Playing games in quantum mechanical settings: Features of quantum games

In this lecture note, we present the implications of playing classical games in quantum mechanical settings where the quantum mechanical toolbox consisting of entanglement, quantum operations and measurement is used. After a brief introduction to the concepts of classical game theory and quantum mechanics, we study quantum games and their corresponding classical analogues to determine the novelties. In addition, we introduce a benchmark which attempts to make a fair comparison of classical games and their quantum extensions. This benchmark exploits the fact that in special settings a classical game should be reproduced as a subgame of its quantum extension. We obtained a rather surprising result that this requirement prevents the use of a large set of entangled states in quantum extension of classical games.