This is an R package for numerically solving discounted infinitely repeated games in which players are risk neutral and can conduct voluntary monetary transfers in each round. It implements the algorithms developed in the article "Infinitely repeated games with public monitoring and monetary transfers" (JET, 2012) by Susanne Goldlücke and Sebastian Kranz.
First you need to install R, which is a very popular and powerful open source statistical programming language. You can download R for Windows, Max or Linux here:
I recommend to additionally install RStudio, which is a great open source IDE for R:
To install the repgame package run the following code in your R console:
install.packages("repgame",
repos = c("https://skranz-repo.github.io/drat/",getOption("repos")))Note that repgame is not hosted on CRAN but on my own Github based repository. You therefore have to specify the repos argument as in the call above.
If you use Windows, binaries are available in my repository for some R version (e.g. 3.3.x and 3.5.x), but not for all. If there is no binary version available and installation fails, you also have to install RTools for Windows to compile the package from source. See
https://cran.r-project.org/bin/windows/Rtools/
It is also possible to install the packages from Github and the dependencies manually from CRAN by pasting the following code (RTools will then always be necessary on Windows):
# Install CRAN Packages
pkgs = c("devtools","glpkAPI","slam","Rcpp","lattice")
for (pkg in pkgs) {
if (!require(pkg, character.only=TRUE))
install.packages(pkg)
}
# Install packages from GITHUB
library(devtools)
install_github(repo="skranz/restorepoint")
install_github(repo="skranz/rowmins")
install_github(repo="skranz/repgame")Here is a Tutorial from 2012 that explains an older version of the package in detail:
Interactively Solving Repeated Games
Installation instructions are outdated (use the ones above) and there where small changes in the package name, but most stuff hopefully still works. It is unfortunately not trivial to update the tutorial since my Lyx-R link is somehow broken.
The subfolder examples contains updated versions of the tutorial's examples. Here is just the first example for an illustration:
##################################################################
# Section 3:
# Abreu's simple Cournot Game
##################################################################
# 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) # Player 2's payoff matrix is simply the transpose of that of player 1
# Load package
library(repgame)
# Initialize the model of the repeated game
m = init.game(g1=g1,g2=g2,lab.ai=c("L","M","H"),
name="Simple Cournot Game",symmetric=FALSE)
# Solve the model
m = solve.game(m, keep.only.opt.rows=!TRUE)
# Show matrix with critical delta, optimal action structures and payoffs
m$opt.mat
# Plot optimal payoffs and show matrix that characterizes optimal strategy profiles and the cutoffs of the discount factor
plot(m,xvar="delta",yvar=c("Ue","V"))
# Try the same plot with interactive mode. You can click with the left mouse
# button on the plot
plot(m,xvar="delta",yvar=c("Ue","V"),identify=TRUE)
# Solve the model with grim-trigger strategies
m.gt = set.to.grim.trigger(m)
m.gt = solve.game(m.gt)
m.gt$opt.mat
plot(m.gt)
# Plot comparision of optimal equilibria and grim trigger equilibria
plot.compare.models(m,m.gt,xvar="delta",yvar="Ue",legend.pos="topleft",
m1.name = "opt", m2.name="grim",identify=TRUE)If you find a bug or have a suggestion, please send me an email (sebastian.kranz@uni-ulm.de) or file an issue for this github project.