My research has spanned four domains: quantum game theory, game theory applications, geometric algebra applications, and mathematical modelling.

Quantum game theory: As my primary research focus for many years, the field of quantum game theory is a novel interdisciplinary pursuit that extends the principles of classical game theory into the enigmatic world of quantum mechanics. This discipline is currently encompassed within the broader quantum information and computation research, where the implications of quantum mechanics are probed and applied to game theory, thereby opening new vistas in its analytical prowess.

My scholarly contributions in this domain encompass:

• The concept of Evolutionarily Stable Strategy (ESS), first introduced by mathematical biologists in the 1970s [6 ,7 ], provides a model for an evolving population under evolutionary pressures. Widely recognized as the cornerstone of evolutionary game theory's stability solution, an ESS mathematically refines the set of symmetric Nash equilibria. My work [8 ,9 ,10 ,11 ,12 ,13 ] delves into determining the destiny of an ESS when interactions among players within a population, engaged in pairwise symmetric contests under evolutionary pressures, become quantum mechanical i.e. they involve complex superposition and/or entanglement. A review of this topic has been published as a chapter in the book “Quantum Aspects of Life” by the Imperial College Press [14 ];
• Investigation into the fate of well-established game-theoretic solution concepts within a quantum game has been a focus of my research. This includes exploration of concepts such as "Social Optimality" [15 ], "Value of Coalition" [16 ], "Backwards-Induction Outcome" [17 ], and "Sub-Game Perfect Outcome" [18 ] within the quantum domain;
• In-depth study of the Einstein-Podolsky-Rosen (EPR) framework for executing quantum games [19 ,20 ], which facilitates the identification of the genuinely quantum components of a quantum game;
• Development of innovative strategies for creating quantum games, including schemes for quantizing games derived from the concept of non-factorizable joint probabilities [21 ] and from a system of Bell's inequalities [22 ];
• Study of quantum games that are played on networks [23 ]. This research explores the impact of quantum strategies on player behaviour in network games, where player interactions are modelled via network topology. Our findings reveal that quantum correlations can significantly influence the equilibrium strategies and outcomes of games that are played on networks;
• My work also extends to quantum Bayesian games [24 , 25 ], which possess a more intricate underlying probability structure and offer a rich backdrop to examine the role of quantum probabilities. These papers open a new pathway for applying quantum games to analyse decision-making and information exchange in games characterized by incomplete information;
• Investigating [26 ] the application of quantum games to improve our understanding and portrayal of concept combinations in human cognition;
• My recent scholarly pursuits encompass: The introduction of a novel quantization scheme [40 ] wherein each player's quantum strategy is implemented through directional choices across three dimensions. This methodology provides an innovative, geometric, and intuitive means of representing quantum strategies. The formulation of an inventive scheme  [41 ] to derive the quantum version of a classical game, grounded in Fine's theorem from the early 1980s. Utilizing Positive Operator-Valued Measures (POVMs), we ascertain the quantum states that rectify inherent paradoxes in classical games.

Game theory applications: My contributions in this field encompass:

• Developing an extension of Selten's game [27 ];
• A review article [40 ] discussing applications of game theory;
• Study [44] of a sequential game, particularly focusing on Stackelberg equilibrium and backwards induction.

Geometric algebra applications: Geometric Algebra (GA) marries the algebraic structure of Clifford’s algebra with a discernible geometric interpretation, thus enhancing geometric intuition with the precision of an algebraic system. My collaborative work on applying GA includes:

• A GA-driven analysis of Meyer's quantum penny-flip game [28 ];
• A study of two-player and three-player quantum games in an EPR-type setup, leveraging GA [29 , 30 ];
• Exploration of special relativity through the mathematical formalism of GA [31 ];
• An investigation of N-player quantum games within an EPR context [32 ];
• Advancement of an enhanced formalism for quantum computation grounded in GA and its implementation in Grover's search algorithm [33 ];
• An investigation into the advantages of GA formalism for engineers [34 ];
• A study of the functions of multivector variables within GA [35 ];
• Examination of time as a geometric property within the GA-conceived perception of space [36 ];
• Showing how the structure of Minkowski's four dimensional spacetime continuum emerges as a natural property of physical three-dimensional space, if it is modeled with GA [43].

Mathematical modeling: This field involves the use of mathematical concepts and language for system descriptions. My contributions include:

• Formulation of mathematical models for memristive devices, and their applications in circuits and system simulations [37 ,38 ,39 ]. Memristors, a class of passive circuit element, can store information and maintain a relationship between the time integrals of current and voltage across a two-terminal element;
• Supervision of a research project concentrating on the mathematical modeling of the COVID-19 outbreak in Bahrain [41 ,42].

To view my research impact indicators, please visit the following links: ORCID , Web of Science , Google Scholar , Scopus , Loop , ResearchGate , and Academia .