Azhar Iqbal

Dr Azhar Iqbal

Senior Lecturer

School of Electrical and Mechanical Engineering

Faculty of Sciences, Engineering and Technology

My research can essentially be divided into four areas: 1) Quantum game theory 2) Game theory 3) Applications of geometric algebra, and 4) Mathematical modelling.

1) Quantum game theory: Most of my research is in this area. Quantum game theory extends classical game theory towards the quantum domain. It is now considered a research area within the broader field of quantum information and computation.

Essentially, quantum game theory is the study of strategic interaction among rational agents who share resources of quantum information and quantum computation i.e. quantum superposition and entanglement.

A quantum game can be considered as strategic manoeuvring of a quantum system by agents---considered as players---and in many physical implementations of quantum games, local unitary transformations and quantum measurements are involved.

Each player’s payoff, or utility, in a quantum game depends on the strategic choices of all players participating in the considered game and is obtained from outcomes of quantum measurements.

In literature, the history of quantum games is traced to the year 1999 when David Meyer reported [1,2,3] that the 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 plays classically.

Soon afterwards, Eisert, Wilkens, and Lewenstein [4,5] quantized version of the well-known game of Prisoners' Dilemma.

In summary, the possibility to view quantum algorithms, as games between quantum and classical players, has added game theory to the set of mathematical tools that are used in present efforts to further extend the list of quantum algorithms.

My contributions in this research area are:

  • Study of evolutionary stability in the quantum regime: Introduced in the 1970s by mathematical biologists, the game-theoretical notion of an Evolutionarily Stable Strategy [6,7], usually called an ESS, models an evolving population under evolutionary pressures. It is a refinement notion on the set of symmetric Nash equilibria and is widely believed to be the central stability solution concept of evolutionary game theory. My work on this topic, that appeared in several articles [8,9,10,11,12,13], determined the fate of Evolutionarily Stable Strategies when the interactions among the players of a population, that is engaged in pairwise symmetric games and subjected to evolutionary pressures, become quantum-mechanical. In this work, I showed that with the pairwise games becoming quantum mechanical, quantum entanglement can also decide the fate of Evolutionarily Stable Strategies. That is, the presence of quantum entanglement can result in not only the emergence of new Nash equilibria, as has been shown previously, but that entanglement can also decide fate of the refinement notion of the Nash equilibrium concept. My work anticipated that there can be quantum mechanical underpinnings for the emergence of self-organization and complexity at molecular level interactions. A review of this work has appeared as a chapter in the book “Quantum Aspects of Life”, published by the Imperial College Press [14].
  • Study of the fate of some well-known game-theoretic solution-concepts in a quantum game: This work includes, “Social Optimality” [15], “Value of Coalition” [16], “Backwards-induction outcome” [17] and “Sub-game Perfect Outcome” [18].
  • Developing an EPR setting for quantum games: To identify the truly quantum content of a quantum game, I developed Einstein-Podolsky-Rosen (EPR) setting for enacting quantum games [19,20].
  • Developing new scheme in constructing quantum games: I developed schemes for quantization of games from the concept of non-factorizable joint probabilities [21] and from a system of Bell's inequalities [22]. My recent work [40] develops a new scheme for quantum games in which each player's quantum strategy is implemented by using directional choices in three-dimensions.
  • Quantum games played on networks: In a collaborative work with Dr Qiang Li, we developed a study of quantum games that are played on networks [23].
  • Quantum Bayesian games: Bayesian games have more complex underlying probabilities structure and offer a richer environment to study the role of quantum probabilities in quantum games. I presented the first investigations of quantum Bayesian games in two articles [24, 25].
  • Using quantum games to describe concept combinations: In a collaborative work [26] with Prof Peter Bruza at Queensland University of Technology, we used quantum games to gain an improved understanding and description of concept combinations in human cognition.

2) Game theory: Game theory is an established branch of mathematics, in which my contributions are:

  • An article [27] that develops an extension of the well-known Selten's game model of ransom kidnapping, and
  • Applications of game theory in network/cybersecurity as presented in a review article [40].

3) Applications of geometric algebra: Geometric Algebra, or GA, combines the algebraic structure of Clifford’s algebra with an explicit geometric meaning. It is a coherent mathematical language that augments the powerful geometric intuition with the precision of an algebraic system. My collaborative work with Dr James Chappell on the applications of GA consists of:

  • Study of Meyer’s quantum penny-flip game using GA [28];
  • 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 the 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].

4) Mathematical modelling: Mathematical modelling uses mathematical concepts and language in the description of a system. My work in mathematical modelling consists of:

  • Collaborative work [37,38,39] with Dr Omid Kavehei on memristive devices and its applications to circuits and systems simulation;

(Memristor, a portmanteau of “memory” and “resistor”, is a type of passive circuit element that maintains a relationship between the time integrals of current and voltage across a two-terminal element.)

  • Research supervision of work [41,42] on mathematical modelling of COVID-19 outbreak in Bahrain

    My author IDs, also containing information of my research impact indicators, and the LinkIn profile are at these links:


    Web of Science

    Google Scholar







    • Appointments

      Date Position Institution name
      2022 - ongoing Senior Lecturer University of Adelaide
      2022 - ongoing Founder Quantum Interactive Decisions
      2020 - 2022 Associate Professor University of Bahrain
      2019 - ongoing Senior Associate Game Theory Sage International Australia
      2019 - ongoing 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, Level B) 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 PhD in Applied Mathematics
      2002 - 2006 University of Hull United Kingdom Postgraduate Certificate in Research Training
      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):

    2nd Semester 2020-2021:

    • Fluid Mechanics (Level 3)
    • Calculus II (Level 1)
    • Calculus & Analytical Geometry II (Level 1)
    • Calculus & Analytical Geometry III (Level 2)

    1st Semester 2020-2021:

    • Analytical Mechanics (Level 3)
    • Methods of Applied Mathematics (Level 3)
    • Calculus II (Level 1)

    2nd Semester 2019-2020:

    • 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), July-Nov 2006

    Riphah International University (RUI):

    • Engineering Electromagnetics (Level 2), Sep 2000-Sep 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
    • Position: Senior Lecturer
    • Phone: 83135589
    • Email:
    • Campus: North Terrace
    • Building: Ingkarni Wardli, floor Level Three
    • Org Unit: Electrical and Electronic Engineering

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