Aspects of quantum game theory

Abstract

Quantum game theory is an exciting new topic that combines the physical behaviour of information in quantum mechanical systems with game theory, the mathematical description of conflict and competition situations, to shed new light on the fields of quantum control and quantum information. This thesis presents quantizations of some classic game-theoretic problems, new results in existing quantization schemes for two player, two strategy non-zero sum games, and in quantum versions of Parrondo's games, where the combination of two losing games can result in a winning game. In addition, quantum cellular automata and quantum walks are discussed, with a history-dependent quantum walk being presented.