R/GPGame-package.R

In vpicheny/GPGame: Solving Complex Game Problems using Gaussian Processes

#' Sequential strategies for finding game equilibria in a black-box setting (expensive pay-off evaluations, no derivatives).
#' Handles noiseless or noisy evaluations. Two acquisition functions are available. Graphical outputs can be generated automatically.
#' @title Package GPGame
#' @author Victor Picheny, Mickael Binois
#' @name GPGame
#' @references
#' V. Picheny, M. Binois, A. Habbal (2016+), A Bayesian Optimization approach to find Nash equilibria,
#' \emph{https://arxiv.org/abs/1611.02440}.
#' 
#' M. Binois, V. Picheny, A. Habbal, "The Kalai-Smorodinski solution for many-objective Bayesian optimization", 
#' NIPS BayesOpt workshop, December 2017, Long Beach, USA,
#' \emph{https://bayesopt.github.io/papers/2017/28.pdf}.
#' 
#' @details
#' Important functions: \cr
#' \code{\link[GPGame]{solve_game}} \cr
#' \code{\link[GPGame]{plotGame}} \cr
#'
#' @seealso \code{\link[DiceKriging]{DiceKriging-package}}, \code{\link[DiceOptim]{DiceOptim-package}}, \code{\link[KrigInv]{KrigInv-package}}, \code{\link[GPareto]{GPareto-package}}
#' @examples
#' \donttest{
#' # To use parallel computation (turn off on Windows)
#' library(parallel)
#' parallel <- FALSE # TRUE # 
#' if(parallel) ncores <- detectCores() else ncores <- 1
#'
#' ##############################################
#' # 2 variables, 2 players, Nash equilibrium
#' # Player 1 (P1) wants to minimize fun1 and player 2 (P2) fun2
#' # P1 chooses x2 and P2 x2
#'
#' ##############################################
#' # First, define objective function fun: (x1,x2) -> (fun1,fun2)
#' fun <- function (x)
#' {
#'   if (is.null(dim(x)))    x <- matrix(x, nrow = 1)
#'   b1 <- 15 * x[, 1] - 5
#'   b2 <- 15 * x[, 2]
#'   return(cbind((b2 - 5.1*(b1/(2*pi))^2 + 5/pi*b1 - 6)^2 + 10*((1 - 1/(8*pi)) * cos(b1) + 1),
#'                -sqrt((10.5 - b1)*(b1 + 5.5)*(b2 + 0.5)) - 1/30*(b2 - 5.1*(b1/(2*pi))^2 - 6)^2-
#'                 1/3 * ((1 - 1/(8 * pi)) * cos(b1) + 1)))
#' }
#'
#' ##############################################
#' # x.to.obj indicates that P1 chooses x1 and P2 chooses x2
#' x.to.obj   <- c(1,2)
#'
#' ##############################################
#' # Define a discretization of the problem: each player can choose between 21 strategies
#' # The ensemble of combined strategies is a 21x21 cartesian grid
#'
#' # n.s is the number of strategies (vector)
#' n.s <- rep(21, 2)
#' # gridtype is the type of discretization
#' gridtype <- 'cartesian'
#'
#' integcontrol <- list(n.s=n.s, gridtype=gridtype)
#'
#' ##############################################
#' # Run solver with 6 initial points, 14 iterations
#' n.init <- 6 # number of initial points (space-filling)
#' n.ite <- 14 # number of iterations (sequential infill points)
#'
#' res <- solve_game(fun, equilibrium = "NE", crit = "sur", n.init=n.init, n.ite=n.ite,
#'                   d = 2, nobj=2, x.to.obj = x.to.obj, integcontrol=integcontrol,
#'                   ncores = ncores, trace=1, seed=1)
#'
#' ##############################################
#' # Get estimated equilibrium and corresponding pay-off
#' NE <- res$Eq.design
#' Poff <- res$Eq.poff
#'
#' ##############################################
#' # Draw results
#' plotGame(res)
#'
#' ##############################################
#' # See solve_game for other examples
#' ##############################################
#' }
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