A formalism for quantum games and an application

Abstract
This paper presents a new mathematical formalism that describes the quantization of games. The study of so-called quantum games is quite new, arising from a seminal paper of D. Meyer published in Physics Review Letters in 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. What has clouded many of the issues is the lack of a mathematical formalism for the subject in which these various issues can be clearly and precisely expressed, and which provides a context in which to present their resolution. Such a formalism is presented here, along with proposed resolutions to some of the issues discussed in the literature. One in particular, the question of whether there can exist equilibria in a quantized version of a game that do not correspond to classical correlated equilibria of that game and also deliver better payoffs than the classical correlated equilibria is answered in the affirmative for the Prisoner’s Dilemma and Simplified Poker.

Three player, two strategy, maximally entangled quantum games

Abstract
We develop an octonionic representation of the payoff function for a three player, two strategy, maximally entangled quantum game.

Quaternionization of two player game with maximal entanglement

Abstract
An expository review of the quaternionization scheme for two player quantum games with maximal entanglement developed by Steve Landsburg.in the article found here.