Equilibria in Quantum Three-Player Dilemma Game
Aden Omar Ahmed *
Department of Mathematics, Texas A&M University – Kingsville, Texas 78363-8202, USA.
*Author to whom correspondence should be addressed.
Abstract
After a brief exploration of certain topological features of the unit octonions, we identify the Nash equilibria in a quantized version of three-player dilemma game using an octonionic representation of the payoff function. This representation is an important tool for the relative ease in working with octonionic arithmetic as opposed to multi-variant tensors and provides a fresh computational framework that can be utilized for the classification of Nash equilibria in generic three-player two-strategy games. While the full classification of equilibria remains a goal of future research, our representation has already established certain family of equilibria in a quantized version of three-player dilemma game.
Keywords: Quaternions, octonions, quantum Games, Nash equilibrium