Markov queue game with virtual reality strategies

Abstract

A non cooperative markov game with several unique characteristics was introduced. Some of these characteristics include: the existence of a single phase multi server queuing model and markovian transition matrix/matrices for each game, introduction of virtual situations (virtual reality) or dummies to improve the chances of winning or dominating the opponent, existence of payoff reduction factor as a result of introduction of the virtual realities/dummies etc. The game had two variants: variant 1 for games with customer/input based virtual reality strategies and variant 2 games without customer/input based virtual reality strategies. Based on some of these characteristics enumerated above, as well as other characteristics and assumptions, a mathematical model was formulated for studying the games. From the model, nash equilibria was proved to exist. The model could be effectively
used in studying competitive queuing systems which involves crowd renting, crowd hiding and other virtual reality and dummy strategies.

Keywords: Markov games; Queuing; Virtual reality strategies;
nash equilibrium, MSC CLASSIFICATION: 91A43