Interactively Solving Repeated Games
Current Version: 0.2 (March 2012)

Here you can download the software package repgames for R that implements the algorithms of my paper Infinitely Repeated Games with Public Monitoring and Monetary Transfers (with Susanne Goldluecke) to compute for all discount factors the sets of equilibrium payoffs in repeated games. Installation instructions are given in the documentation.



Documentation: Interactively Solving Repeated Games: A Toolbox.pdf
Package Binaries for Windows (32 Bit): skUtils.zip repgames.zip
Package Sources: skUtils.tar.gz repgames.tar.gz
Examples: Part I Games with Perfect Monitoring
Part II Games with Imperfect Public Monitoring
Download R: R CRAN

Short Example 1: Collusion with Optimal Penal Codes vs Grim-Trigger Strategies in a simple Cournot Model<\p> 

# Solving Abreu's (1988) Cournot Game with Transfers for all Discount Factors

# Load package
library(repgames,warn.conflicts=FALSE)

# Define Payoff Matrices for player 1 and 2
              #L #M  #H
g1 = rbind(c( 10, 3, 0),    # L
           c( 15, 7, -4),   # M
           c(  7, 5,-15))   # H
g2 = t(g1)

# Initialize game
m = init.game(g1=g1,g2=g2,lab.ai=c("L","M","H"),
    name="Simple Cournot Game", symmetric=FALSE)
# Solve game (optimal penal codes)
m = solve.game(m, keep.only.opt.rows=TRUE)
# Solve game (grim-trigger strategies)
m.gt = set.to.grim.trigger(m)
m.gt = solve.game(m.gt)

# Compare maximal collusive payoffs of optimal penal codes and grim-trigger
plot.compare.models(m,m.gt,xvar="delta",yvar="Ue",
  legend.pos="topleft",m1.name = "optimal penal", m2.name="grim-trigger",
  main="Collusive Payoffs: Optimal Penal Codes vs Grim-Trigger")

Short Example 2: Maximum Payoffs in a Repeated Noisy Prisoner's Dilemma Game<\p> 


library(repgames)

init.noisy.pd.game = function(d,s,lambda,mu,alpha,beta,psi) {
  store.objects("init.noisy.pd.game")
  # restore.objects("init.noisy.pd.game")

  # Payoff matrix of player 1 (that of player 2 is symmetric)
  g1 = matrix(c(
    1,    -s,
    1+d,   0),2,2,byrow=TRUE)
  lab.ai = c("C","D")

  # Create phi.mat, which stores the signal distributions
  prob.yC = c(1-2*alpha-lambda,         1-2*alpha-lambda-mu-beta,
              1-2*alpha-lambda-mu-beta, 1-psi)

  phi.mat = matrix(c(
    #CC       CD          DC         DD 
    prob.yC,                                #yC
    lambda,   lambda+mu,  lambda+mu , psi,  #yD
    alpha,    alpha,      alpha+beta, 0,    #y1
    alpha,    alpha+beta, alpha     , 0     #y2
  ), 4,4,byrow=TRUE)
  lab.y = c("yC","yD","y1","y2")
  m=init.game(g1=g1,phi.mat=phi.mat, symmetric=TRUE,
              lab.ai = lab.ai,lab.y=lab.y, name="Noisy PD")
  m
}

d=1;s=1.5;lambda=0.1;mu=0.2;alpha=0.1;beta=0.2;psi = 1
m = init.noisy.pd.game(d,s,lambda,mu,alpha,beta,psi)
m = solve.game(m)


plot(m,xvar="delta",delta.seq=seq(0.5,1,by=0.001),
     yvar=c("Ue","V"),lwd=2,main="Highest and Lowest PPE Payoffs in Noisy Prisoner's Dilemma")