Quantum Information, Games and Computation

Takeshi Kawakami

Edward W. Piotrowski, Jan Sładkowski

Recent development in quantum computation and quantum information theory allows to extend the scope of game theory for the quantum world. The paper presents the history, basic ideas and recent development in quantum game theory. On grounds of the discussed material, we reason about possible future development of quantum game theory and its impact on information processing and the emerging information society.

Dmitrijs Kravcenko

Quantum mechanics and game theory were developed at almost the same time, during the first half of 20th century.Classical game theory is one of the most developed in mathematics and computer science.It has many applications in economics, biology, and different kinds of social science.In computer science, many cryptographic protocols are also based on the elements of game theory.Quantum computing is a relatively new branch of computer science.It unites different aspects of complexity theory and quantum physics.Our intention is to take it one step further and combine classical game theory with the acquired knowledge of quantum computing; in particular, to study the effects of using quantum information in the well-known problems of game theory.In this thesis, we obtain several bounds on the values of some special classes of nonlocal quantum games, and we present a new scheme for games quantization.

V. Ravishankar

Steven A. Bleiler

Poker has become a popular pastime all over the world. At any given moment one can find tens, if not hundreds, of thousands of players playing poker via their computers on the major on-line gaming sites. Indeed, according to the Vancouver, B.C. based pokerpulse.com estimates, more than 190 million US dollars daily is bet on-line poker rooms. But communication and computation are changing as the relentless application of Moore's Law brings computation and information into the quantum realm. The quantum theory of games concerns the behavior of classical games when played the coming quantum computing environment or when played with quantum information. In almost all cases, the versions of these games afford many new strategic options to the players. The study of so-called quantum games is quite new, arising from a seminal paper of D. Meyer \cite{Meyer} published Physics Review Letters 1999. The ensuing near decade has seen an explosion of contributions and controversy over what exactly a quantized game really is and if there is indeed anything new for game theory. With the settling of some of these controversies \cite{Bleiler}, it is now possible to fully analyze some of the basic endgame models from the game theory of Poker and predict with confidence just how the optimal play of Poker will change when played the coming quantum computation environment. The analysis here shows that for certain players, entangled poker will allow results that outperform those available to players in real life.