R/QDuelsPlot4.R

In QGameTheory: Quantum Game Theory Simulator

##############################################################################
#                                                                            #
#                     QUANTUM TWO PERSON DUEL GAME                           #
#                                                                            #
##############################################################################

#' @title
#' Quantum Two Person Duel game
#'
#' @description
#' This function helps us to plot the improvement in Bob's expected payoff as a function of \code{a} and \code{b}, if Bob chooses to fire at the air in her second shot, in a two round game. \code{Psi} is the initial state of the quantum game, \code{n} is the number of rounds, \code{a} is the probability of Alice missing the target, \code{b} is the probability of Bob missing the target, and
#' \code{alpha1, alpha2, beta1, beta2} are arbitrary phase factors that lie in -pi to pi that control the outcome of a poorly performing player.
#'
#' @param Psi a vector representing the initial quantum state
#' @param alpha1 a number
#' @param alpha2 a number
#'
#' @usage
#' QDuelsPlot4(Psi, alpha1, alpha2)
#'
#' @return No return value, plots the improvement in Bob's expected payoff as a function of \code{a} and \code{b}, if Bob chooses to fire at the air in her second shot, in a two round game.
#'
#' @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/pdf/quant-ph/0305058.pdf}\cr
#'
#'
#' @examples
#' init()
#' Qs <- (Q$Q0+Q$Q1)/sqrt(2)
#' Psi <- kronecker(Q$Q1, Qs)
#' QDuelsPlot4(Psi, pi/3, pi/6)
#'
#' @export
#'

QDuelsPlot4 <- function(Psi, alpha1, alpha2){
  Psi <- as.vector(Psi)
  a <- seq(0, 1, length=20)
  b <- seq(0, 1, length=20)
  z <- matrix(data=NA, nrow=length(a), ncol=length(b))
  for(i in 1:length(a)){
    for (j in 1:length(b)){
      d <- QDuels_Alice_payoffs(Psi, 2, a[[i]], b[[j]], alpha1, alpha2, 0, 0)
      z[i, j] <- d[[3]] - (1-d[[1]])
    }
  }
  persp(a, b, z, xlab="a", ylab="b", zlab="<pi_Bob_diff>", theta=20, phi=50, r=2, shade=0.4, axes=TRUE, scale=TRUE, box=TRUE, nticks=5, ticktype = "detailed", col="green")
}