R/games.R

In learnPopGen: Population Genetic Simulations & Numerical Analysis

## hawk-dove game theory model
## written by Liam J. Revell

hawk.dove<-function(p=c(0.01,0.99),M=NULL,time=100){
	if(length(p)==1) p<-c(p,1-p)
	if(is.null(M)) M<-matrix(c(0.6,1.5,0.5,1.0),2,2,byrow=T)
	if(is.null(dimnames(M))) dimnames(M)<-list(c("hawk","dove"),c("hawk","dove"))
	interactors<-rownames(M)
	message("Pay-off matrix:")
	print(M)
	if(sum(p)!=1) p<-p/sum(p)
	hawk<-p[1]; dove<-p[2]
	wbar<-hawk*hawk*M[1,1]+hawk*dove*M[1,2]+dove*hawk*M[2,1]+dove*dove*M[2,2]
	whawk<-hawk*M[1,1]+dove*M[1,2]
	wdove<-hawk*M[2,1]+dove*M[2,2]
	for(i in 2:time){
		hawk[i]<-hawk[i-1]*whawk[i-1]/wbar[i-1]
		dove[i]<-dove[i-1]*wdove[i-1]/wbar[i-1]
		whawk[i]<-hawk[i]*M[1,1]+dove[i]*M[1,2]
		wdove[i]<-hawk[i]*M[2,1]+dove[i]*M[2,2]
		wbar[i]<-hawk[i]*whawk[i]+dove[i]*wdove[i]
	}
	time<-1:time
	layout(c(1,2))
	par(mar=c(5.1,4.1,1.1,2.1))
	plot(time,dove,type="l",ylim=c(0,1),ylab="frequency",col="blue",lwd=2)
	lines(time,hawk,type="l",col="red",lwd=2)
	legend(max(time),1,interactors,col=c("red","blue"),
		bg=make.transparent("gray90",0.5),lwd=2,
		xjust=1,yjust=1,box.col="transparent")
	plot(time,wbar,type="l",lwd=2,ylim=c(0,max(M)),ylab="mean fitness")
	lines(time,wdove,type="l",col="blue",lwd=2)
	lines(time,whawk,type="l",col="red",lwd=2)
	legend(max(time),max(M),c("overall",interactors),col=c("black","red","blue"),
		bg=make.transparent("gray90",0.5),lwd=2,xjust=1,yjust=1,box.col="transparent")
	object<-list(p=p,M=M,time=time[length(time)],
		dove=dove,hawk=hawk,wbar=wbar,
		wdove=wdove,whawk=whawk)
	class(object)<-"hawk.dove"
	invisible(object)
}

print.hawk.dove<-function(x,...){
	cat("\nObject of class \"hawk.dove\" consisting of the results of a")
	cat("\nnumerical analysis of the so-called Hawk-Dove model in which")
	cat("\nfitness is assumed to be proportional to the payoff from")
	cat("\ninteractions between the two alternative strategies as given")
	cat("\nby the matrix:\n")
	print(x$M)
	cat("\n\nTo plot enter plot(\'object_name\') at the command line\ninterface.\n\n")
}

plot.hawk.dove<-function(x,...){
	time<-1:x$time
	layout(c(1,2))
	par(mar=c(5.1,4.1,1.1,2.1))
	plot(time,x$dove,type="l",ylim=c(0,1),ylab="frequency",
		col="blue",lwd=2)
	lines(time,x$hawk,type="l",col="red",lwd=2)
	legend(max(time),1,rownames(x$M),col=c("red","blue"),
		bg=make.transparent("gray90",0.5),lwd=2,
		xjust=1,yjust=1,box.col="transparent")
	plot(time,x$wbar,type="l",lwd=2,ylim=c(0,max(x$M)),
		ylab="mean fitness")
	lines(time,x$wdove,type="l",col="blue",lwd=2)
	lines(time,x$whawk,type="l",col="red",lwd=2)
	legend(max(time),max(x$M),c("overall",rownames(x$M)),
		col=c("black","red","blue"),
		bg=make.transparent("gray90",0.5),lwd=2,xjust=1,yjust=1,
		box.col="transparent")
}