# Dr Azhar Iqbal

ORCID: 0000-0002-5221-9384.

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 the Japan Society for the Promotion of Science (JSPS). During 2007-2011 I was with the University of Adelaide on a postdoctoral research fellowship from the Australian Research Council (ARC) and in 2012 as a senior research associate. From early 2013 I was with the King Fahd University of Petroleum & Minerals (KFUPM), Saudi Arabia, as an academic and returned to the University of Adelaide in mid-2014. My Erdos Number is 4.

ORCID: 0000-0002-5221-9384.

**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 building on the research field of quantum information/computation. It studies the strategic interaction among rational agents who also share the two quantum information resources: **(i)** quantum superposition and **(ii)** entanglement.

A quantum game is the strategic manoeuvring of a quantum system by agents and involves unitary transformations and quantum measurement. Agents’ utilities are functions of their strategic actions (strategies) and are obtained from the outcomes of measurements performed on the quantum system. In 1999 it was observed 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. The list of known quantum algorithms is small and this observation led to the exploration of game theory for improving the understanding of the working of quantum algorithms. Quantum game theory analyses strategic interaction in the presence of quantum entanglement as game theory is added to the set of existing mathematical tools in the continuing efforts to develop further quantum algorithms.

**Quantum game theory:** In this core area of my research expertise, l have made the following contributions:

*Evolutionary stability in the quantum regime:*Introduced in the 1970s by mathematical biologists, the game theoretical notion of an Evolutionarily Stable Strategy (ESS) models an evolving population under evolutionary pressures. Being a refinement notion on the set of Nash equilibria, the ESS concept is the central stability solution concept of evolutionary game theory. My work 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 view of this work appeared in the book chapter in the book Quantum Aspects of Life, Imperial College Press, 2008 (pp. 251–288).*Entanglement determining the game-theoretic outcomes:*The area of quantum games was pioneered by work showing how sharing quantum entanglement results in the emergence of non-classical Nash equilibria. This motivated my work analysing the fate of other game-theoretic solution-concepts when players have access to quantum entanglement, including “Social Optimality” (Physica A: Stat. Mech. Applic. 436:798–805, 2015), “Value of Coalition” (Phys. Lett. A 293(3-4): 103-108, 2002), “Backwards-induction outcome” (Phys. Rev. A. 65(5): 052328, 2002) and “Sub-game Perfect Outcome” (Phys. Lett. A, 300(6): 541–546, 2002).*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 (J. Phys. A: Math. Theor. 37(22): 5873-5885, 2004) as part of my PhD thesis at the University of Hull, UK.*Quantum games from non-factorizable joint probabilities:*As part of my postdoctoral work during a prestigious research fellowship from Japan Society for the Promotion of Science, and while working under Prof Taksu Cheon at the Kochi University of Technology, Japan, I developed a new approach in constructing quantum games from the concept of non-factorizable joint probabilities (Physical Review E 76(6): 061122, 2007). A follow up of this work appeared in a number of other publications, including the joint work with Dr James M. Chappell (Physics Letters A 374(40): 4104–4111, 2010).*Quantum games from Bell’s inequalities:*During my Australian Postdoctoral Research Fellowship (APD), and working under Prof Derek Abbott, I developed a new approach to constructing quantum games directly from a system of Bell's inequalities (Phys. Lett. A 374 (31–32), 3155-3163 (2010).*Quantum games on networks:*In collaboration with Dr Qiang Li, Chongqing University, China, I presented investigations on quantum games played on networks (Scientific Reports (Nature) 3, 1–7 (2013)).*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. Jointly with Prof Taksu Cheon, I developed the first investigation on quantum Bayesian games (J. Phys. Soc. Japan 77(2):024801, 2008). Its follow up paper (Q. Inform. Process. 13, 2783-2800 (2014)) appeared later with my colleagues at the University of Adelaide.*Concept combinations using quantum games:*In joint work with Prof Peter Bruza, Queensland University of Technology, I contributed to the first investigation of using quantum games in the understanding and description of concept combinations in human cognition (AAAI-Fall 2010 Symp. Quant. Inform. Processes, Washington DC, November 11–13, 2010).

Some open questions in quantum game theory are:

- 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?
- Can we find new ways of quantizing the classical games and develop existing quantization schemes?
- Quantization of static and dynamic games with finite, countable, and uncountable strategy sets.
- Can quantum games improve the understanding of quantum probabilities, and if so, how?
- Application of quantum games to quantum information/computation.

I have also done work in classical game theory, geometric algebra, and the mathematical modelling of the memristive devices, as described below.

**Game theory:** In a recent paper (A. Iqbal, V. Masson, and D. Abbott, Kidnapping model: an extension of Selten's game, Royal Society Open Science, Vol. 4, Art. No. 171484 (2017)), I have developed an extension of the well-known Selten's game model of ransom kidnapping.

**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. In a number of joint works with Dr James M. Chappell and Prof Derek Abbott and others, l contributed to the first studies of quantum games using GA. This includes the following:

- Study of Meyer’s quantum penny-flip game using GA (J. Phys. Soc. Japan 78: 54801, 2009) building upon Meyer’s pioneering work in the area of quantum game theory;
- Developing the GA-based analysis of the two-player (PLOSONE 7(1): 29015, 2012) and the three-player quantum games in an EPR type setup (PLOSONE 6(7): 1–11, 2011);
- Study of special relativity using the mathematical formalism of GA (PLOSONE 7(12): 1–10, 2012);
- Investigation of N-player quantum games in an EPR setting (PLOSONE 7(5), 1–9, 2012);
- Development of an improved formalism for quantum computation based on GA and applying it to Grover's search algorithm (Q. Inform. Process. 12(4):1719–1735, 2013);
- Exploration of the benefits of GA formalism for engineers (Proc. IEEE. 102(9): 1340–1363, 2014);
- Study of the functions of multivector variables in GA (PLOSONE 10(3): 0116943, 2015); and
- Study of time as a geometric property of the GA-based conception of space (Front. Phys. 4: 44, 2016).

**Mathematical modelling of memristive devices:** 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. In collaboration with my colleagues at the University of Adelaide, I developed mathematical modelling of memristive devices (Proc. R. Soc. Lond. Ser. A-Math. Phys. Eng. Sci. 466(2120):2175–2202, 2010) and (Proc. Int. Conf. Comm., Circuits and Systems, ICCCAS, pp. 921-927, 2009) and its applications to circuits and systems simulation (Proc. IEEE 100(6): 1991–2007, 2012).

## 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

## Book Chapters

## Conference Papers

## Working Paper

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

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. 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 (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

## 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 | 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 | COSNet-Complex Open Systems Research Network | Australia |

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

## 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 |