dorsal/arxiv
View SchemaStudies in the Theory of Quantum Games
| Authors | Azhar Iqbal |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0503176 |
| URL | https://arxiv.org/abs/quant-ph/0503176 |
Abstract
Theory of quantum games is a new area of investigation that has gone through rapid development during the last few years. Initial motivation for playing games, in the quantum world, comes from the possibility of re-formulating quantum communication protocols, and algorithms, in terms of games between quantum and classical players. The possibility led to the view that quantum games have a potential to provide helpful insight into working of quantum algorithms, and even in finding new ones. This thesis analyzes and compares some interesting games when played classically and quantum mechanically. A large part of the thesis concerns investigations into a refinement notion of the Nash equilibrium concept. The refinement, called an evolutionarily stable strategy (ESS), was originally introduced in 1970s by mathematical biologists to model an evolving population using techniques borrowed from game theory. Analysis is developed around a situation when quantization changes ESSs without affecting corresponding Nash equilibria. Effects of quantization on solution-concepts other than Nash equilibrium are presented and discussed. For this purpose the notions of value of coalition, backwards-induction outcome, and subgame-perfect outcome are selected. Repeated games are known to have different information structure than one-shot games. Investigation is presented into a possible way where quantization changes the outcome of a repeated game. Lastly, two new suggestions are put forward to play quantum versions of classical matrix games. The first one uses the association of De Broglie's waves, with travelling material objects, as a resource for playing a quantum game. The second suggestion concerns an EPR type setting exploiting directly the correlations in Bell's inequalities to play a bi-matrix game.
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"abstract": "Theory of quantum games is a new area of investigation that has gone through\nrapid development during the last few years. Initial motivation for playing\ngames, in the quantum world, comes from the possibility of re-formulating\nquantum communication protocols, and algorithms, in terms of games between\nquantum and classical players. The possibility led to the view that quantum\ngames have a potential to provide helpful insight into working of quantum\nalgorithms, and even in finding new ones. This thesis analyzes and compares\nsome interesting games when played classically and quantum mechanically. A\nlarge part of the thesis concerns investigations into a refinement notion of\nthe Nash equilibrium concept. The refinement, called an evolutionarily stable\nstrategy (ESS), was originally introduced in 1970s by mathematical biologists\nto model an evolving population using techniques borrowed from game theory.\nAnalysis is developed around a situation when quantization changes ESSs without\naffecting corresponding Nash equilibria. Effects of quantization on\nsolution-concepts other than Nash equilibrium are presented and discussed. For\nthis purpose the notions of value of coalition, backwards-induction outcome,\nand subgame-perfect outcome are selected. Repeated games are known to have\ndifferent information structure than one-shot games. Investigation is presented\ninto a possible way where quantization changes the outcome of a repeated game.\nLastly, two new suggestions are put forward to play quantum versions of\nclassical matrix games. The first one uses the association of De Broglie\u0027s\nwaves, with travelling material objects, as a resource for playing a quantum\ngame. The second suggestion concerns an EPR type setting exploiting directly\nthe correlations in Bell\u0027s inequalities to play a bi-matrix game.",
"arxiv_id": "quant-ph/0503176",
"authors": [
"Azhar Iqbal"
],
"categories": [
"quant-ph"
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"title": "Studies in the Theory of Quantum Games",
"url": "https://arxiv.org/abs/quant-ph/0503176"
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