Azhar Iqbal

Dr Azhar Iqbal

Adjunct Senior Lecturer

School of Electrical and Electronic Engineering

Faculty of Engineering, Computer and Mathematical Sciences

ORCID: 0000-0002-5221-9384.
My research explores intriguing and counter-intuitive aspects of quantum entanglement and complex superposition using mathematical tools and solution-concepts of game theory, and the applications of game theory to cybersecurity and bargaining/negotiations.

I have published research in quantum games, game theory, applications of geometric algebra, and mathematical modelling in electromagnetics:

Quantum games: Quantum games extends game theory towards the quantum domain and, generally speaking, it studies the strategic interaction among rational agents who share quantum information resources of quantum superposition and entanglement. A quantum game can be considered as the strategic manoeuvring of a quantum system by agents or players and usually it involves unitary transformations and quantum measurement. Players’ utilities are functions of their strategic moves and are obtained from the outcomes of measurements performed on the quantum system. In 1999 Meyer observed (1,2,3) that quantum algorithm for an oracle problem can be understood as a quantum strategy for a player in a two-player zero-sum game in which the other player is constrained to play classically. Soon afterwards, Eisert, Wilkens, and Lewenstein (4,5) developed a quantized version of the well-known game of Prisoners' Dilemma. The possibility to view quantum algorithms as games between quantum and classical players introduced game theory to the set of available mathematical tools in present efforts to extend the list of quantum algorithms. My contributions in this research area include:

  • Evolutionary stability in the quantum regime: Introduced in the 1970s by mathematical biologists, the game-theoretical notion of an Evolutionarily Stable Strategy (ESS) (6,7) models an evolving population under evolutionary pressures. It is a refinement notion on the set of symmetric Nash equilibria and is the central stability solution concept of evolutionary game theory. My work (8,9,10,11,12,13) determined how an ESS becomes susceptible when the interactions among agents (players) of a population, under evolutionary pressures, become quantum-mechanical. The work showed that the quantum entanglement is relevant not only for Nash equilibrium but also for its refinements. A review of this work appeared as a book chapter (14).
  • Entanglement determining the game-theoretic outcomes: The earliest work in quantum games showed that sharing quantum entanglement results in the emergence of non-classical Nash equilibria. This motivated my work on the fate of other game-theoretic solution-concepts when players have access to quantum entanglement, including, “Social Optimality” (15), “Value of Coalition” (16), “Backwards-induction outcome” (17) and “Sub-game Perfect Outcome” (18).
  • Introducing Einstein-Podolsky-Rosen (EPR) setting for quantum games: In order to identify the truly quantum content of quantum games, l developed an EPR setting for enacting quantum games (19,20).
  • Quantum games from non-factorizable joint probabilities: In my postdoctoral work during a prestigious research fellowship from Japan Society for the Promotion of Science (JSPS), I developed a new approach in constructing quantum games from the concept of non-factorizable joint probabilities (21).
  • Quantum games from Bell’s inequalities: During my Australian Postdoctoral Research Fellowship at the University of Adelaide, I developed a new approach to constructing quantum games directly from a system of Bell's inequalities (22).
  • Quantum games on networks: I contributed to Qiang Li's work on quantum games played on networks (23).
  • Bayesian quantum games: Bayesian games have more complex underlying probabilities structure and offer a richer environment in studying the role of quantum probabilities in quantum games. I contributed to Taksu Cheon's first investigation of quantum Bayesian games (24). A follow-up paper (25) on this topic appeared with my colleagues at the University of Adelaide.
  • Concept combinations using quantum games: I contributed to Peter Bruza's work (26) at Queensland University of Technology on using quantum games in the understanding and description of concept combinations in human cognition.

Some open questions in quantum game theory include:

  • To what extent are game-theoretic quantum strategies a faithful extension of classical strategies?
  • Under which situations do quantum strategies include solutions to their classical counterparts and how can quantum game theory elucidate paradoxes in classical game theory?
  • How can existing quantization schemes be developed further?
  • How can quantum games improve the understanding of quantum probabilities?

Game theory: My work in (classical) game theory consists of developing an extension of the well-known Selten's game model of ransom kidnapping (27) and a review article on the applications of game theory in network/cybersecurity (40).

Applications of geometric algebra: Geometric Algebra (GA) combines the algebraic structure of Clifford’s algebra with the explicit geometric meaning of its mathematical elements at its foundation. It is a coherent mathematical language that augments the powerful geometric intuition of the human mind with the precision of an algebraic system. I have contributed to James Chappell's work on the applications of GA:

  • Study of Meyer’s quantum penny-flip game using GA (28) building up on Meyer’s pioneering work in the area of quantum game theory;
  • Developing a GA-based analysis of the two-player (29) and the three-player quantum games in an EPR type setup (30);
  • Study of special relativity using the mathematical formalism of GA (31);
  • Investigation of N-player quantum games in an EPR setting (32);
  • Development of an improved formalism for quantum computation based on GA and applying it to Grover's search algorithm (33);
  • Exploration of the benefits of GA formalism for engineers (34);
  • Study of the functions of multivector variables in GA (35); and
  • Study of time as a geometric property of the GA-based conception of space (36).

Mathematical modelling in electromagnetics: Memristor, a portmanteau of “memory” and “resistor”, and is a type of passive circuit elements that maintain a relationship between the time integrals of current and voltage across a two-terminal element. I contributed to Omid Kavehei's work on memristive devices (37,38) and its applications to circuits and systems simulation (39).

Author research IDs and impact indicators (updated in July 2021):


ResearcherID (h=index =18; Citations>955)

Google Scholar (h-index=23; i10-index=39; Citations>1695)

Scopus (h-index = 19; Citation > 1100)

Loop (Views>14,600)

ResearchGate (Reads>20,000)



  • Appointments

    Date Position Institution name
    2020 Associate Professor University of Bahrain
    2019 Senior Associate Sage International Australia
    2019 Founder Interactive Decisions
    2013 - 2022 Adjunct Senior Lecturer University of Adelaide
    2013 - 2015 Assistant Professor King Fahd University of Petroleum & Minerals
    2012 - 2012 Senior Research Associate (ARC grant-funded) University of Adelaide
    2007 - 2011 Australian Research Council's (ARC) Postdoctoral Research Fellow (Level A) University of Adelaide
    2006 - 2007 Japan Society for the Promotion of Science (JSPS) Postdoctoral Research Fellow and Visiting Associate Professor 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 Postgraduate Certificate in Research Training
    2002 - 2006 University of Hull United Kingdom PhD
    1992 - 1995 University of Sheffield United Kingdom BSc (Honours)
  • Research Interests

  • 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 (2016-2017)
  • Discovery Research Grant DP0771453 and Fellowship (Principal Investigator) from Australian Research Council (ARC) at University of Adelaide, AU$ 247,092 (2007-2011)
  • 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 (2006-2007)
  • Fully funded PhD Research Scholarship from the University of Hull, UK, for overseas research students (2002-2005)
  • Fully funded Merit Scholarship from the Government of Pakistan for studying overseas at the University of Sheffield, UK (1992-1995)

Department of Mathematics, College of Science, University of Bahrain (UoB):

Course                                                            Credit Hours             Number of Students

2nd Semester 2020-2021:

Calculus II (Maths 102)                                                         3                                  128

Calculus & Analytical Geometry II (Maths 122)                4                                  71

Calculus & Analytical Geometry III (Maths 204)               3                                  47

Fluid Mechanics (Maths 387)                                              3                                  8

1st Semester 2020-2021:

Calculus II (Maths 102)                                                        3                                  246

Methods of Applied Mathematics (Maths 381)               3                                  35

Analytical Mechanics (Maths 385)                                     3                                  39

2nd Semester 2019-2020:

Calculus II (Maths 102)                                                        3                                  88

Maths for Business Management I (Maths 103)             3                                  99

Calculus & Analytic Geometry III (Maths 204)                 3                                  29

School of Electrical & Electronic Engineering, University of Adelaide:

  • Avionic Sensors & Systems Combined (Level 4), 2014 Semester 2: Guest Lecturer (approximate class size: 20).
  • Communications/Principles of Communication Systems (Combined) (Level 4), 2012 Semester 1: Guest Lecturer (approximate class size: 20).
  • Communications/Principles of Communication Systems (Combined) (Level 4), 2011 Semester 1: Guest Lecturer (approximate class size: 20).

Department of Mathematics & Statistics, King Fahd University of Petroleum & Minerals (KFUPM), Saudi Arabia:

  • 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

(I taught these courses to classes of Mechanical, Electrical, and Aerospace Engineering students. The class size was approximately 40. In the year 2012 the Department of Mathematics & Statistics at KFUPM was ranked 50th in the world by the Academic Ranking of the World Universities.

National University of Sciences & Technology (NUST), Pakistan:

  • Mathematical Foundations of Quantum Mechanics (Level 4), July-Nov 2006

(I created the course contents at NUST’s School of Natural Sciences (SNS), approximate class size: 20).

Riphah International University (RUI), Islamabad, Pakistan:

  • Engineering Electromagnetics (Level 2), Sep 2000-Sep 2001

(I taught this course twice as Visiting Faculty while I was a PhD student at the Quaid-i-Azam University. The classes consisted of students in Electrical Engineering and the approximate class size was 20. The course was focused on both Vector Calculus and the Electromagnetism)

Tutoring experience

School of Electrical & Electronic Engineering, University of Adelaide:

  • 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, University of Adelaide:

  • Undergrad Maths courses (Various Levels), 2017 to 2019.
  • Position: Adjunct Senior Lecturer
  • Phone: 83135589
  • Email:
  • Campus: North Terrace
  • Building: Ingkarni Wardli, floor 3
  • Room: 3 49
  • Org Unit: School of Electrical and Electronic Engineering

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