# Dr Azhar Iqbal

I graduated with a BSc (Hons) in Physics from the University of Sheffield, UK, in 1995 and worked for several years in the area of Photonics at the Pakistan Institute of Lasers and Optics, before receiving a PhD in Applied Mathematics from the University of Hull, UK, in 2006. In 2006 I was with the National University of Sciences & Technology (NUST), Pakistan. During 2006-2007 I was with the Kochi University of Technology, Japan, on a postdoctoral research fellowship from Japan Society for the Promotion of Science. During 2007-2011 I was with the University of Adelaide on a postdoctoral research fellowship from the Australian Research Council and in 2012 as a senior research associate. From early 2013 I was with the King Fahd University of Petroleum & Minerals, Saudi Arabia, as an academic and returned to the University of Adelaide in mid-2014. My Erdos Number is 4.

**Introduction and focus:** My core research expertise is in quantum game theory that extends the established branch of mathematics called game theory towards the quantum domain. This research area came into existence in 1999 within the field of quantum information/computation when the game theory was added to the set of available mathematical tools in support of the efforts to discover new quantum algorithms [1,2]. Quantum game theory analyses the strategic interaction among rational agents (players) who share the two quantum information resources: (i) quantum superposition and (ii) entanglement. A quantum game involves unitary transformations and players' utilities are obtained from the quantum measurement(s).

Nash equilibrium (NE) is an established solution concept in game theory. My earliest work in quantum game theory was the study [3,34] of a well-known refinement notion of NE called an Evolutionarily Stable Strategy (ESS) [4] within the setting of playing a quantum game. The ESS concept was originally introduced in the 1970s by mathematical biologists who modeled an evolving population, placed under evolutionary pressures, using game-theoretic techniques. The ESS concept emerged as the central solution concept of evolutionary game theory. My work determined how an ESS becomes susceptible when the interactions among the players of a population, which is under evolutionary pressures, become quantum-mechanical. Quantizing a game was found to have consequences not only for the solution concept of an NE but also for one of its well-known refinement(s) [5,6,7,8,9] from evolutionary game theory.

My other works in quantum game theory include investigations on:

- the fate of the game-theoretic solution concepts of “social optimality” [10], “value of coalition” [11], “backward-induction outcome” [12], and “sub-game perfect outcome” [13] when a game is quantized
- playing quantum games using an Einstein-Podolsky-Rosen (EPR) setting [14,15,16,26]
- constructing quantum games from non-factorizable joint probabilities and from a system of Bell’s inequalities [17,18,19]
- quantum games played on networks [20,21,22,23,24,25]
- quantum games using the mathematical formalism of Clifford's geometric algebra [27,28,29,30]
- quantum Bayesian games [31,32,33]

Some research questions in quantum games are:

- Determining to what extent quantum games are faithful extensions of classical games? When can the outcomes of quantum games be the solutions to classical strategic problems?
- Seeking new ways of quantizing the classical games and developing the existing quantization schemes
- Quantization of static and dynamic games with finite, countable, and uncountable strategy sets
- Obtaining new insights into the paradoxes of classical game theory with the aid of quantum games
- The physical implementation of quantum games: How quantum games could be really played?
- Applications of quantum games in quantum information/computation
- Can quantum games provide more insight into quantum probabilities?

**Other Reseach Interests:**

**Games of asymmetric information:** My recent work [to appear] is on (classical) games involving information that is asymmetrically distributed among the players. These games become relevant to several situations encountered during bargaining and negotiations.

**Geometric Algebra** (GA): The formalism of 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 provides the powerful geometric intuition with the precision of an algebraic system. In a number of joint works, l have contributed to the studies on the applications of GA in quantum games [35,36,37,38], special relativity [39], quantum information [40], and electrical and electronic engineering [41,42].

**Electromagnetics:** At the School of Electrical & Electronic Engineering, I have contributed to works [43,44] on the mathematical modelling of memristors. Memristor is s 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.

## Appointments

Date | Position | Institution name |
---|---|---|

2013 - 2019 | Adjunct Senior Lecturer | University of Adelaide |

2013 - 2014 | Assistant Professor | King Fahd University of Petroleum & Minerals |

2012 - 2012 | Senior Research Associate | University of Adelaide |

2007 - 2011 | Australian Research Council (ARC) Postdoctoral Research Fellow | 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 - 2006 | Assistant Professor | National University of Sciences and Technology |

1995 - 2002 | 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 Sheffield | United Kingdom | BSc (Honours) |

1992 - 1995 | University of Hull | United Kingdom | PhD |

## Postgraduate Training

Date | Title | Institution | Country |
---|---|---|---|

Postgraduate Certificate in Research Training | University of Hull | United Kingdom |

## Research Interests

## Journals

Year | Citation |
---|---|

2016 | Zhou, S., Valchev, D., Dinovitser, A., Chappell, J., Iqbal, A., Ng, B. -. H. ... Abbott, D. (2016). Terahertz signal classification based on geometric algebra. IEEE Transactions on Terahertz Science & Technology, 6, 6, 793-802. 10.1109/TTHZ.2016.2610759 |

2016 | Chappell, J., Hartnett, J., Iannella, N., Iqbal, A. & Abbott, D. (2016). Time as a geometric property of space. D. Baleanu (Ed.). Frontiers in Physics, 4, 44-1-44-6. 10.3389/fphy.2016.00044 |

2016 | Iqbal, A., Chappell, J. & Abbott, D. (2016). On the equivalence between non-factorizable mixed-strategy classical games and quantum games. Royal Society Open Science, 3, 1, 1-11. 10.1098/rsos.150477 |

2016 | Chappell, J., Iqbal, A., Hartnett, J. & Abbott, D. (2016). The vector algebra war: a historical perspective. IEEE Access, 4, 1997-2004. 10.1109/ACCESS.2016.2538262 |

2015 | Iqbal, A., Chappell, J. & Abbott, D. (2015). Social optimality in quantum Bayesian games. Physica A: Statistical Mechanics and its Applications, 436, 798-805. 10.1016/j.physa.2015.05.020 |

2015 | Chappell, J., Iqbal, A., Gunn, L. & Abbott, D. (2015). Functions of multivector variables. PLoS One, 10, 3, e0116943-1-e0116943-21. 10.1371/journal.pone.0116943 |

2014 | 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, 1340-1363. 10.1109/JPROC.2014.2339299 |

2014 | 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, 2783-2800. |

2013 | Li, Q., Iqbal, A., Perc, M., Chen, M. & Abbott, D. (2013). Coevolution of quantum and classical strategies on evolving random networks. A. Barrat (Ed.). PLoS One, 8, 7, 1-10. 10.1371/journal.pone.0068423 |

2013 | 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, 1719-1735. 10.1007/s11128-012-0483-7 |

2013 | Li, Q., Chen, M., Perc, M., Iqbal, A. & Abbott, D. (2013). Effects of adaptive degrees of trust on coevolution of quantum strategies on scale-free networks. Scientific Reports, 3, 1-7. 10.1038/srep02949 |

2012 | Li, Q., Iqbal, A., Chen, M. & Abbott, D. (2012). Evolution of quantum strategies on a small-world network. European Physical Journal B, 85, 11, 1-9. 10.1140/epjb/e2012-30398-1 |

2012 | Eshraghian, K., Kavehei, O., Cho, K. R., Chappell, J., Iqbal, A., Al-Sarawi, S. & Abbott, D. (2012). Memristive device fundamentals and modeling: applications to circuits and systems simulation. Proceedings of the IEEE, 100, 6, 1991-2007. 10.1109/JPROC.2012.2188770 |

2012 | Chappell, J., Iqbal, A. & Abbott, D. (2012). N-player quantum games in an EPR setting. M. Perc (Ed.). PLoS One, 7, 5, 1-9. 10.1371/journal.pone.0036404 |

2012 | 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, 1-13. 10.1088/1367-2630/14/10/103034 |

2012 | Chappell, J., Iqbal, A., Iannella, N. & Abbott, D. (2012). Revisiting special relativity: a natural algebraic alternative to Minkowski spacetime. E. Scalas (Ed.). PLoS One, 7, 12, 1-10. 10.1371/journal.pone.0051756 |

2012 | Li, Q., Iqbal, A., Chen, M. & Abbott, D. (2012). Quantum strategies win in a defector-dominated population. Physica A, 391, 11, 3316-3322. 10.1016/j.physa.2012.01.048 |

2012 | Chappell, J., Chappell, M., Iqbal, A. & Abbott, D. (2012). The gravity field of a cube. Physics International, 3, 2, 50-57. 10.3844/pisp.2012.50.57 |

2012 | Chappell, J., Iqbal, A. & Abbott, D. (2012). Analysis of two-player quantum games in an EPR setting using Clifford's geometric algebra. G. Adesso (Ed.). PLoS One, 7, 1, e29015-1-e29015-8. 10.1371/journal.pone.0029015 |

2011 | Chappell, J., Lohe, M., Von Smekal, L., Iqbal, A. & Abbott, D. (2011). A precise error bound for quantum phase estimation. J. Kurths (Ed.). PLoS One, 6, 5, e19663-1-e19663-4. 10.1371/journal.pone.0019663 |

2011 | Chappell, J., Iqbal, A. & Abbott, D. (2011). Analyzing three-player quantum games in an EPR type setup. A. Szolnoki (Ed.). PLoS One, 6, 7, 1-11. 10.1371/journal.pone.0021623 |

2010 | Iqbal, A. & Abbott, D. (2010). Constructing quantum games from a system of Bell's inequalities. Physics Letters A, 374, 31-32, 3155-3163. 10.1016/j.physleta.2010.05.062 |

2010 | Kavehei, O., Iqbal, A., Kim, Y., Eshraghian, K., Al-Sarawi, S. & Abbott, D. (2010). The fourth element: characteristics, modelling and electromagnetic theory of the memristor. Proceedings of the Royal Society of London Series A-Mathematical Physical and Engineering Sciences, 466, 2120, 2175-2202. 10.1098/rspa.2009.0553 |

2010 | Chappell, J., Iqbal, A. & Abbott, D. (2010). Constructing quantum games from symmetric non-factorizable joint probabilities. Physics Letters A, 374, 40, 4104-4111. 10.1016/j.physleta.2010.08.024 |

2009 | Iqbal, A. & Abbott, D. (2009). Non-factorizable joint probabilities and evolutionarily stable strategies in the quantum prisoner's dilemma game. Physics Letters A, 373, 30, 2537-2541. 10.1016/j.physleta.2009.05.020 |

2009 | 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, 1-4. 10.1143/JPSJ.78.054801 |

2008 | Cheon, T. & Iqbal, A. (2008). Bayesian Nash equilibria and Bell inequalities. Journal of the Physical Society of Japan, 77, 2, 024801-. 10.1143/JPSJ.77.024801 |

2008 | Iqbal, A., Cheon, T. & Abbott, D. (2008). Probabilistic analysis of three-player symmetric quantum games played using the Einstein-Podolsky-Rosen-Bohm setting. Physics Letters A, 372, 44, 6564-6577. 10.1016/j.physleta.2008.09.026 |

2008 | Iqbal, A. & Abbott, D. (2008). Quantum matching pennies game. Journal of the Physical Society of Japan, 78, 1, 014803-1-014803-8. 10.1143/JPSJ.78.014803 |

2007 | Iqbal, A. & Cheon, T. (2007). Constructing quantum games from nonfactorizable joint probabilities. Physical Review E. (Statistical, Nonlinear, and Soft Matter Physics), 76, 6, 061122-1-061122-12. 10.1103/PhysRevE.76.061122 |

2005 | Iqbal, A. (2005). Playing games with EPR-type experiments. Journal of Physics A: Mathematical and Theoretical (Print Edition), 38, 43, 9551-9564. 10.1088/0305-4470/38/43/009 |

2004 | Iqbal, A. (2004). Quantum correlations and Nash equilibria of a bi-matrix game. Journal of Physics A: Mathematical and Theoretical (Print Edition), 37, 29, L353-L359. 10.1088/0305-4470/37/29/L04 |

2004 | Iqbal, A. & Weigert, S. (2004). Quantum correlation games. Journal of Physics A: Mathematical and Theoretical (Print Edition), 37, 22, 5873-5885. 10.1088/0305-4470/37/22/012 |

2004 | Iqbal, A. & Toor, A. (2004). Stability of mixed Nash equilibria in symmetric quantum game. Communications in Theoretical Physics, 42, 3, 335-338. 10.1088/0253-6102/42/3/335 |

2003 | Iqbal, A. (2003). Quantum games with a multi-slit electron diffraction set-up. Societa Italiana di Fisica Nuovo Cimento B: General Physics, Relativity Astronomy and Mathematical Physics and Methods, 118, 5, 463-468. 10.1393/ncb/i2002-10005-2 |

2002 | Iqbal, A. & Toor, A. (2002). Backwards-induction outcome in a quantum game. Physical Review A, 65, 5, 052328-1-052328-8. 10.1103/PhysRevA.65.052328 |

2002 | Iqbal, A. & Toor, A. (2002). Quantum repeated games. Physics Letters A, 300, 6, 541-546. 10.1016/S0375-9601(02)00893-9 |

2002 | Iqbal, A. & Toor, A. (2002). Darwinism in quantum systems?. Physics Letters A, 294, 5-6, 261-270. 10.1016/S0375-9601(02)00067-1 |

2002 | Iqbal, A. & Toor, A. (2002). Quantum cooperative games. Physics Letters A, 293, 3-4, 103-108. 10.1016/S0375-9601(02)00003-8 |

2002 | Iqbal, A. & Toor, A. (2002). Quantum mechanics gives stability to a Nash equilibrium. Physical Review A, 65, 2, 022306-1-022306-5. 10.1103/PhysRevA.65.022306 |

2001 | Iqbal, A. & Toor, A. (2001). Evolutionarily stable strategies in quantum games. Physics Letters A, 280, 5-6, 249-256. 10.1016/S0375-9601(01)00082-2 |

2001 | Iqbal, A. & Toor, A. (2001). Entanglement and dynamic stability of Nash equilibria in a symmetric quantum game. Physics Letters A, 286, 4, 245-250. 10.1016/S0375-9601(01)00428-5 |

## Book Chapters

Year | Citation |
---|---|

2008 | Iqbal, A. & Cheon, T. (2008). Evolutionary stability in quantum games. In D. Abbott, P. C. W. Davies & A. K. Pati (Eds.), Quantum Aspects of Life (pp. 251-288). London: Imperial College Press. 10.1142/9781848162556_0013 |

## Conference Papers

Year | Citation |
---|---|

2016 | Zhou, S., Valchev, D., Dinovitser, A., Chappell, J., Iqbal, A., Ng, B. ... Abbot, D. (2016). Dispersion-independent terahertz classification based on Geometric Algebra for substance detection. 41st International Conference on Infrared, Millimeter, and Terahertz Waves (IRMMW-THz). Copenhagen, DENMARK. 10.1109/IRMMW-THz.2016.7758626 |

2010 | Bruza, P., Iqbal, A. & Kitto, K. (2010). The role of non-factorizability in determining ''Pseudo-classical' non-separability. Quantum Informatics. Virginia. |

2009 | Kavehei, O., Kim, Y. S., Iqbal, A., Eshraghian, K., Al-Sarawi, S. & Abbott, D. (2009). The fourth element: Insights into the Memristor. ICCCAS. California. 10.1109/ICCCAS.2009.5250370 |

2008 | Iqbal, A. & Cheon, T. (2008). Constructing multi-player quantum games from non-factorizable joint probabilities - art. no. 68020A. Conference on Complex Systems II. D. Abbott, T. Aste, M. Batchelor, R. Dewar, T. DiMatteo & T. Guttmann (Eds.) Canberra, AUSTRALIA. |

2007 | Iqbal, A. & Cheon, T. (2007). Constructing multi-player quantum games from non-factorizable joint probabilities. SPIE Microelectronics, MEMS, and Nanotechnology. Canberra. 10.1117/12.774374 |

## Working Paper

Year | Citation |
---|---|

2017 | Iqbal, A., Masson, V. & Abbott, D.; (2017); Kidnapping Model: An Extension of Selten's Game; |

2015 | Iqbal, A., Chappell, J. M. & Abbott, D. E. R. E. K.; (2015); The equivalence of Bell's inequality and the Nash inequality in a quantum game-theoretic setting; |

## Internet Publications

Year | Citation |
---|---|

2016 | Iqbal, A.; (2016); Looking at World Events Through the Prism of Game Theory; |

- 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)

School of Electrical & Electronic Engineering, University of Adelaide:

- Electronic Circuits (Level 2), first semesters 2016 & 2017: tutor
- Electronic Systems (Level1), first semester 2016: tutor
- Avionics Sensors & Systems (Level 4), second semester 2014: part-time lecturer
- Communications (Level 4), first semesters 2012 & 2011: guest lecturer

Math Learning Centre, University of Adelaide:

- Undergrad Mathematics, 2017: tutor

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

- Methods of Applied Mathematics (Level 3), Jan 2013-May 2014: lecturer
- Elements of Differential Equations (Level 2), Jan 2013-May 2014: lecturer

National University of Sciences & Technology, Pakistan:

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

- 2017 and 2016 Masters Projects at the School of Electrical & Electronic Engineering: advisor

Provided assistance in research supervision of:

- Dr Omid Kavehei (completed his PhD at the School of Electrical & Electronic Engineering in 2012)
- Dr James M. Chappell (completed his PhD at the School of Chemistry & Physics in 2011)
- Dr Qiang Li (our research visitor from early 2011 to mid 2012 from the Chongqing University, People Republic of China)

## Memberships

Date | Role | Membership | Country |
---|---|---|---|

2017 - ongoing | Member | Game Theory Society | United States |

2017 - ongoing | Member | Australian Mathematical Society | Australia |

2016 - ongoing | Member | JSPS Alumni Association of Australia | Australia |

2011 - ongoing | Member | Australian Institute of Physics | Australia |

2006 - ongoing | Member | Australian Nanotechnology Network | Australia |

2006 - ongoing | Member | COSNet-Complex Open Systems Research Network | Australia |

## Committee Memberships

Date | Role | Committee | Institution | Country |
---|---|---|---|---|

2013 - 2014 | Member | Research Committee | Department of Mathematics & Statistics, King Fahd University of Petroleum & Minerals | Saudi Arabia |

## Consulting/Advisories

Date | Institution | Department | Organisation Type | Country |
---|---|---|---|---|

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 |