Dr Azhar Iqbal
Adjunct Senior Lecturer
School of Electrical and Electronic Engineering
Faculty of Engineering, Computer and Mathematical Sciences
ORCID: 0000000252219384.
My research explores intriguing and counterintuitive aspects of quantum entanglement and complex superposition using mathematical tools and solutionconcepts 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 modeling 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 maneuvering 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 twoplayer zerosum 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 wellknown 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 gametheoretical 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 quantummechanical. 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 gametheoretic outcomes: The earliest work in quantum games showed that sharing quantum entanglement results in the emergence of nonclassical Nash equilibria. This motivated my work on the fate of other gametheoretic solutionconcepts when players have access to quantum entanglement, including, “Social Optimality” (15), “Value of Coalition” (16), “Backwardsinduction outcome” (17) and “Subgame Perfect Outcome” (18).
 Introducing EinsteinPodolskyRosen (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 nonfactorizable 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 nonfactorizable 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 followup 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 gametheoretic 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 wellknown 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 pennyflip game using GA (28) building up on Meyer’s pioneering work in the area of quantum game theory;
 Developing a GAbased analysis of the twoplayer (29) and the threeplayer quantum games in an EPR type setup (30);
 Study of special relativity using the mathematical formalism of GA (31);
 Investigation of Nplayer 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 GAbased conception of space (36).
Mathematical modeling 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 twoterminal element. I contributed to Omid Kavehei's work on memristive devices (37,38) and its applications to circuits and systems simulation (39).

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Appointments
Date Position Institution name 2020 Associate Professor University of Bahrain 2019 Head of GameTheoretical & Mathematical Modelling Sage International Australia 2019 Founder Interactive Decisions 2016  2019 Teaching Lecturer and Research Academic University of Adelaide 2013  2022 Adjunct Senior Lecturer (Level C) University of Adelaide 2013  2015 Assistant Professor King Fahd University of Petroleum & Minerals 2012  2012 Australian Research Council's (ARC) Senior Research Associate (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 2006  2010 Assistant Professor National University of Sciences and Technology 2001  2002 Senior Scientific Officer Pakistan Institute of Lasers and Optics 1995  2000 Scientific Officer Pakistan Institute of Lasers and Optics 
Language Competencies
Language Competency English Can read, write, speak, understand spoken and peer review Panjabi; Punjabi 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 1999  2002 QuaidiAzam University Pakistan PhD 1992  1995 University of Sheffield United Kingdom BSc (Honours) 1989  1991 University of the Punjab Pakistan BSc in Pure & Applied Mathematics with Physics 
Research Interests

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Journals

Book Chapters

Conference Papers

Internet Publications
Year Citation 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)
School of Electrical & Electronic Engineering, University of Adelaide:
 Electronic Circuits (Level 2), first semesters 2016, 2017, & 2018: tutor
 Electronic Systems (Level1), first semester 2016: tutor
 Avionics Sensors & Systems (Level 4), second semester 2014: parttime lecturer
 Communications (Level 4), first semesters 2012 & 2011: guest lecturer
Math Learning Centre, University of Adelaide:
 Undergrad Mathematics, 2017present: tutor
Department of Mathematics & Statistics, King Fahd University of Petroleum & Minerals, Saudi Arabia:
 Methods of Applied Mathematics (Level 3), Jan 2013May 2014: lecturer
 Elements of Differential Equations (Level 2), Jan 2013May 2014: lecturer
National University of Sciences & Technology, Pakistan:
 Mathematical Foundations of Quantum Mechanics (Level 4), JulyNov 2006: lecturer

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Committee Memberships
Date Role Committee Institution Country 2013  2014 Member Research Committee Department of Mathematics & Statistics, King Fahd University of Petroleum & Minerals Saudi Arabia 
Memberships
Date Role Membership Country 2017  ongoing Member Game Theory Society Netherlands 2017  ongoing Member Australian Mathematical Society Australia 2016  ongoing Member JSPS Alumni Association of Australia Australia 2011  2014 Member Australian Institute of Physics Australia 2006  ongoing Member COSNetComplex Open Systems Research Network Australia 2006  ongoing Member Australian Nanotechnology Network Australia 
Consulting/Advisories
Date Institution Department Organisation Type Country 2019  ongoing Australian Research Council (ARC) National Competitive Grants Program Scientific research Australia 2019  ongoing Interactive Decisions Management Business and professional Australia 2017  ongoing University of Wollongong Exam Office/Student Services Division — Australia 2017  ongoing National Science Centre (Narodowe Centrum Nauki  NCN) — Scientific research Poland 2015  ongoing University of Sydney Faculty of Engineering & IT — Australia
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