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 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 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 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 twoterminal 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):

Expand

Appointments
Date Position Institution name 2020 Associate Professor University of Bahrain 2019 Senior Associate Sage International Australia 2019 Founder Interactive Decisions 2013  2025 Adjunct Senior Lecturer University of Adelaide 2013  2015 Assistant Professor King Fahd University of Petroleum & Minerals 2012  2012 Senior Research Associate (ARC grantfunded) 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

Expand

Journals
Year Citation 2021 AlSayegh, M. A. K., & Iqbal, A. (2021). The impact of the precautionary measures taken in the kingdom of Bahrain to contain the outbreak of COVID19. Arab Journal of Basic and Applied Sciences, 28(1), 195203.
Scopus22019 Iqbal, A., Gunn, L. J., Guo, M., Babar, M., & Abbott, D. (2019). Game theoretical modelling of network/cybersecurity. IEEE Access, 7, 154167154179.
Scopus5 WoS52018 Iqbal, A., Chappell, J., & Abbott, D. (2018). The equivalence of Bell's inequality and the Nash inequality in a quantum gametheoretic setting. Physics Letters A, 382(40), 29082913.
Scopus5 WoS52018 Iqbal, A., & Abbott, D. (2018). A game theoretical perspective on the quantum probabilities associated with a GHZ state. Quantum Information Processing, 17(11), 313131313.
Scopus2 WoS22017 Iqbal, A., Masson, V., & Abbott, D. (2017). Kidnapping model: an extension of Selten’s game. Royal Society Open Science, 4(12), 171484117148410.
Scopus2 WoS32016 Zhou, S., Valchev, D. G., Dinovitser, A., Chappell, J. M., Iqbal, A., Ng, B. W. H., . . . Abbott, D. (2016). Terahertz signal classification based on geometric algebra. IEEE Transactions on Terahertz Science and Technology, 6(6), 793802.
Scopus8 WoS82016 Chappell, J. M., Hartnett, J. G., Iannella, N., Iqbal, A., & Abbott, D. (2016). Time as a geometric property of space. Frontiers in Physics, 4(NOV), 44.
Scopus1 WoS22016 Chappell, J., Iqbal, A., Hartnett, J., & Abbott, D. (2016). The vector algebra war: a historical perspective. IEEE Access, 4, 19972004.
Scopus11 WoS102016 Iqbal, A., Chappell, J., & Abbott, D. (2016). On the equivalence between nonfactorizable mixedstrategy classical games and quantum games. Royal Society Open Science, 3(1), 111.
Scopus13 WoS13 Europe PMC32015 Chappell, J., Iqbal, A., Gunn, L., & Abbott, D. (2015). Functions of multivector variables. PLoS One, 10(3), e01169431e011694321.
Scopus6 WoS92015 Iqbal, A., Chappell, J., & Abbott, D. (2015). Social optimality in quantum Bayesian games. Physica A: Statistical Mechanics and its Applications, 436, 798805.
Scopus19 WoS172014 Chappell, J. M., Drake, S. P., Seidel, C. L., Gunn, L. J., Iqbal, A., Allison, A., & Abbott, D. (2014). Geometric algebra for electrical and electronic engineers. Proceedings of the IEEE, 102(9), 13401363.
Scopus29 WoS322014 Iqbal, A., Chappell, J. M., Li, Q., Pearce, C. E. M., & Abbott, D. (2014). A probabilistic approach to quantum Bayesian games of incomplete information. Quantum Information Processing, 13(2), 27832800.
Scopus20 WoS192013 Li, Q., Chen, M., Perc, M., Iqbal, A., & Abbott, D. (2013). Effects of adaptive degrees of trust on coevolution of quantum strategies on scalefree networks. Scientific Reports, 3, 17.
Scopus28 WoS25 Europe PMC72013 Li, Q., Iqbal, A., Perc, M., Chen, M., & Abbott, D. (2013). Coevolution of quantum and classical strategies on evolving random networks. PLoS One, 8(7), 110.
Scopus27 WoS20 Europe PMC82013 Chappell, J., Iqbal, A., Lohe, M., Von Smekal, L., & Abbott, D. (2013). An improved formalism for quantum computation based on geometric algebra  case study: Grover's search algorithm. Quantum Information Processing, 12(4), 17191735.
Scopus4 WoS32012 Eshraghian, K., Kavehei, O., Cho, K. R., Chappell, J., Iqbal, A., AlSarawi, S., & Abbott, D. (2012). Memristive device fundamentals and modeling: applications to circuits and systems simulation. Proceedings of the IEEE, 100(6), 19912007.
Scopus88 WoS822012 Chappell, J., Iqbal, A., & Abbott, D. (2012). Nplayer quantum games in an EPR setting. PLoS One, 7(5), 19.
Scopus19 WoS16 Europe PMC32012 Li, Q., Iqbal, A., Chen, M., & Abbott, D. (2012). Quantum strategies win in a defectordominated population. Physica A, 391(11), 33163322.
Scopus26 WoS252012 Chappell, J., Iqbal, A., & Abbott, D. (2012). Analysis of twoplayer quantum games in an EPR setting using Clifford's geometric algebra. PLoS One, 7(1), e290151e290158.
Scopus10 WoS10 Europe PMC42012 Chappell, J., Chappell, M., Iqbal, A., & Abbott, D. (2012). The gravity field of a cube. Physics International, 3(2), 5057.
2012 Chappell, J., Iqbal, A., Iannella, N., & Abbott, D. (2012). Revisiting special relativity: a natural algebraic alternative to Minkowski spacetime. PLoS One, 7(12), 110.
Scopus6 WoS5 Europe PMC12012 Li, Q., Iqbal, A., Chen, M., & Abbott, D. (2012). Evolution of quantum strategies on a smallworld network. European Physical Journal B, 85(11), 19.
Scopus5 WoS52012 Li, Q., Iqbal, A., Chen, M., & Abbott, D. (2012). Evolution of quantum and classical strategies on networks by group interactions. New Journal of Physics, 14(10), 113.
Scopus15 WoS132011 Chappell, J., Iqbal, A., & Abbott, D. (2011). Analyzing threeplayer quantum games in an EPR type setup. PLoS One, 6(7), 111.
Scopus16 WoS17 Europe PMC82011 Chappell, J., Lohe, M., Von Smekal, L., Iqbal, A., & Abbott, D. (2011). A precise error bound for quantum phase estimation. PLoS One, 6(5), e196631e196634.
Scopus3 WoS12010 Chappell, J., Iqbal, A., & Abbott, D. (2010). Constructing quantum games from symmetric nonfactorizable joint probabilities. Physics Letters A, 374(40), 41044111.
Scopus10 WoS112010 Kavehei, O., Iqbal, A., Kim, Y., Eshraghian, K., AlSarawi, S., & Abbott, D. (2010). The fourth element: characteristics, modelling and electromagnetic theory of the memristor. Proceedings of the Royal Society of London Series AMathematical Physical and Engineering Sciences, 466(2120), 21752202.
Scopus135 WoS1002010 Iqbal, A., & Abbott, D. (2010). Constructing quantum games from a system of Bell's inequalities. Physics Letters A, 374(3132), 31553163.
Scopus20 WoS192009 Iqbal, A., & Abbott, D. (2009). Nonfactorizable joint probabilities and evolutionarily stable strategies in the quantum prisoner's dilemma game. Physics Letters A, 373(30), 25372541.
Scopus11 WoS82009 Chappell, J., Iqbal, A., Lohe, M., & Von Smekal, L. (2009). An analysis of the quantum penny flip game using geometric algebra. Journal of the Physical Society of Japan, 78(54801), 14.
Scopus19 WoS182009 Iqbal, A., & Abbott, D. (2009). Quantum matching pennies game. Journal of the Physical Society of Japan, 78(1), 01480310148038.
Scopus21 WoS182008 Iqbal, A., Cheon, T., & Abbott, D. (2008). Probabilistic analysis of threeplayer symmetric quantum games played using the EinsteinPodolskyRosenBohm setting. Physics Letters A, 372(44), 65646577.
Scopus31 WoS292008 Cheon, T., & Iqbal, A. (2008). Bayesian Nash equilibria and Bell inequalities. Journal of the Physical Society of Japan, 77(2), 024801 (6 pages).
Scopus40 WoS382007 Iqbal, A., & Cheon, T. (2007). Constructing quantum games from nonfactorizable joint probabilities. Physical Review E. (Statistical, Nonlinear, and Soft Matter Physics), 76(6), 061122106112212.
Scopus24 WoS202005 Iqbal, A. (2005). Playing games with EPRtype experiments. Journal of Physics A: Mathematical and Theoretical (Print Edition), 38(43), 95519564.
Scopus15 WoS142004 Iqbal, A., & Toor, A. (2004). Stability of mixed Nash equilibria in symmetric quantum game. Communications in Theoretical Physics, 42(3), 335338.
Scopus12 WoS102004 Iqbal, A., & Weigert, S. (2004). Quantum correlation games. Journal of Physics A: Mathematical and Theoretical (Print Edition), 37(22), 58735885.
Scopus31 WoS282004 Iqbal, A. (2004). Quantum correlations and Nash equilibria of a bimatrix game. Journal of Physics A: Mathematical and Theoretical (Print Edition), 37(29), L353L359.
Scopus8 WoS52003 Iqbal, A. (2003). Quantum games with a multislit electron diffraction setup. Societa Italiana di Fisica Nuovo Cimento B: General Physics, Relativity Astronomy and Mathematical Physics and Methods, 118(5), 463468.
Scopus12002 Iqbal, A., & Toor, A. (2002). Quantum mechanics gives stability to a Nash equilibrium. Physical Review A, 65(2), 02230610223065.
Scopus57 WoS492002 Iqbal, A., & Toor, A. (2002). Quantum cooperative games. Physics Letters A, 293(34), 103108.
Scopus45 WoS422002 Iqbal, A., & Toor, A. (2002). Quantum repeated games. Physics Letters A, 300(6), 541546.
Scopus28 WoS252002 Iqbal, A., & Toor, A. (2002). Darwinism in quantum systems?. Physics Letters A, 294(56), 261270.
Scopus21 WoS182002 Iqbal, A., & Toor, A. (2002). Backwardsinduction outcome in a quantum game. Physical Review A, 65(5), 05232810523288.
Scopus61 WoS602001 Iqbal, A., & Toor, A. H. (2001). Evolutionarily stable strategies in quantum games. Physics Letters A, 280(56), 249256.
Scopus96 WoS862001 Iqbal, A., & Toor, A. (2001). Entanglement and dynamic stability of Nash equilibria in a symmetric quantum game. Physics Letters A, 286(4), 245250.
Scopus25 WoS22 
Book Chapters
Year Citation 2008 Iqbal, A., & Cheon, T. (2008). Evolutionary stability in quantum games. In D. Abbott, P. Davies, & A. Pati (Eds.), Quantum Aspects of Life (pp. 251288). London: Imperial College Press.
Scopus7 
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. 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).
Scopus32010 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.
Scopus23 WoS242008 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.

Working Paper
Year Citation 2021 Iqbal, A., & Abbott, D. (2021). A new quantum game framework: When player strategies are via directional choices. 
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):
Course Credit Hours Number of Students
2^{nd} Semester 20202021:
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
1^{st} Semester 20202021:
Calculus II (Maths 102) 3 246
Methods of Applied Mathematics (Maths 381) 3 35
Analytical Mechanics (Maths 385) 3 39
2^{nd} Semester 20192020:
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), JulyNov 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 2000Sep 2001
(I taught this course twice as Visiting Faculty while I was a PhD student at the QuaidiAzam 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.

Expand

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
Connect With Me
External Profiles