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Azhar Iqbal

The University of Adelaide, School of Computer & Mathematical Sciences, Department Member

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Experienced researcher with a proven track record in the higher education sector, specializing in quantum computing, game theory, and mathematical modeling. My expertise spans the intersection of applied mathematics and emerging technologies, with a focus on driving innovation and solving complex problems. Passionate about pushing the boundaries of knowledge, I am committed to driving impactful advancements in these dynamic fields of research. My researcher profile: https://researchers.adelaide.edu.au/profile/azhar.iqbal
Address: Adelaide, South Australia

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Papers by Azhar Iqbal

Vulnerability and Defence: A Case for Stackelberg Game Dynamics

Games, 2024

This paper examines the tactical interaction between drones and tanks in modern warfare through g... more This paper examines the tactical interaction between drones and tanks in modern warfare through game theory, particularly focusing on Stackelberg equilibrium and backward induction. It describes a high-stakes conflict between two teams: one using advanced drones for attack, and the
other defending using tanks. The paper conceptualizes this as a sequential game, illustrating the complex strategic dynamics similar to Stackelberg competition, where moves and countermoves are carefully analyzed and predicted.

A new derivation of the Minkowski metric

Journal of Physics Communications, 2023

The four dimensional spacetime continuum, as first conceived by Minkowski, has become the dominan... more The four dimensional spacetime continuum, as first conceived by Minkowski, has become the dominant framework within which to describe physical laws. In this paper, we show how this fourdimensional structure is a natural property of physical three-dimensional space, if modeled with Clifford geometric algebra Cl(R3). We find that Minkowski spacetime can be embedded within a larger eight-dimensional structure. This then allows a generalisation of the invariant interval and the Lorentz transformations. Also, with this geometric oriented approach the fixed speed of light, the laws of special relativity and a generalised form of Maxwell's equations, arise naturally from the intrinsic properties of the algebra without recourse to physical arguments. We also find new insights into the nature of time, which can be described as two-dimensional. Some philosophical implications of this approach as it relates to the foundations of physical theories are also discussed.

Two-player quantum games: When player strategies are via directional choices

Quantum Information Processing

We propose a scheme for a quantum game based on performing an EPR-type experiment and in which ea... more We propose a scheme for a quantum game based on performing an EPR-type experiment and in which each player’s spatial directional choices are considered as their strategies. A classical mixed-strategy game is recovered by restricting the players’ choices to specific spatial trajectories. We show that for players’ directional choices for which the Bell-CHSH inequality is violated, the players’ payoffs in the quantum game have no mapping within the classical mixed-strategy game. The scheme provides a more direct link between classical and quantum games.

Looking at world events through the prism of game theory

Sage International internet publication, 2016

This is the pdf of the internet publication by Sage International: https://sageinternational.com.... more

Two-player quantum games: When player strategies are via directional choices

We propose a scheme for a quantum game based on performing an EPR-type experiment and in which ea... more We propose a scheme for a quantum game based on performing an EPR-type experiment and in which each player's spatial directional choices are considered as their strategies. A classical mixed-strategy game is recovered by restricting the players' choices to specific spatial trajectories. We show that for players' directional choices for which the Bell-CHSH inequality is violated, the players' payoffs in the quantum game have no mapping within the classical mixed-strategy game. The scheme provides a more direct link between classical and quantum games.

Quantum strategies and evolutionary stability (in Urdu)

arXiv: Quantum Physics, 2019

This article in Urdu presents an introduction to extension of an established branch of mathematic... more

The Role of Non-Factorizability in Determining "Pseudo-Classical "Non-separability

This article introduces a "pseudo classical" notion of modelling non-separability. This... more This article introduces a "pseudo classical" notion of modelling non-separability. This form of non-separability can be viewed as lying between separability and quantum-like non-separability. Non-separability is formalized in terms of the non-factorizabilty of the underlying joint probability distribution. A decision criterium for determining the non-factorizability of the joint distribution is related to determining the rank of a matrix as well as another approach based on the chi-square-goodness-of-fit test. This pseudo-classical notion of non-separability is discussed in terms of quantum games and concept combinations in human cognition.

Game theoretical modelling of network/cybersecurity

IEEE Access

Kidnapping model: an extension of Selten's game

Royal Society open science, 2017

Selten's game is a kidnapping model where the probability of capturing the kidnapper is indep... more Selten's game is a kidnapping model where the probability of capturing the kidnapper is independent of whether the hostage has been released or executed. Most often, in view of the elevated sensitivities involved, authorities put greater effort and resources into capturing the kidnapper if the hostage has been executed, in contrast with the case when a ransom is paid to secure the hostage's release. In this paper, we study the asymmetric game when the probability of capturing the kidnapper depends on whether the hostage has been executed or not and find a new uniquely determined perfect equilibrium point in Selten's game.

Time As a Geometric Property of Space

Frontiers in Physics, 2016

The vector algebra war: a historical perspective

IEEE Access, 2016

The impact of the vaccination and booster shots in containing the COVID-19 epidemic in Bahrain: a game theory approach

In this study, game theory is used to determine the effect of vaccination and booster shots in co... more In this study, game theory is used to determine the effect of vaccination and booster shots in containing COVID-19 in Bahrain. The study is divided into three parts and in each part, the payoff matrix and the biometric is generated. The Nash equilibrium points are determined by marking the maximum value in the first entry of each column and the maximum value in the second entry of each row. The results show that the vaccination and the booster shots significantly reduce the number of infected individuals, the number of patients reaching the ICU, and the number of deaths due to COVID-19.

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

by Azhar Iqbal and Derek Abbott

A game-theoretic setting provides a mathematical basis for analysis of strategic interaction amon... more 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.

The impact of the precautionary measures taken in the kingdom of Bahrain to contain the outbreak of COVID-19

Can Quantum-Mechanical Description of Physical Reality Be Considered Complete? (An Urdu Translation)

An Urdu translation of the landmark article by Einstein, Podolsky and Rosen from the year 1935 is... more

Game theoretical modelling of network/cybersecurity

https://arxiv.org/abs/1901.08426, 2019

Game theory is an established branch of mathematics that offers a rich set of mathematical tools ... more Game theory is an established branch of mathematics that offers a rich set of mathematical tools for multiperson strategic decision making that can be used to model the interactions of decision makers in security problems who compete for limited and shared resources. This article presents a review of the literature in the area of game theoretical modelling of network/cybersecurity and identifies a number of challenges in
this area that need to be addressed.

Quantum strategies and evolutionary stability (in Urdu)

https://arxiv.org/abs/1901.09741, 2019

This article in Urdu presents an introduction to the extension of an established branch of mathem... more

A game theoretical perspective on the quantum probabilities associated with a GHZ state

In the standard approach to quantum games, players' strategic moves are local unitary transformat... more In the standard approach to quantum games, players' strategic moves are local unitary transformations on an entangled state that is subsequently measured. Players' payoffs are then obtained as expected values of the entries in the payoff matrix of the classical game on a set of quantum probabilities obtained from the quantum measurement. In this paper, we approach quantum games from a diametrically opposite perspective. We consider a classical three-player symmetric game along with a known expression for a set of quantum probabilities relevant to a tripartite Einstein–Podolsky–Rosen (EPR) experiment that depends on three players' directional choices in the experiment. We define the players' strategic moves as their directional choices in an EPR setting and then express their payoff relations in the resulting quantum game in terms of their directional choices, the entries of the payoff matrix, and the quantum probability distribution relevant to the tripartite EPR experiment.

The equivalence of Bell's inequality and the Nash inequality in a quantum game-theoretic setting

The interaction of competing agents is described by classical game theory. It is now well known t... more The interaction of competing agents is described by classical game theory. It is now well known that this can be extended to the quantum domain, where agents obey the rules of quantum mechanics. This is of emerging interest for exploring quantum foundations, quantum protocols, quantum auctions, quantum cryptography, and the dynamics of quantum cryptocurrency, for example. In this paper, we investigate two-player games in which a strategy pair can exist as a Nash equilibrium when the games obey the rules of quantum mechanics. Using a generalized Einstein–Podolsky–Rosen (EPR) setting for two-player quantum games, and considering a particular strategy pair, we identify sets of games for which the pair can exist as a Nash equilibrium only when Bell's inequality is violated. We thus determine specific games for which the Nash inequality becomes equivalent to Bell's inequality for the considered strategy pair.

Kidnapping model: an extension of Selten's game

by Azhar Iqbal and Virginie Masson

Selten's game is a kidnapping model where the probability of capturing the kidnapper is independe... more Selten's game is a kidnapping model where the probability of capturing the kidnapper is independent of whether the hostage has been released or executed. Most often, in view of the elevated sensitivities involved, authorities put greater effort and resources into capturing the kidnapper if the hostage has been executed, in contrast with the case when a ransom is paid to secure the hostage's release. In this paper, we study the asymmetric game when the probability of capturing the kidnapper depends on whether the hostage has been executed or not and find a new uniquely determined perfect equilibrium point in Selten's game.

Vulnerability and Defence: A Case for Stackelberg Game Dynamics

Games, 2024

This paper examines the tactical interaction between drones and tanks in modern warfare through g... more This paper examines the tactical interaction between drones and tanks in modern warfare through game theory, particularly focusing on Stackelberg equilibrium and backward induction. It describes a high-stakes conflict between two teams: one using advanced drones for attack, and the
other defending using tanks. The paper conceptualizes this as a sequential game, illustrating the complex strategic dynamics similar to Stackelberg competition, where moves and countermoves are carefully analyzed and predicted.

A new derivation of the Minkowski metric

Journal of Physics Communications, 2023

The four dimensional spacetime continuum, as first conceived by Minkowski, has become the dominan... more The four dimensional spacetime continuum, as first conceived by Minkowski, has become the dominant framework within which to describe physical laws. In this paper, we show how this fourdimensional structure is a natural property of physical three-dimensional space, if modeled with Clifford geometric algebra Cl(R3). We find that Minkowski spacetime can be embedded within a larger eight-dimensional structure. This then allows a generalisation of the invariant interval and the Lorentz transformations. Also, with this geometric oriented approach the fixed speed of light, the laws of special relativity and a generalised form of Maxwell's equations, arise naturally from the intrinsic properties of the algebra without recourse to physical arguments. We also find new insights into the nature of time, which can be described as two-dimensional. Some philosophical implications of this approach as it relates to the foundations of physical theories are also discussed.

Two-player quantum games: When player strategies are via directional choices

Quantum Information Processing

We propose a scheme for a quantum game based on performing an EPR-type experiment and in which ea... more We propose a scheme for a quantum game based on performing an EPR-type experiment and in which each player’s spatial directional choices are considered as their strategies. A classical mixed-strategy game is recovered by restricting the players’ choices to specific spatial trajectories. We show that for players’ directional choices for which the Bell-CHSH inequality is violated, the players’ payoffs in the quantum game have no mapping within the classical mixed-strategy game. The scheme provides a more direct link between classical and quantum games.

Looking at world events through the prism of game theory

Sage International internet publication, 2016

This is the pdf of the internet publication by Sage International: https://sageinternational.com.... more

Two-player quantum games: When player strategies are via directional choices

We propose a scheme for a quantum game based on performing an EPR-type experiment and in which ea... more We propose a scheme for a quantum game based on performing an EPR-type experiment and in which each player's spatial directional choices are considered as their strategies. A classical mixed-strategy game is recovered by restricting the players' choices to specific spatial trajectories. We show that for players' directional choices for which the Bell-CHSH inequality is violated, the players' payoffs in the quantum game have no mapping within the classical mixed-strategy game. The scheme provides a more direct link between classical and quantum games.

Quantum strategies and evolutionary stability (in Urdu)

arXiv: Quantum Physics, 2019

This article in Urdu presents an introduction to extension of an established branch of mathematic... more

The Role of Non-Factorizability in Determining "Pseudo-Classical "Non-separability

This article introduces a "pseudo classical" notion of modelling non-separability. This... more This article introduces a "pseudo classical" notion of modelling non-separability. This form of non-separability can be viewed as lying between separability and quantum-like non-separability. Non-separability is formalized in terms of the non-factorizabilty of the underlying joint probability distribution. A decision criterium for determining the non-factorizability of the joint distribution is related to determining the rank of a matrix as well as another approach based on the chi-square-goodness-of-fit test. This pseudo-classical notion of non-separability is discussed in terms of quantum games and concept combinations in human cognition.

Game theoretical modelling of network/cybersecurity

IEEE Access

Kidnapping model: an extension of Selten's game

Royal Society open science, 2017

Selten's game is a kidnapping model where the probability of capturing the kidnapper is indep... more Selten's game is a kidnapping model where the probability of capturing the kidnapper is independent of whether the hostage has been released or executed. Most often, in view of the elevated sensitivities involved, authorities put greater effort and resources into capturing the kidnapper if the hostage has been executed, in contrast with the case when a ransom is paid to secure the hostage's release. In this paper, we study the asymmetric game when the probability of capturing the kidnapper depends on whether the hostage has been executed or not and find a new uniquely determined perfect equilibrium point in Selten's game.

Time As a Geometric Property of Space

Frontiers in Physics, 2016

The vector algebra war: a historical perspective

IEEE Access, 2016

The impact of the vaccination and booster shots in containing the COVID-19 epidemic in Bahrain: a game theory approach

In this study, game theory is used to determine the effect of vaccination and booster shots in co... more In this study, game theory is used to determine the effect of vaccination and booster shots in containing COVID-19 in Bahrain. The study is divided into three parts and in each part, the payoff matrix and the biometric is generated. The Nash equilibrium points are determined by marking the maximum value in the first entry of each column and the maximum value in the second entry of each row. The results show that the vaccination and the booster shots significantly reduce the number of infected individuals, the number of patients reaching the ICU, and the number of deaths due to COVID-19.

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

by Azhar Iqbal and Derek Abbott

A game-theoretic setting provides a mathematical basis for analysis of strategic interaction amon... more 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.

The impact of the precautionary measures taken in the kingdom of Bahrain to contain the outbreak of COVID-19

Can Quantum-Mechanical Description of Physical Reality Be Considered Complete? (An Urdu Translation)

An Urdu translation of the landmark article by Einstein, Podolsky and Rosen from the year 1935 is... more

Game theoretical modelling of network/cybersecurity

https://arxiv.org/abs/1901.08426, 2019

Game theory is an established branch of mathematics that offers a rich set of mathematical tools ... more Game theory is an established branch of mathematics that offers a rich set of mathematical tools for multiperson strategic decision making that can be used to model the interactions of decision makers in security problems who compete for limited and shared resources. This article presents a review of the literature in the area of game theoretical modelling of network/cybersecurity and identifies a number of challenges in
this area that need to be addressed.

Quantum strategies and evolutionary stability (in Urdu)

https://arxiv.org/abs/1901.09741, 2019

This article in Urdu presents an introduction to the extension of an established branch of mathem... more

A game theoretical perspective on the quantum probabilities associated with a GHZ state

In the standard approach to quantum games, players' strategic moves are local unitary transformat... more In the standard approach to quantum games, players' strategic moves are local unitary transformations on an entangled state that is subsequently measured. Players' payoffs are then obtained as expected values of the entries in the payoff matrix of the classical game on a set of quantum probabilities obtained from the quantum measurement. In this paper, we approach quantum games from a diametrically opposite perspective. We consider a classical three-player symmetric game along with a known expression for a set of quantum probabilities relevant to a tripartite Einstein–Podolsky–Rosen (EPR) experiment that depends on three players' directional choices in the experiment. We define the players' strategic moves as their directional choices in an EPR setting and then express their payoff relations in the resulting quantum game in terms of their directional choices, the entries of the payoff matrix, and the quantum probability distribution relevant to the tripartite EPR experiment.

The equivalence of Bell's inequality and the Nash inequality in a quantum game-theoretic setting

The interaction of competing agents is described by classical game theory. It is now well known t... more The interaction of competing agents is described by classical game theory. It is now well known that this can be extended to the quantum domain, where agents obey the rules of quantum mechanics. This is of emerging interest for exploring quantum foundations, quantum protocols, quantum auctions, quantum cryptography, and the dynamics of quantum cryptocurrency, for example. In this paper, we investigate two-player games in which a strategy pair can exist as a Nash equilibrium when the games obey the rules of quantum mechanics. Using a generalized Einstein–Podolsky–Rosen (EPR) setting for two-player quantum games, and considering a particular strategy pair, we identify sets of games for which the pair can exist as a Nash equilibrium only when Bell's inequality is violated. We thus determine specific games for which the Nash inequality becomes equivalent to Bell's inequality for the considered strategy pair.

Kidnapping model: an extension of Selten's game

by Azhar Iqbal and Virginie Masson

Selten's game is a kidnapping model where the probability of capturing the kidnapper is independe... more Selten's game is a kidnapping model where the probability of capturing the kidnapper is independent of whether the hostage has been released or executed. Most often, in view of the elevated sensitivities involved, authorities put greater effort and resources into capturing the kidnapper if the hostage has been executed, in contrast with the case when a ransom is paid to secure the hostage's release. In this paper, we study the asymmetric game when the probability of capturing the kidnapper depends on whether the hostage has been executed or not and find a new uniquely determined perfect equilibrium point in Selten's game.

An Urdu translation of the Australian National Anthem

Available at this link: https://archive.org/details/australian-national-anthem-an-urdu-translatio... more