. On the other hand, players’ choices can be correlated due to a classical probability distribution, and if no player benefits by a unilateral deviation from the vector of recommended strategies, the probability distribution is a correlated equilibrium. The aim of this paper is to investigate relation between correlated equilibria and Nash equilibria in the MW-type schemes for quantum games.

scholarly journals ANALYSIS OF TREMBLING HAND PERFECT EQUILIBRIA IN QUANTUM GAMES

2008 ◽  
Vol 08 (01) ◽  
pp. L23-L30 ◽  
Author(s):  
IRENEUSZ PAKUŁA
Keyword(s):  
Game Theory ◽  
Probability Distribution ◽  
Distribution Functions ◽  
Quantum Game ◽  
Quantum Games ◽  
Probability Distribution Functions ◽  
Perfect Equilibria ◽  
Quantum Strategies

We analyse Selten' concept of trembling hand perfect equilibria in the context of quantum game theory. We define trembles as mixed quantum strategies by replacing discrete probabilities with probability distribution functions. Explicit examples of analysis are given.

scholarly journals Efficiency of Classical and Quantum Games Equilibria

Entropy ◽  
2021 ◽  
Vol 23 (5) ◽  
pp. 506
Author(s):  
Marek Szopa
Keyword(s):  
Nash Equilibria ◽  
Prisoner’S Dilemma ◽  
Pareto Efficiency ◽  
Pareto Optimal ◽  
Quantum Games ◽  
Game Of Chicken ◽  
Battle Of The Sexes ◽  
Correlated Equilibria ◽  
Relationship Of ◽  
The Relationship

Nash equilibria and correlated equilibria of classical and quantum games are investigated in the context of their Pareto efficiency. The examples of the prisoner’s dilemma, battle of the sexes and the game of chicken are studied. Correlated equilibria usually improve Nash equilibria of games but require a trusted correlation device susceptible to manipulation. The quantum extension of these games in the Eisert–Wilkens–Lewenstein formalism and the Frąckiewicz–Pykacz parameterization is analyzed. It is shown that the Nash equilibria of these games in quantum mixed Pauli strategies are closer to Pareto optimal results than their classical counter-parts. The relationship of mixed Pauli strategies equilibria and correlated equilibria is also studied.

scholarly journals ALTRUISTIC BEHAVIOR AND CORRELATED EQUILIBRIUM SELECTION

2011 ◽  
Vol 13 (04) ◽  
pp. 363-381 ◽  
Author(s):  
GIUSEPPE DE MARCO ◽  
JACQUELINE MORGAN
Keyword(s):  
Nash Equilibria ◽  
Equilibrium Selection ◽  
Altruistic Behavior ◽  
Correlated Equilibrium ◽  
Topological Properties ◽  
Equilibrium Refinements ◽  
Correlated Equilibria

This paper studies new refinement concepts for correlated equilibria based on altruistic behavior of the players and generalizes some refinement concepts previously developed by the authors for Nash equilibria. Effectiveness of the concepts, relations with the corresponding notions for Nash equilibria and with other correlated equilibrium refinements are investigated. The analysis of the topological properties of the set of solutions concludes the paper.

scholarly journals Quantum Games with Unawareness with Duopoly Problems in View

Entropy ◽  
2019 ◽  
Vol 21 (11) ◽  
pp. 1097 ◽  
Author(s):  
Piotr Frąckiewicz ◽  
Jakub Bilski
Keyword(s):  
Common Knowledge ◽  
The Other ◽  
Pareto Optimal ◽  
Quantum Game ◽  
Optimal Outcome ◽  
Cournot Duopoly ◽  
Equilibrium Outcome ◽  
Quantum Games ◽  
Quantum Domain ◽  
Duopoly Model

Playing the Cournot duopoly in the quantum domain can lead to the optimal strategy profile in the case of maximally correlated actions of the players. However, that result can be obtained if the fact that the players play the quantum game is common knowledge among the players. Our purpose is to determine reasonable game outcomes when players’ perceptions about what game is actually played are limited. To this end, we consider a collection consisting of the classical and quantum games that specifies how each player views the game and how each player views the other players’ perceptions of the game. We show that a slight change in how the players perceive the game may considerably affect the result of the game and, in the case of maximally correlated strategies, may vary from the inefficient Nash equilibrium outcome in the classical Cournot duopoly to the Pareto optimal outcome. We complete our work by investigating in the same way the Bertrand duopoly model.

scholarly journals CORRELATED EQUILIBRIA OF CLASSICAL STRATEGIC GAMES WITH QUANTUM SIGNALS

2005 ◽  
Vol 03 (01) ◽  
pp. 183-188 ◽  
Author(s):  
PIERFRANCESCO LA MURA
Keyword(s):  
Nash Equilibria ◽  
Correlated Equilibrium ◽  
Strategic Games ◽  
Strategic Game ◽  
Correlated Equilibria

Correlated equilibria are sometimes more efficient than the Nash equilibria of a game without signals. We investigate whether the availability of quantum signals in the context of a classical strategic game may allow the players to achieve even greater efficiency than in any correlated equilibrium with classical signals, and find the answer to be positive.

scholarly journals Weak Berge Equilibrium in Finite Three-person Games: Conception and Computation

2020 ◽  
Vol 11 (1) ◽  
pp. 127-134
Author(s):  
Konstantin Kudryavtsev ◽  
Ustav Malkov
Keyword(s):  
Cooperative Games ◽  
Hippocratic Oath ◽  
The Other ◽  
Mixed Strategies ◽  
Finite Games ◽  
Moral Basis ◽  
Other Hand ◽  
Berge Equilibrium ◽  
Do No Harm ◽  
Non Cooperative Games

AbstractThe paper proposes the concept of a weak Berge equilibrium. Unlike the Berge equilibrium, the moral basis of this equilibrium is the Hippocratic Oath “First do no harm”. On the other hand, any Berge equilibrium is a weak Berge equilibrium. But, there are weak Berge equilibria, which are not the Berge equilibria. The properties of the weak Berge equilibrium have been investigated. The existence of the weak Berge equilibrium in mixed strategies has been established for finite games. The weak Berge equilibria for finite three-person non-cooperative games are computed.

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.

scholarly journals Quantum Physical Unclonable Functions: Possibilities and Impossibilities

Quantum ◽  
2021 ◽  
Vol 5 ◽  
pp. 475
Author(s):  
Myrto Arapinis ◽  
Mahshid Delavar ◽  
Mina Doosti ◽  
Elham Kashefi
Keyword(s):  
Large Family ◽  
Quantum States ◽  
The Other ◽  
Quantum Game ◽  
Physical Unclonable Function ◽  
Physical Unclonable Functions ◽  
Quantum Analogue ◽  
Universal Quantum ◽  
Different Levels ◽  
Comprehensive Study

A Physical Unclonable Function (PUF) is a device with unique behaviour that is hard to clone hence providing a secure fingerprint. A variety of PUF structures and PUF-based applications have been explored theoretically as well as being implemented in practical settings. Recently, the inherent unclonability of quantum states has been exploited to derive the quantum analogue of PUF as well as new proposals for the implementation of PUF. We present the first comprehensive study of quantum Physical Unclonable Functions (qPUFs) with quantum cryptographic tools. We formally define qPUFs, encapsulating all requirements of classical PUFs as well as introducing a new testability feature inherent to the quantum setting only. We use a quantum game-based framework to define different levels of security for qPUFs: quantum exponential unforgeability, quantum existential unforgeability and quantum selective unforgeability. We introduce a new quantum attack technique based on the universal quantum emulator algorithm of Marvin and Lloyd to prove no qPUF can provide quantum existential unforgeability. On the other hand, we prove that a large family of qPUFs (called unitary PUFs) can provide quantum selective unforgeability which is the desired level of security for most PUF-based applications.

scholarly journals OCTONIONIZATION OF THREE PLAYER, TWO STRATEGY MAXIMALLY ENTANGLED QUANTUM GAMES

2010 ◽  
Vol 08 (03) ◽  
pp. 411-434 ◽  
Author(s):  
ADEN OMAR AHMED ◽  
STEVEN A. BLEILER ◽  
FAISAL SHAH KHAN
Keyword(s):  
Nash Equilibria ◽  
Payoff Function ◽  
Quantum Games ◽  
Computational Capability

We develop an octonionic representation of the payoff function for three player, two strategy, maximally entangled quantum games in order to obtain computationally friendly version of this function. This computational capability is then exploited to analyze and potentially classify the Nash equilibria in the quantum games.

scholarly journals The Evolutionary Status of the Secondaries of Cataclysmic Binaries

1983 ◽  
Vol 72 ◽  
pp. 257-262
Author(s):  
H. Ritter
Keyword(s):  
Probability Distribution ◽  
Main Sequence ◽  
The Other ◽  
Initial Mass ◽  
Evolutionary Status ◽  
Mass Ratio ◽  
Main Sequence Stars ◽  
Cataclysmic Binaries ◽  
Low Mass ◽  
Orbital Periods

ABSTRACTIt is shown that the secondary components of cataclysmic binaries with orbital periods of less than ~10 hours are indistinguishable from ordinary low-mass main-sequence stars and that, therefore, they are essentially unevolved. On the other hand, it is shown that, depending on the mass ratio of the progenitor system, the secondary of a cataclysmic binary could be significantly evolved. The fact that nevertheless most of the observed secondaries are essentially unevolved can be accounted for by assuming that the probability distribution for the initial mass ratio is not strongly peaked towards unity mass ratio.

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