GPGame {GPGame}

Package GPGame

Description

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.

Details

Important functions:
solve_game
plotGame

Author(s)

Victor Picheny, Mickael Binois

References

V. Picheny, M. Binois, A. Habbal (2016+), A Bayesian Optimization approach to find Nash equilibria, 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, https://bayesopt.github.io/papers/2017/28.pdf.

See Also

DiceKriging-package, DiceOptim-package, KrigInv-package, GPareto-package

Examples

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