Variants of strategy estimation (Dal Bo & Frechette, 2011, ), including the model with parameters for the choice probabilities of the strategies (Breitmoser, 2015, ), and the model with individual level covariates for the selection of strategies by individuals (Dvorak & Fehrler, 2018, ).

stratEst is a statistical software package which implements variants of
the strategy estimation method (Dal Bo & Frechette, 2011). Strategies
can be estimated from the data or supplied by the user in the form of
deterministic finite-state automata. The package uses the EM algorithm
(Dempster, 1977) and the Newton-Raphson method to obtain
maximum-likelihood estimates of the population shares and choice
parameters of the strategies. The number and the complexity of
strategies can be restricted by the user or selected based on
information criteria. The package also features an extension of strategy
estimation in the spirit of latent class regression to assess the
effects of covariates on strategy use.

Installation

To install the stratEst package from CRAN:

install.packages("stratEst")

You can install the development version of stratEst from github:

install.packages("devtools")

devtools::install_github("fdvorak/stratEst")

Example

This example shows how to replicate the results in column 1 of table 7
on page 424 of Dal Bo and Frechette (2011). The results for the first
treatment with delta = 1/2 and R = 32 can be obtained with the following
code.

library(stratEst)

data <- DF2011[DF2011$treatment == 1,]

strats <- rbind(ALLD,ALLC,GRIM,TFT,T2,WSLS)

model <- stratEst(data,strats,print.messages = F)

round(model$shares,3)

#> [,1]

#> [1,] 0.92

#> [2,] 0.00

#> [3,] 0.00

#> [4,] 0.08

#> [5,] 0.00

#> [6,] 0.00

References

Breitmoser, Y. (2015): Cooperation, but no reciprocity: Individual
strategies in the repeated prisoner’s dilemma, American Economic
Review, 105, 2882-2910.

Dal Bo, P. and G. R. Frechette (2011): The evolution of cooperation
in infinitely repeated games: Experimental evidence, American
Economic Review, 101, 411-429.

Dempster, A., N. Laird, and D. B. Rubin (1977): Maximum likelihood
from incomplete data via the EM algorithm," Journal of the Royal
Statistical Society Series B, 39, 1-38.

Eddelbuettel, D. and R. Francois (2011): Rcpp: Seamless R and C++
Integration, Journal of Statistical Software, 40, 1-18.

Sanderson, C. and R. Curtin (2016): Armadillo: a template-based C++
library for linear algebra. Journal of Open Source Software, 1-26.