% Generated by roxygen2: do not edit by hand
% Please edit documentation in R/crit_SUR.R
\name{crit_SUR_Eq}
\alias{crit_SUR_Eq}
\title{SUR criterion for equilibria}
\usage{
crit_SUR_Eq(idx, model, integcontrol, Simu, precalc.data = NULL, equilibrium,
  n.ynew = NULL, cross = FALSE, IS = FALSE, plot = FALSE)
}
\arguments{
\item{idx}{is the index on the grid of the strategy evaluated}

\item{model}{is a list of \code{nobj} \code{\link[DiceKriging]{km}} models}

\item{integcontrol}{is a list containing: \code{integ.pts}, a [\code{npts x dim}] matrix defining the grid,
\code{expanded.indices} a matrix containing the indices of the \code{integ.pts} on the grid and \code{n.s},
a \code{nobj} vector containing the number of strategies per player}

\item{Simu}{is a matrix of size [\code{npts x nsim*nobj}] containing the trajectories of the
objective functions (one column per trajectory,
first all the trajectories for obj1, then obj2, etc.)}

\item{precalc.data}{is a list of length \code{nobj} of precalculated data (based on kriging models at integration points)
for faster computation - computed if not provided}

\item{equilibrium}{equilibrium type: either "\code{NE}", "\code{KSE}" or "\code{NKSE}"}

\item{n.ynew}{is the number of \code{ynew} simulations (if not provided, equal to the number of trajectories)}

\item{cross}{if \code{TRUE}, all the combinations of trajectories are used (increases accuracy but also cost)}

\item{IS}{if \code{TRUE}, importance sampling is used for ynew}

\item{plot}{if \code{TRUE}, draws equilibria samples (should always be turned off)}
}
\description{
Computes the SUR criterion associated to an equilibrium for a given \code{xnew} and a set of trajectories of objective functions
on a predefined grid.
}
\examples{
\dontrun{
##############################################
# 2 variables, 2 players
##############################################
library(DiceKriging)
set.seed(42)

# Objective function (R^2 -> R^2)
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)))
}

# Grid definition
n.s <- rep(14, 2)
x.to.obj   <- c(1,2)
gridtype <- 'cartesian'
integcontrol <- generate_integ_pts(n.s=n.s, d=4, nobj=2, x.to.obj = x.to.obj, gridtype=gridtype)
integ.pts <- integcontrol$integ.pts
expanded.indices <- integcontrol$expanded.indices

# Kriging models
n.init <- 11
design <- integ.pts[sample.int(n=nrow(integ.pts), size=n.init, replace=FALSE),]
response <- t(apply(design, 1, fun))
mf1 <- km(~., design = design, response = response[,1], lower=c(.1,.1))
mf2 <- km(~., design = design, response = response[,2], lower=c(.1,.1))
model <- list(mf1, mf2)

# Conditional simulations
Simu <- t(Reduce(rbind, lapply(model, simulate, nsim=10, newdata=integ.pts, cond=TRUE,
                                   checkNames=FALSE, nugget.sim = 10^-8)))

# Useful precalculations
library(KrigInv)
precalc.data <- lapply(model, FUN=KrigInv:::precomputeUpdateData, integration.points=integ.pts)

# Compute criterion for all points on the grid
crit_grid <- lapply(X=1:prod(n.s), FUN=crit_SUR_Eq, model=model,
                    integcontrol=integcontrol, equilibrium = "NE",
                    Simu=Simu, precalc.data=precalc.data, n.ynew=10, IS=FALSE, cross=FALSE)
crit_grid <- unlist(crit_grid)

# Draw contour of the criterion
filled.contour(seq(0, 1, length.out = n.s[1]), seq(0, 1, length.out = n.s[2]),
               matrix(pmax(0, crit_grid), n.s[1], n.s[2]), main = "SUR criterion",
               xlab = expression(x[1]), ylab = expression(x[2]), color = terrain.colors,
               plot.axes = {axis(1); axis(2);
                            points(design[,1], design[,2], pch = 21, bg = "white")
                           }
)
}

}
\references{
V. Picheny, M. Binois, A. Habbal (2016+), A Bayesian optimization approach to find Nash equilibria,
\emph{https://arxiv.org/abs/1611.02440}.
}
\seealso{
\code{\link[GPGame]{crit_PNash}} for an alternative infill criterion
}