Dr Azhar Iqbal
Research Fellow (A) (with PhD)
School of Computer and Mathematical Sciences
Faculty of Sciences, Engineering and Technology
Eligible to supervise Masters and PhD  email supervisor to discuss availability.
My research spans four domains: quantum game theory, game theory applications, geometric algebra applications, and mathematical modelling.
Quantum Game Theory: My primary research focus lies in the emergent field of quantum game theory, a novel interdisciplinary pursuit that extends the principles of classical game theory into the enigmatic world of quantum mechanics. This pioneering discipline is currently encompassed within the broader quantum information and computation research, where the implications of quantum mechanics are probed and applied to game theory, thereby opening new vistas in its analytical prowess.
Quantum game theory investigates the dynamics of strategic decisionmaking among rational agents, who possess quantum resources like quantum superposition and entanglement. The objective is to blend the principles of quantum mechanics into conventional game theory scenarios, shedding light on the potential of quantum technology to fundamentally transform our understanding of strategic interactions and decisionmaking processes.
In this novel realm, a quantum game can be described as strategic interaction among rational agents or 'players', who manipulate a quantum system. Several realworld implementations of quantum games employ local unitary transformations and quantum measurements to encapsulate the strategic manoeuvres and decisionmaking processes among players.
The payoffs or rewards for each player in a quantum game are shaped by the strategic choices of all participating players and are ultimately derived from the outcomes of quantum measurements. Consequently, the quantum state of the system is impacted by the collective decisions of the players, triggering a complex web of probabilities that dictate each player's payoff. By dissecting these probabilities and the strategic decisions leading to them, quantum game theory can illuminate the intricacies of strategic decisionmaking in a quantum context. This, in turn, could enable unprecedented applications of quantum technology across various disciplines.
The genesis of quantum games can be traced back to 1999 when David Meyer presented groundbreaking research [1 ,2 ,3 ] illustrating that the quantum algorithm for an oracle problem could be interpreted as a quantum strategy for a player in a twoplayer zerosum game. Here, the other player adheres to classical strategy. Meyer's seminal contribution laid the groundwork for quantum game theory, forging a crucial link between quantum computing and game theory that has facilitated continued exploration of quantum technology within the landscape of strategic decisionmaking.
Soon after Meyer's pioneering work, Eisert, Wilkens, and Lewenstein [4 ,5 ] extended his findings by formulating a quantized interpretation of the famous Prisoners' Dilemma game. This quintessential game theory scenario involves two players who face the strategic dilemma of either cooperating or defecting, with their rewards contingent on the other player's decision. Through their investigation, Eisert, Wilkens, and Lewenstein substantiated the capacity of quantum technology to augment strategic decisionmaking, underscoring the compelling potential of quantum game theory within the broader domain of quantum information and computation research.
In essence, the capacity to construe quantum algorithms as strategic contests between quantum and classical players has led to the incorporation of game theory into the set of mathematical tools leveraged in the quest to expand the roster of viable quantum algorithms. By assimilating insights from game theory into the design of new quantum algorithms, researchers can acquire a more profound understanding of the intricate relationship between strategic decisionmaking and quantum mechanics. This, in turn, is instrumental in propelling the ongoing progression of quantum information and computation research.
My scholarly contributions in this domain encompass:
 The concept of Evolutionarily Stable Strategy (ESS), first introduced by mathematical biologists in the 1970s [6 ,7 ], provides a model for an evolving population under evolutionary pressures. Widely recognized as the cornerstone of evolutionary game theory's stability solution, an ESS mathematically refines the set of symmetric Nash equilibria. My work in this area [8 ,9 ,10 ,11 ,12 ,13 ] delves into the destiny of an ESS when interactions among players within a population, engaged in pairwise symmetric games under evolutionary pressures, adopt quantum mechanics. My research has demonstrated that when pairwise games take on a quantum mechanical nature, quantum entanglement can facilitate the emergence of new Nash equilibria and concurrently influence the future of Nash equilibrium refinements. The manifestation of entanglement can significantly alter the evolution of strategies within a population, indicating potential quantum mechanical foundations for the emergence of selforganization and complexity in molecularlevel interactions. A comprehensive review of this topic has been published as a chapter in the book “Quantum Aspects of Life” by the Imperial College Press [14 ];
 Investigation into the fate of wellestablished gametheoretic solution concepts within a quantum game has been a focus of my research. This includes exploration of concepts such as "Social Optimality" [15 ], "Value of Coalition" [16 ], "BackwardsInduction Outcome" [17 ], and "SubGame Perfect Outcome" [18 ] within the quantum domain;
 Indepth study of the EinsteinPodolskyRosen (EPR) framework for executing quantum games [19 ,20 ], which facilitates the identification of the genuinely quantum components of a quantum game;
 Development of innovative strategies for creating quantum games, including schemes for quantizing games derived from the concept of nonfactorizable joint probabilities [21 ] and from a system of Bell's inequalities [22 ];
 My recent scholarly pursuits encompass: The introduction of a novel quantization scheme [40 ] wherein each player's quantum strategy is implemented through directional choices across three dimensions. This methodology provides an innovative, geometric, and intuitive means of representing quantum strategies. The formulation of an inventive scheme [41 ] to derive the quantum version of a classical game, grounded in Fine's theorem from the early 1980s. Utilizing Positive OperatorValued Measures (POVMs), we ascertain the quantum states that rectify inherent paradoxes in classical games;
 Study of quantum games that are played on networks [23 ]. This research explores the impact of quantum strategies on player behaviour in network games, where player interactions are modelled via network topology. Our findings reveal that quantum correlations can significantly influence the equilibrium strategies and outcomes of games that are played on networks;
 My work also extends to quantum Bayesian games [24 , 25 ], which possess a more intricate underlying probability structure and offer a rich backdrop to examine the role of quantum probabilities. These papers open a new pathway for applying quantum games to analyse decisionmaking and information exchange in games characterized by incomplete information;
 Investigating [26 ] the application of quantum games to improve our understanding and portrayal of concept combinations in human cognition.
Game Theory Applications: My notable contributions in this field encompass:
 The development of an extension to Selten's widely recognized ransom kidnapping game model [27 ];
 An insightful review article [40 ] discussing the applications of game theory in the domain of network and cybersecurity.
Geometric Algebra Applications: Geometric Algebra (GA) marries the algebraic structure of Clifford’s algebra with a discernible geometric interpretation, thus enhancing geometric intuition with the precision of an algebraic system. My work on applying GA includes:
 A GAdriven analysis of Meyer's quantum pennyflip game [28 ];
 A study of twoplayer and threeplayer quantum games in an EPRtype setup, leveraging GA [29 , 30 ];
 Exploration of special relativity through the mathematical formalism of GA [31 ];
 An investigation of Nplayer quantum games within an EPR context [32 ];
 Advancement of an enhanced formalism for quantum computation grounded in GA and its implementation in Grover's search algorithm [33 ];
 An investigation into the advantages of GA formalism for engineers [34 ];
 A study of the functions of multivector variables within GA [35 ];
 Examination of time as a geometric property within the GAconceived perception of space [36 ];
 Showing how the structure of Minkowski's four dimensional spacetime continuum emerges as a natural property of physical threedimensional space, if it is modeled with GA [43].
Mathematical Modelling: This field involves the use of mathematical concepts and language for system descriptions. My contributions include:
 Formulation of mathematical models for memristive devices, and their applications in circuits and system simulations [37 ,38 ,39 ]. Memristors, a class of passive circuit element, can store information and maintain a relationship between the time integrals of current and voltage across a twoterminal element;
 Supervision of a research project concentrating on the mathematical modeling of the COVID19 outbreak in Bahrain [41 ,42].
To view my research impact indicators, please visit the following links: ORCID , Web of Science , Google Scholar , Scopus , Loop , ResearchGate , and Academia .

Appointments
Date Position Institution name 2007  ongoing Researcher University of Adelaide 2006  2007 JSPS Postdoctoral Research Fellow Kochi University of Technology 
Language Competencies
Language Competency English Can read, write, speak, understand spoken and peer review Urdu Can read, write, speak, understand spoken and peer review 
Education
Date Institution name Country Title 2002  2006 University of Hull United Kingdom PhD in Applied Mathematics 1992  1995 University of Sheffield United Kingdom BSc (Honours) in Physics 
Research Interests

Journals

Book Chapters

Conference Papers
Year Citation 2021 AlSayegh, M. A. K., & Iqbal, A. (2021). The impact of the vaccination and booster shots in containing the COVID19 epidemic in Bahrain: a game theory approach. In 2021 Third International Sustainability and Resilience Conference: Climate Change (SRC 2021) (pp. 16). Virtual online: IEEE.
2016 Zhou, S. L., Valchev, D. G., Dinovitser, A., Chappell, J. M., Iqbal, A., Ng, B. W. H., . . . Abbott, D. (2016). Dispersionindependent terahertz classification based on Geometric Algebra for substance detection. In Infrared, Millimeter, and Terahertz waves (IRMMWTHz), 2016 41st International Conference on Vol. 2016November (pp. 12). online: IEEE.
Scopus12010 Bruza, P., Iqbal, A., & Kitto, K. (2010). The role of nonfactorizability in determining "pseudoclassical" nonseparability. In AAAI Fall Symposium  Technical Report Vol. FS1008 (pp. 2631).
Scopus42010 Bruza, P., Iqbal, A., & Kitto, K. (2010). The role of nonfactorizability in determining ''Pseudoclassical' nonseparability. In Proceedings of Quantum Informatics 2010 (pp. 16). www.aaai.org: AAAI. 2009 Kavehei, O., Kim, Y. S., Iqbal, A., Eshraghian, K., AlSarawi, S., & Abbott, D. (2009). The fourth element: Insights into the Memristor. In Proceedings of ICCCAS 2009 (pp. 921927). USA: IEEE.
Scopus26 WoS272008 Iqbal, A., & Cheon, T. (2008). Constructing multiplayer quantum games from nonfactorizable joint probabilities  art. no. 68020A. In D. Abbott, T. Aste, M. Batchelor, R. Dewar, T. DiMatteo, & T. Guttmann (Eds.), COMPLEX SYSTEMS II Vol. 6802 (pp. A8020). Canberra, AUSTRALIA: SPIEINT SOC OPTICAL ENGINEERING.
WoS22007 Iqbal, A., & Cheon, T. (2007). Constructing multiplayer quantum games from nonfactorizable joint probabilities. In SPIE Microelectronics, MEMS, and Nanotechnology 2007 Proceedings Vol. 6802 (pp. 19). Sydney: SPIE.
Scopus8 
Conference Items
Year Citation 2017 32nd Annual Meeting and PreConference Programs of the Society for Immunotherapy of Cancer (SITC 2017): LateBreaking Abstracts (2017). Poster session presented at the meeting of Journal for ImmunoTherapy of Cancer. BMJ.

Internet Publications
Year Citation 2022 Iqbal, A. (2022). An Urdu translation of the Australian National Anthem. 2022 Iqbal, A. (2022). An Urdu translation of the Australian National Anthem. 2019 Iqbal, A., & Abbott, D. (2019). Quantum strategies and evolutionary stability (in Urdu). Eqbal Ahmad Centre for Public Education: https://eacpe.org/. 2019 Iqbal, A., Hoodbhoy, P., & Abbott, D. (2019). Can QuantumMechanical Description of Physical Reality Be Considered Complete? (An Urdu Translation). Eqbal Ahmad Centre for Public Education. 2016 Iqbal, A. (2016). Looking at World Events Through the Prism of Game Theory. SAGE International Australia.
 Faculty of Engineering, Computer & Mathematical Sciences (ECMS) Interdisciplinary Research Grant Scheme 2016 (jointly with Prof Derek Abbott & Dr Virginie Masson) at the University of Adelaide, AU$ 30,000 (20162017)
 Discovery Research Grant DP0771453 and Fellowship (Principal Investigator) from Australian Research Council (ARC) at University of Adelaide, AU$ 247,092 (20072011)
 Research Grant P06330 and Fellowship (Principal Investigator) from Japan Society for the Promotion of Science (JSPS) at Kochi University of Technology, Japanese Yen 4,958,500 (20062007)
 Fully funded PhD Research Scholarship from the University of Hull, UK, for overseas research students (20022005)
 Fully funded Merit Scholarship from the Government of Pakistan for studying overseas at the University of Sheffield, UK (19921995)
Department of Mathematics, College of Science, University of Bahrain (UoB):
2^{nd} Semester 20202021:
 Fluid Mechanics (Level 3)
 Calculus II (Level 1)
 Calculus & Analytical Geometry II (Level 1)
 Calculus & Analytical Geometry III (Level 2)
1^{st} Semester 20202021:
 Analytical Mechanics (Level 3)
 Methods of Applied Mathematics (Level 3)
 Calculus II (Level 1)
2^{nd} Semester 20192020:
 Calculus II (Level 1)
 Maths for Business Management (Level 1)
 Calculus & Analytic Geometry III (Level 2)
School of Electrical & Electronic Engineering, University of Adelaide:
 Avionic Sensors & Systems Combined (Level 4), 2014 Semester 2: Guest Lecturer
 Communications/Principles of Communication Systems (Combined) (Level 4), 2012 Semester 1: Guest Lecturer
 Communications/Principles of Communication Systems (Combined) (Level 4), 2011 Semester 1: Guest Lecturer
Department of Mathematics & Statistics, King Fahd University of Petroleum & Minerals (KFUPM):
 Methods of Applied Mathematics (Level 3), Jan 2013 to May 2014, taught this course 4 times
 Elements of Differential Equations (Level 2), Jan 2013 to May 2014, taught this course twice
School of Natural Sciences, National University of Sciences & Technology (NUST):
 Mathematical Foundations of Quantum Mechanics (Level 4), JulyNov 2006
Riphah International University (RUI):
 Engineering Electromagnetics (Level 2), Sep 2000Sep 2001
Tutoring experience
School of Electrical & Electronic Engineering, University of Adelaide:
 Vector Calculus & Electromagnetics (Level 2), 2022 Semester 2
 Electronic Circuits (Level 2), 2022 Semester 1
 Electronic Circuits (Level 2), 2018 Semester 1
 Electronic Circuits (Level 2), 2017 Semester 1
 Electronic Circuits (Level 2), 2016 Semester 1
 Electronic Systems (Level 1), 2016 Semester 1
Maths Learning Centre (MLC), University of Adelaide:
 Undergrad Maths courses (Various Levels), 2017 to 2019
Connect With Me
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