タカ・ハトゲーム
タカ戦略とハト戦略のみが存在する世界において進化的に安定な状態を探るゲーム。
### 設定
# pay-offは以下の通り：
タカ vs. ハト、餌(food)を総取り
タカ vs. タカ、餌からコストを引いたものを2分割
ハト vs. タカ、無し（０）
ハト vs. ハト、餌を2分割
# 引数：
個体数の初期値（[タカ、ハト])、世代数、コスト、餌
# 個体数の推移
p.hawk[i_gen]=(p.hawk[i_gen-1]*(p.hawk[i_gen-1]*eHawkHawk+p.dove[i_gen-1]*eHawkDove))
　/mean.W;

HDgame<-function(N,generation,cost,food){
  N.hawk=N[1]; N.dove=N[2]; 
  p.hawk=rep(0,generation);p.hawk[1]=N.hawk/(N.dove+N.hawk)
  p.dove=rep(0,generation);p.dove[1]=1-p.hawk[1]
  eHawkHawk=0.5*(food-cost);eHawkDove=food
  eDoveHawk=0;eDoveDove=0.5*food
  for (i_gen in 2:generation){
    mean.W=p.hawk[i_gen-1]^2*eHawkHawk+p.hawk[i_gen-1]*p.dove[i_gen-1]*
     (eHawkDove+eDoveHawk)+p.dove[i_gen-1]^2*eDoveDove
    p.hawk[i_gen]=(p.hawk[i_gen-1]*(p.hawk[i_gen-1]*eHawkHawk
      +p.dove[i_gen-1]*eHawkDove))/mean.W;
    p.dove[i_gen]=1-p.hawk[i_gen]
  }
  plot(1:generation,p.hawk,type='o',col='red',ylim=c(0,1),pch=19,
    main="Result of Hawk-Dove Game",ylab="Proportion",xlab="Generation")
  lines(1:generation, p.dove,type='o',col='blue',pch=17)
  legend("topright",c("Hawk","Dove"),pch=c(19,17),col=c('red','blue'))
}
# 実行例
HDgame(c(20,80),50,10,6)

# 実装例、その２
HDgameDE<-function(N,generation,cost,food){
  N.hawk=N[1]; N.dove=N[2]; 
  tStep=0.01;ts=seq(0,generation,tStep);Nts=length(ts);
  p.hawk=rep(0,Nts);p.hawk[1]=N.hawk/(N.dove+N.hawk)
  p.dove=rep(0,Nts);p.dove[1]=1-p.hawk[1]
  eHawkHawk=0.5*(food-cost);eHawkDove=food
  eDoveHawk=0;eDoveDove=0.5*food
  for (i_gen in 2:Nts){
    mean.W=p.hawk[i_gen-1]^2*eHawkHawk+p.hawk[i_gen-1]*p.dove[i_gen-1]*
     (eHawkDove+eDoveHawk)+p.dove[i_gen-1]^2*eDoveDove
    p.hawk[i_gen]=p.hawk[i_gen-1]+(p.hawk[i_gen-1]*(p.hawk[i_gen-1]*eHawkHawk
     +p.dove[i_gen-1]*eHawkDove-mean.W)/mean.W)*tStep;
    p.dove[i_gen]=1-p.hawk[i_gen]
  }
  plot(1:Nts,p.hawk,type='l',col='red',ylim=c(0,1),lwd=5,
   main="Result of Hawk-Dove Game",ylab="Proportion",xlab="Generation")
  lines(1:Nts, p.dove,type='l',col='blue',lwd=5)
  legend("topright",c("Hawk","Dove"),lwd=5,col=c('red','blue'))
}
# 実行例
HDgameDE(c(20,80),50,10,6)

読みやすい？例

## a simple version ##
HDgame<-function(N,food,cost,n_gen){
  p.hawk=N[1]/sum(N);p.dove=N[2]/sum(N)
  e.HH=1/2*(food-cost);e.HD=food;e.DH=0;e.DD=1/2*(food)
  p.vec=c(p.hawk,p.dove);p.mat<-outer(p.vec,p.vec)
  payMat<-matrix(c(e.HH,e.DH,e.HD,e.DD),ncol=2)
  hist=matrix(0,n_gen,2);hist[1,]=p.vec
  for (i_gen in 2:n_gen){
    w.H=sum(p.vec*payMat[1,])
    w.D=sum(p.vec*payMat[2,])
    w.mean=sum(p.mat*payMat)
    p.vec=c(p.vec[1]*w.H/w.mean,p.vec[2]*w.D/w.mean)
    p.mat<-outer(p.vec,p.vec)
    hist[i_gen,]=p.vec
  }
  plot(1:n_gen,hist[,1],pch=20,type='o',lwd=2,cex=2,col='red',
   ylim=c(0,1),ylim=c(0,1.25),xlab="time",ylab="proportion",cex.lab=2)
  lines(1:n_gen,hist[,2],pch=20,type='o',lwd=2,cex=2,col='blue')
  legend("topright",c("Hawk","Dove"),col=c('red','blue'),lwd=2,pch=20)
}

## DE version ##
HDgameDE<-function(N,food,cost,n_gen){
  p.hawk=N[1]/sum(N);p.dove=N[2]/sum(N)
  e.HH=1/2*(food-cost);e.HD=food;e.DH=0;e.DD=1/2*(food)
  p.vec=c(p.hawk,p.dove);p.mat<-outer(p.vec,p.vec)
  payMat<-matrix(c(e.HH,e.DH,e.HD,e.DD),ncol=2)
  ts=0.01;Nts=length(seq(1,n_gen,ts));
  hist=matrix(0,Nts,2);hist[1,]=p.vec
  for (i_gen in 2:Nts){
    w.H=sum(p.vec*payMat[1,])
    w.D=sum(p.vec*payMat[2,])
    w.mean=sum(p.mat*payMat)
    p.vec[1]=p.vec[1]+ts*p.vec[1]*(w.H-w.mean)/w.mean
    p.vec[2]=p.vec[2]+ts*p.vec[2]*(w.D-w.mean)/w.mean
    p.mat<-outer(p.vec,p.vec)
    hist[i_gen,]=p.vec
  }
  plot(1:Nts,hist[,1],type='l',lwd=4,cex=2,col='red',ylim=c(0,1.25),
    xlab="time",ylab="proportion",cex.lab=2)
  lines(1:Nts,hist[,2],type='l',lwd=4,cex=2,col='blue')
  legend("topright",c("Hawk","Dove"),col=c('red','blue'),lwd=4)
  return(hist)
}