##############################################################################

# #

# QUANTUM BATTLE OF THE SEXES GAME #

# #

##############################################################################

#' @title

#' Quantum Battle of the Sexes game

#'

#' @description

#' This function returns the expected payoffs to Alice and Bob with respect to the probabilities \code{p} and \code{q}. \code{p+q} should equal 1 and \code{moves} is a list of two possible strategies for each of the players and \code{alpha, beta, gamma} are the payoffs for the players corresponding to the choices available to them with the chain of inequalities, \code{alpha>beta>gamma}.

#'

#' @param p a real number between 0 and 1 including the end points

#' @param q a real number between 0 and 1 including the end points

#' @param moves alist of matrices

#' @param alpha a number

#' @param beta a number

#' @param gamma a number

#'

#' @usage

#' QBOS(p, q, moves, alpha, beta, gamma)

#'

#' @return A vector consisting of the Payoffs to Alice and Bob as its two elements depending on the inputs.

#'

#' @references

#' \url{https://arxiv.org/pdf/quant-ph/0506219.pdf}\cr

#' \url{https://arxiv.org/pdf/quant-ph/0208069.pdf}\cr

#' \url{https://arxiv.org/abs/quant-ph/0110096}\cr

#'

#'

#' @examples

#' init()

#' moves <- list(Q$I2, sigmaX(Q$I2))

#' QBOS(0, 1, moves, 5, 3, 1)

#' QBOS(1, 1, moves, 5, 3, 1)

#' QBOS(0.5, 0.5, moves, 5, 3, 1)

#'

#' @export

#'

QBOS <- function(p, q, moves, alpha, beta, gamma){

}