Strategy Estimation

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.


To install the stratEst package from CRAN:


You can install the development version of stratEst from github:



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.

data <- DF2011[DF2011$treatment == 1,]
strats <- rbind(ALLD,ALLC,GRIM,TFT,T2,WSLS)
model <- stratEst(data,strats,print.messages = F)
#>      [,1]
#> [1,] 0.92
#> [2,] 0.00
#> [3,] 0.00
#> [4,] 0.08
#> [5,] 0.00
#> [6,] 0.00


  • 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.


Reference manual

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1.0.1 by Fabian Dvorak, 4 months ago

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Browse source code at

Authors: Fabian Dvorak

Documentation:   PDF Manual  

GPL-3 license

Imports Rcpp, stats

Suggests testthat, spelling

Linking to Rcpp, RcppArmadillo

See at CRAN