Properties of iterated quantum games played on networks. 
Aims and Objectives: The main purpose of this PhD will be to investigate optimal strategies in quantum evolutionary games that are played on a network. As such, this is 
a model for calculating the behaviour of quantum agents. This new field of research is being developed at NUI, Galway, marrying ideas from Evolutionary Computation with ideas from Quantum Game Theory. Game theory is a well-established area of mathematics that has key applications in Computer Science (Agents) and Economics (Nobel Prize in 1994 for work of John Nash). In recent years, classical game theory has 
been generalized to the quantum domain, with many new features. In parallel with this - studies on iterated games and policy choices therein have been well developed in the Computer Science community. More recently, iterated games played on a graph have been studied (where 2 agents play a game with one another if they are connected by an edge on the graph). This PhD will study properties of quantum iterated games played on a network. Initial investigations will focus on the (well studied) prisoner’s dilemma, played on the cyclic graph. 
We will investigate questions such as: 
1) The effect of the initial entanglement (local or global) on the dynamics. 
2) The effect of the network/graph structure on the dynamics. 
3) The conditions for certain strategy choices to become optimal/dominant. 
4) The differences between classical and quantum iterated games. 
As well as theoretical studies using exact models, simulations will be caried out using suitable 
software (such as MATLAB) to check results, and present features in a graphical manner. 
Collaboration will build on existing work being carried out by Dr. Michael Mc Gettrick (Maths) and Dr. Colm O'Riordan (IT) at NUI, Galway.  

Our research plan is as follows:

Year 1: Familiarization with existing results in Quantum Game Theory and in 
Evolutionary Computation
Years 1 to 4: Participation in weekly seminars in the School of Maths
Years 1 to 4: Colaboration with Colm O'Riordan (IT Discipline, NUI, Galway) and 
his group.
Years 2 and 3: Colaboration with Jarek Miszczak (Polish Academy of Sciences).
Years 2 and 3: Main body of the work: Mathematical calculations and simulations
described above.
Years 3 and 4: Presentation of results at international conferences. Publication
of a peer-reviewed article in an international journal.
Years 1 and 2: Participation in relevant Summer Schools and Winter Schools in 
Quantum Computation held in Europe.
Year 4: Writing up of PhD thesis.