R/gt_brgraph.R
In macartan/hop: Generates plots for various games used in **Political Games**
Defines functions
gt_brgraph
Documented in
gt_brgraph
#' Plot best reactions for two person normal form games
#'
#' This function plots best reactions. Intersections are Nash equilibria. Thanks to Neelan Sircar for developing much of this code.
#' To show utilities for players use \code{util = TRUE}. To show best response functions use \code{BR = TRUE}. Both can be done also
#' with output either aligned horizontally or vertically, using \code{vert}.
#' @param R Row payoffs
#' @param C Column payoffs
#' @param PR Name of row player
#' @param PC Name of column player
#' @param P1 alternative argument for Row Name
#' @param P2 alternative argument for Col Name
#' @param overrow Switch to have utilty plots plotted over row player (player 1)
#' @keywords Payoff matrix, Nash, Best responses
#' @export
#' @examples
#' C <- matrix(c(1,0,0,1),2,2)
#' R <- matrix(c(1,0,0,1),2,2)
#' gt_brgraph(R, C, PR="Country R", PC="Country C", leglocBR=c(.8,.2))
#' # A chicken game:
#'
#' gt_brgraph(Chicken, BR = FALSE, util = TRUE,
#' cthighlight = TRUE, rthighlight = TRUE,
#' labelsC = c("Jill A", "Jill B"),
#' labelsC = c("Jack A", "Jack B"),
#' ur = TRUE,
#' PC = "Jill", PR = "Jack")
gt_brgraph <- function(
X,
Y=t(X),
players = c("Row", "Col"),
PR=players[1],
P1=PR,
PC=players[2],
P2 = PC,
labelsR = c("C", "D"),
labels1 = labelsR,
labelsC=labels1,
labels2 = labelsC,
legBR=TRUE, # Legend for the best response graph
legr=TRUE,
legc=TRUE,
leglocBR=c(.8,.2),
legxyr=c(c(.8, 3*(min(C)+max(C))/4)),
legxyc=c(c(.8, (min(C)+max(C))/4)),
ulegend = TRUE, # legend for the utilies graph
BR=TRUE,
br = BR,
draw1=TRUE,
draw2=TRUE,
vert=TRUE,
util=FALSE,
overrow = TRUE,
Rloc=NULL,
Cloc=NULL,
ur=TRUE, # Graph ROWS's utility given range of COLUMN actions (for each of row's two actions)
u1 = ur,
uc=TRUE, # Graph COLUMN's utility given range of column actions (for each of row's two actions),
u2 = uc,
cthighlight=FALSE, rthighlight=FALSE, # Highlight minimax / maximin 1
cbhighlight=FALSE, rbhighlight=FALSE, # Highlight minimax / maximin 2
colr = "red", # P1 / Row color
colc = gray(.4), # P2 / Col color
col1 = colr, # Column color
col2 = colc, # Row color
mmcol_r="pink",
mmcol_c=grey(.8),
mmcol_1=mmcol_r,
mmcol_2=mmcol_c,
xlabu=paste("Probability on", labelsR[1], "for", PR),
ylabu= NULL,
legtextr=c(paste(PR, "'s utility | ", PC, " plays ", labelsC[1], ")", sep=""),
paste(PR, "'s utility | ", PC, " plays ", labelsC[2], ")", sep="")),
legtextc=c(paste(PC, "'s utility | ", PC, " plays ", labelsC[1], ")", sep=""),
paste(PC, "'s utility | ", PC, " plays ", labelsC[2], ")", sep="")),
mainbr = "", mainu = "",
hl_lwd = 8,
lwd = 2) {
# Allow naming by row or by column
R = X
C = Y
PR = P1
PC = P2
ur = u1
uc = u2
colr <- col1
colc <- col2
mmcol_r <- mmcol_1
mmcol_c <- mmcol_2
labelsR <- labels1
labelsC <- labels2
BR = br
if (BR & util){ if(vert) par(mfrow=c(2,1), mar=c(2, 4, 2, 2) + 0.1)#, pty="s")
else par(mfrow=c(1,2), pty="s") }
probC <- round(((R[2,2] - R[1,2])/(R[1,1]+R[2,2]-R[2,1]-R[1,2])),2);
probR <- round(((C[2,2] - C[2,1])/(C[1,1]+C[2,2]-C[2,1]-C[1,2])),2)
pR <- ifelse(probR<0|probR>1,as.numeric(probR<0),probR)
pC <- ifelse(probC<0|probC>1,as.numeric(probC<0),probC)
if(is.null(Rloc)) Rloc <- (rep(pR+.075,2))*(pR<=.5)+(rep(pR-.075,2))*(pR>.5)
if(is.null(Cloc)) Cloc <- (c(pC-.075,pC-.125- .035*(BR & util & vert)))*(pC>=.5)+(c(pC+.125, pC+.075))*(pC<.5)
# Best responses to low and high probabilities on strategy 1
R_pl <- as.numeric(R[2,1]>R[1,1]); C_pl <- as.numeric(C[1,2]> C[1,1])
R_ph <- as.numeric(R[2,2]>R[1,2]); C_ph <- as.numeric(C[2,2]> C[2,1])
# Graph best responses
if(BR){ plot(1,1, xlim=c(0,1), ylim=c(0,1),
xlab=paste("Probability on", labelsC[1], "for", PC),
ylab= paste("Probability on", labelsR[1], "for", PR),
cex.lab=1-.3*(BR & util), cex.axis=1-.3*(BR & util), type="n", main=mainbr)
if(draw1){points(c(0,pC,pC,1), c(R_pl,R_pl,R_ph,R_ph), type="l", lwd=5, col=gray(.3))}
if(draw2){points(c(C_pl,C_pl,C_ph,C_ph),c(0,pR,pR,1), type="l", lwd=5, col=gray(.3), lty=3)}
if (draw1 & draw2) {gt_shadowtext(Rloc[1], Cloc[1],
paste("Prob ", PR, " plays ", labelsR[1], "=", pR,sep=""),
cex=1-.3*(BR & util & vert));
gt_shadowtext(Rloc[2], Cloc[2], paste("Prob ", PC, " plays ", labelsC[1], "=", pC,sep=""), cex=1-.3*(BR & util & vert))}
if(legBR) legend(leglocBR[1], leglocBR[2], c(PR ,PC),
lty=c(1,3), lwd=5, col=gray(.3), xjust=.5, yjust=.5, cex=1-.3*(BR & util))}
# Graph utilities
if(util & overrow){
# Default is to graph with row player strategies on X.
# overrow redefines everything to switch around
if(is.null(ylabu) & !uc) ylabu <- (paste("Utility for", PR))
if(is.null(ylabu) & !ur) ylabu <- (paste("Utility for", PC))
if(is.null(ylabu) & ur & uc) ylabu <- paste("Utility for", PC, "and ", PR)
plot(0,0, xlim=c(0,1), ylim=c(min(C,R),max(C,R)), xlab=xlabu, ylab=ylabu,
cex.lab=1-.3*(BR & util), cex.axis=1-.3*(BR & util), type="n", main=mainu)
if(ur) {
if(rthighlight) {x = (0:100)/100; points(x, sapply(x, function(i) max(R[2,1]+i*(R[1,1]-R[2,1]), R[2,2]+i*(R[1,2]-R[2,2]))),
type ="l", lwd=8, col=mmcol_r)}
if(rbhighlight) {x = (0:100)/100; points(x, sapply(x, function(i) min(R[2,1]+i*(R[1,1]-R[2,1]), R[2,2]+i*(R[1,2]-R[2,2]))),
type ="l", lwd=8, col=mmcol_r)}
points(c(0,1), c(R[2,1],R[1,1]), type ="l",
lwd=lwd, col=colr) # row's utility from COLUMN taking first action given range of row actions on horizontal
points(c(0,1), c(R[2,2],R[1,2]), type ="l",
lwd=lwd, col=colr, lty=3) # row's utility from COLUMN taking second action given range of row actions on horizontal
if(ulegend) if(legr & !uc) { legend(legxyr[1], legxyr[2], legtextr, lty=c(1,3),
lwd=5, col=c(colr, colr), xjust=.5, yjust=.5,
cex=1-.3*(BR & util)) }
}
if(uc) {if(cthighlight) {
x = (0:100)/100;
points(x, sapply(x, function(i) max(C[2,1]+i*(C[1,1]-C[2,1]), C[2,2]+i*(C[1,2]-C[2,2]))),
type ="l", lwd=8, col=mmcol_c)}
if(cbhighlight) {x <- (0:100)/100
points(x, sapply(x, function(i) min(C[2,1]+i*(C[1,1]-C[2,1]), C[2,2]+i*(C[1,2]-C[2,2]))),
type ="l", lwd=hl_lwd, col=mmcol_c)
}
points(c(0,1), c(C[2,1],C[1,1]), type ="l",
lwd=lwd, col=colc) # column's utility from COLUMN taking first action given range of row actions on horizontal
points(c(0,1), c(C[2,2],C[1,2]), type ="l",
lwd=lwd, col=colc, lty=3) # column's utility from COLUMN taking second action given range of row actions on horizontal
if(ulegend) if(legc & !ur) { legend(
legxyc[1],
legxyc[2],
legtextc,
lty=c(1,3),
lwd=5,
col=c(colc, colc),
xjust=.5,
yjust=.5,
cex=1-.3*(BR & util)) }
}
if(ulegend) if(ur&uc&legr&legc) {
legend(legxyr[1], legxyr[2], c(legtextr, legtextc), lty=c(1,3), lwd=5,
col=c(colr, colr, colc,colc ), xjust=.5, yjust=.5, cex=1-.3*(BR & util))
}
}
if(util & !overrow){
# Default is to graph with row player strategies on X.
# overrow redefines everything to switch around
# Switch payoff matrix and labels
R <- t(Y)
C <- t(X)
PR <- P2
PC <- P1
colr <- col2
colc <- col1
mmcol_r <- mmcol_2
mmcol_c <- mmcol_1
labelsR <- labels2
labelsC <- labels1
if(is.null(ylabu) & !uc) ylabu <- (paste("Utility for", PR))
if(is.null(ylabu) & !ur) ylabu <- (paste("Utility for", PC))
if(is.null(ylabu) & ur & uc) ylabu <- paste("Utility for", PC, "and ", PR)
plot(0,0, xlim=c(0,1), ylim=c(min(C,R),max(C,R)), xlab=xlabu, ylab=ylabu,
cex.lab=1-.3*(BR & util), cex.axis=1-.3*(BR & util), type="n", main=mainu)
if(ur) {
if(rthighlight) {x = (0:100)/100; points(x, sapply(x, function(i) max(R[2,1]+i*(R[1,1]-R[2,1]), R[2,2]+i*(R[1,2]-R[2,2]))),
type ="l", lwd=8, col=mmcol_r)}
if(rbhighlight) {x = (0:100)/100; points(x, sapply(x, function(i) min(R[2,1]+i*(R[1,1]-R[2,1]), R[2,2]+i*(R[1,2]-R[2,2]))),
type ="l", lwd=8, col=mmcol_r)}
points(c(0,1), c(R[2,1],R[1,1]), type ="l",
lwd=lwd, col=colr) # row's utility from COLUMN taking first action given range of row actions on horizontal
points(c(0,1), c(R[2,2],R[1,2]), type ="l",
lwd=lwd, col=colr, lty=3) # row's utility from COLUMN taking second action given range of row actions on horizontal
if(ulegend) if(legr & !uc) { legend(legxyr[1], legxyr[2], legtextr, lty=c(1,3),
lwd=5, col=c(colr, colr), xjust=.5, yjust=.5,
cex=1-.3*(BR & util)) }
}
if(uc) {if(cthighlight) {
x = (0:100)/100;
points(x, sapply(x, function(i) max(C[2,1]+i*(C[1,1]-C[2,1]), C[2,2]+i*(C[1,2]-C[2,2]))),
type ="l", lwd=8, col=mmcol_c)}
if(cbhighlight) {x <- (0:100)/100
points(x, sapply(x, function(i) min(C[2,1]+i*(C[1,1]-C[2,1]), C[2,2]+i*(C[1,2]-C[2,2]))),
type ="l", lwd=hl_lwd, col=mmcol_c)
}
points(c(0,1), c(C[2,1],C[1,1]), type ="l",
lwd=lwd, col=colc) # column's utility from COLUMN taking first action given range of row actions on horizontal
points(c(0,1), c(C[2,2],C[1,2]), type ="l",
lwd=lwd, col=colc, lty=3) # column's utility from COLUMN taking second action given range of row actions on horizontal
if(ulegend) if(legc & !ur) { legend(
legxyc[1],
legxyc[2],
legtextc,
lty=c(1,3),
lwd=5,
col=c(colc, colc),
xjust=.5,
yjust=.5,
cex=1-.3*(BR & util)) }
}
if(ulegend) if(ur&uc&legr&legc) {
legend(legxyr[1], legxyr[2], c(legtextr, legtextc), lty=c(1,3), lwd=5,
col=c(colr, colr, colc,colc ), xjust=.5, yjust=.5, cex=1-.3*(BR & util))
}
}
}
macartan/hop documentation built on Jan. 4, 2022, 9:21 p.m.
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Defines functions gt_brgraph
Documented in gt_brgraph
#' Plot best reactions for two person normal form games
#'
#' This function plots best reactions. Intersections are Nash equilibria. Thanks to Neelan Sircar for developing much of this code.
#' To show utilities for players use \code{util = TRUE}. To show best response functions use \code{BR = TRUE}. Both can be done also
#' with output either aligned horizontally or vertically, using \code{vert}.
#' @param R Row payoffs
#' @param C Column payoffs
#' @param PR Name of row player
#' @param PC Name of column player
#' @param P1 alternative argument for Row Name
#' @param P2 alternative argument for Col Name
#' @param overrow Switch to have utilty plots plotted over row player (player 1)
#' @keywords Payoff matrix, Nash, Best responses
#' @export
#' @examples
#' C <- matrix(c(1,0,0,1),2,2)
#' R <- matrix(c(1,0,0,1),2,2)
#' gt_brgraph(R, C, PR="Country R", PC="Country C", leglocBR=c(.8,.2))
#' # A chicken game:
#'
#' gt_brgraph(Chicken, BR = FALSE, util = TRUE,
#' cthighlight = TRUE, rthighlight = TRUE,
#' labelsC = c("Jill A", "Jill B"),
#' labelsC = c("Jack A", "Jack B"),
#' ur = TRUE,
#' PC = "Jill", PR = "Jack")
gt_brgraph <- function(
X,
Y=t(X),
players = c("Row", "Col"),
PR=players[1],
P1=PR,
PC=players[2],
P2 = PC,
labelsR = c("C", "D"),
labels1 = labelsR,
labelsC=labels1,
labels2 = labelsC,
legBR=TRUE, # Legend for the best response graph
legr=TRUE,
legc=TRUE,
leglocBR=c(.8,.2),
legxyr=c(c(.8, 3*(min(C)+max(C))/4)),
legxyc=c(c(.8, (min(C)+max(C))/4)),
ulegend = TRUE, # legend for the utilies graph
BR=TRUE,
br = BR,
draw1=TRUE,
draw2=TRUE,
vert=TRUE,
util=FALSE,
overrow = TRUE,
Rloc=NULL,
Cloc=NULL,
ur=TRUE, # Graph ROWS's utility given range of COLUMN actions (for each of row's two actions)
u1 = ur,
uc=TRUE, # Graph COLUMN's utility given range of column actions (for each of row's two actions),
u2 = uc,
cthighlight=FALSE, rthighlight=FALSE, # Highlight minimax / maximin 1
cbhighlight=FALSE, rbhighlight=FALSE, # Highlight minimax / maximin 2
colr = "red", # P1 / Row color
colc = gray(.4), # P2 / Col color
col1 = colr, # Column color
col2 = colc, # Row color
mmcol_r="pink",
mmcol_c=grey(.8),
mmcol_1=mmcol_r,
mmcol_2=mmcol_c,
xlabu=paste("Probability on", labelsR[1], "for", PR),
ylabu= NULL,
legtextr=c(paste(PR, "'s utility | ", PC, " plays ", labelsC[1], ")", sep=""),
paste(PR, "'s utility | ", PC, " plays ", labelsC[2], ")", sep="")),
legtextc=c(paste(PC, "'s utility | ", PC, " plays ", labelsC[1], ")", sep=""),
paste(PC, "'s utility | ", PC, " plays ", labelsC[2], ")", sep="")),
mainbr = "", mainu = "",
hl_lwd = 8,
lwd = 2) {
# Allow naming by row or by column
R = X
C = Y
PR = P1
PC = P2
ur = u1
uc = u2
colr <- col1
colc <- col2
mmcol_r <- mmcol_1
mmcol_c <- mmcol_2
labelsR <- labels1
labelsC <- labels2
BR = br
if (BR & util){ if(vert) par(mfrow=c(2,1), mar=c(2, 4, 2, 2) + 0.1)#, pty="s")
else par(mfrow=c(1,2), pty="s") }
probC <- round(((R[2,2] - R[1,2])/(R[1,1]+R[2,2]-R[2,1]-R[1,2])),2);
probR <- round(((C[2,2] - C[2,1])/(C[1,1]+C[2,2]-C[2,1]-C[1,2])),2)
pR <- ifelse(probR<0|probR>1,as.numeric(probR<0),probR)
pC <- ifelse(probC<0|probC>1,as.numeric(probC<0),probC)
if(is.null(Rloc)) Rloc <- (rep(pR+.075,2))*(pR<=.5)+(rep(pR-.075,2))*(pR>.5)
if(is.null(Cloc)) Cloc <- (c(pC-.075,pC-.125- .035*(BR & util & vert)))*(pC>=.5)+(c(pC+.125, pC+.075))*(pC<.5)
# Best responses to low and high probabilities on strategy 1
R_pl <- as.numeric(R[2,1]>R[1,1]); C_pl <- as.numeric(C[1,2]> C[1,1])
R_ph <- as.numeric(R[2,2]>R[1,2]); C_ph <- as.numeric(C[2,2]> C[2,1])
# Graph best responses
if(BR){ plot(1,1, xlim=c(0,1), ylim=c(0,1),
xlab=paste("Probability on", labelsC[1], "for", PC),
ylab= paste("Probability on", labelsR[1], "for", PR),
cex.lab=1-.3*(BR & util), cex.axis=1-.3*(BR & util), type="n", main=mainbr)
if(draw1){points(c(0,pC,pC,1), c(R_pl,R_pl,R_ph,R_ph), type="l", lwd=5, col=gray(.3))}
if(draw2){points(c(C_pl,C_pl,C_ph,C_ph),c(0,pR,pR,1), type="l", lwd=5, col=gray(.3), lty=3)}
if (draw1 & draw2) {gt_shadowtext(Rloc[1], Cloc[1],
paste("Prob ", PR, " plays ", labelsR[1], "=", pR,sep=""),
cex=1-.3*(BR & util & vert));
gt_shadowtext(Rloc[2], Cloc[2], paste("Prob ", PC, " plays ", labelsC[1], "=", pC,sep=""), cex=1-.3*(BR & util & vert))}
if(legBR) legend(leglocBR[1], leglocBR[2], c(PR ,PC),
lty=c(1,3), lwd=5, col=gray(.3), xjust=.5, yjust=.5, cex=1-.3*(BR & util))}
# Graph utilities
if(util & overrow){
# Default is to graph with row player strategies on X.
# overrow redefines everything to switch around
if(is.null(ylabu) & !uc) ylabu <- (paste("Utility for", PR))
if(is.null(ylabu) & !ur) ylabu <- (paste("Utility for", PC))
if(is.null(ylabu) & ur & uc) ylabu <- paste("Utility for", PC, "and ", PR)
plot(0,0, xlim=c(0,1), ylim=c(min(C,R),max(C,R)), xlab=xlabu, ylab=ylabu,
cex.lab=1-.3*(BR & util), cex.axis=1-.3*(BR & util), type="n", main=mainu)
if(ur) {
if(rthighlight) {x = (0:100)/100; points(x, sapply(x, function(i) max(R[2,1]+i*(R[1,1]-R[2,1]), R[2,2]+i*(R[1,2]-R[2,2]))),
type ="l", lwd=8, col=mmcol_r)}
if(rbhighlight) {x = (0:100)/100; points(x, sapply(x, function(i) min(R[2,1]+i*(R[1,1]-R[2,1]), R[2,2]+i*(R[1,2]-R[2,2]))),
type ="l", lwd=8, col=mmcol_r)}
points(c(0,1), c(R[2,1],R[1,1]), type ="l",
lwd=lwd, col=colr) # row's utility from COLUMN taking first action given range of row actions on horizontal
points(c(0,1), c(R[2,2],R[1,2]), type ="l",
lwd=lwd, col=colr, lty=3) # row's utility from COLUMN taking second action given range of row actions on horizontal
if(ulegend) if(legr & !uc) { legend(legxyr[1], legxyr[2], legtextr, lty=c(1,3),
lwd=5, col=c(colr, colr), xjust=.5, yjust=.5,
cex=1-.3*(BR & util)) }
}
if(uc) {if(cthighlight) {
x = (0:100)/100;
points(x, sapply(x, function(i) max(C[2,1]+i*(C[1,1]-C[2,1]), C[2,2]+i*(C[1,2]-C[2,2]))),
type ="l", lwd=8, col=mmcol_c)}
if(cbhighlight) {x <- (0:100)/100
points(x, sapply(x, function(i) min(C[2,1]+i*(C[1,1]-C[2,1]), C[2,2]+i*(C[1,2]-C[2,2]))),
type ="l", lwd=hl_lwd, col=mmcol_c)
}
points(c(0,1), c(C[2,1],C[1,1]), type ="l",
lwd=lwd, col=colc) # column's utility from COLUMN taking first action given range of row actions on horizontal
points(c(0,1), c(C[2,2],C[1,2]), type ="l",
lwd=lwd, col=colc, lty=3) # column's utility from COLUMN taking second action given range of row actions on horizontal
if(ulegend) if(legc & !ur) { legend(
legxyc[1],
legxyc[2],
legtextc,
lty=c(1,3),
lwd=5,
col=c(colc, colc),
xjust=.5,
yjust=.5,
cex=1-.3*(BR & util)) }
}
if(ulegend) if(ur&uc&legr&legc) {
legend(legxyr[1], legxyr[2], c(legtextr, legtextc), lty=c(1,3), lwd=5,
col=c(colr, colr, colc,colc ), xjust=.5, yjust=.5, cex=1-.3*(BR & util))
}
}
if(util & !overrow){
# Default is to graph with row player strategies on X.
# overrow redefines everything to switch around
# Switch payoff matrix and labels
R <- t(Y)
C <- t(X)
PR <- P2
PC <- P1
colr <- col2
colc <- col1
mmcol_r <- mmcol_2
mmcol_c <- mmcol_1
labelsR <- labels2
labelsC <- labels1
if(is.null(ylabu) & !uc) ylabu <- (paste("Utility for", PR))
if(is.null(ylabu) & !ur) ylabu <- (paste("Utility for", PC))
if(is.null(ylabu) & ur & uc) ylabu <- paste("Utility for", PC, "and ", PR)
plot(0,0, xlim=c(0,1), ylim=c(min(C,R),max(C,R)), xlab=xlabu, ylab=ylabu,
cex.lab=1-.3*(BR & util), cex.axis=1-.3*(BR & util), type="n", main=mainu)
if(ur) {
if(rthighlight) {x = (0:100)/100; points(x, sapply(x, function(i) max(R[2,1]+i*(R[1,1]-R[2,1]), R[2,2]+i*(R[1,2]-R[2,2]))),
type ="l", lwd=8, col=mmcol_r)}
if(rbhighlight) {x = (0:100)/100; points(x, sapply(x, function(i) min(R[2,1]+i*(R[1,1]-R[2,1]), R[2,2]+i*(R[1,2]-R[2,2]))),
type ="l", lwd=8, col=mmcol_r)}
points(c(0,1), c(R[2,1],R[1,1]), type ="l",
lwd=lwd, col=colr) # row's utility from COLUMN taking first action given range of row actions on horizontal
points(c(0,1), c(R[2,2],R[1,2]), type ="l",
lwd=lwd, col=colr, lty=3) # row's utility from COLUMN taking second action given range of row actions on horizontal
if(ulegend) if(legr & !uc) { legend(legxyr[1], legxyr[2], legtextr, lty=c(1,3),
lwd=5, col=c(colr, colr), xjust=.5, yjust=.5,
cex=1-.3*(BR & util)) }
}
if(uc) {if(cthighlight) {
x = (0:100)/100;
points(x, sapply(x, function(i) max(C[2,1]+i*(C[1,1]-C[2,1]), C[2,2]+i*(C[1,2]-C[2,2]))),
type ="l", lwd=8, col=mmcol_c)}
if(cbhighlight) {x <- (0:100)/100
points(x, sapply(x, function(i) min(C[2,1]+i*(C[1,1]-C[2,1]), C[2,2]+i*(C[1,2]-C[2,2]))),
type ="l", lwd=hl_lwd, col=mmcol_c)
}
points(c(0,1), c(C[2,1],C[1,1]), type ="l",
lwd=lwd, col=colc) # column's utility from COLUMN taking first action given range of row actions on horizontal
points(c(0,1), c(C[2,2],C[1,2]), type ="l",
lwd=lwd, col=colc, lty=3) # column's utility from COLUMN taking second action given range of row actions on horizontal
if(ulegend) if(legc & !ur) { legend(
legxyc[1],
legxyc[2],
legtextc,
lty=c(1,3),
lwd=5,
col=c(colc, colc),
xjust=.5,
yjust=.5,
cex=1-.3*(BR & util)) }
}
if(ulegend) if(ur&uc&legr&legc) {
legend(legxyr[1], legxyr[2], c(legtextr, legtextc), lty=c(1,3), lwd=5,
col=c(colr, colr, colc,colc ), xjust=.5, yjust=.5, cex=1-.3*(BR & util))
}
}
}
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