In skranz/gtree: gtree basic functionality to model and solve games

knitr::opts_chunk$set(echo = TRUE, error=TRUE)
library(gtree)

Author: Sebastian Kranz, Ulm University

gtree is an R package that allows you to specify extensive form games using stages, similar as one specifies economic experiments with ztree or otree. The game is internally converted to a formal game tree and one can find its equilibria using a Gambit solver or an internal solver. The equilibria are presented in a format that facilitates comparison with experimental results. One can also conveniently study the effects of non-standard preferences characterized e.g. by inequality aversion or loss aversion.

Here is an example of a game definition:

library(gtree)
game = new_game(
  gameId = "Ultimatum_Dictator",
  options = make_game_options(verbose=FALSE),
  params = list(numPlayers=2,cake=10, autoAcceptProb=0.1),
  stages = list(
    stage("proposerStage",
      player=1,
      actions = list(
        action("offer",~0:cake)
      )
    ),
    stage("autoAcceptStage",
      nature = list(
        natureMove("autoAccept", 
          set=c(TRUE,FALSE),
          probs = ~ c(autoAcceptProb, 1-autoAcceptProb)
        )
      )  
    ),
    stage("responderStage",
      player=2,
      condition =  ~ autoAccept == FALSE,
      observe = c("offer","autoAccept"),
      actions = list(
        action("accept",c(FALSE,TRUE))
      )
    ),
    stage("payoffStage",
      player=1:2,
      compute=list(
        payoff_1 ~ ifelse(accept | autoAccept, cake-offer,0),
        payoff_2 ~ ifelse(accept | autoAccept, offer,0)
      )
    )
  )
)

This is a modified Ultimatum Game. Player 1 (the proposer) can decide how much of the parameter cake she offers to player 2 (the responder). With probability autoAcceptProb the responder has no choice and the offer is automatically accepted. Otherwise the responder can decide to accept or reject the offer. If he rejects, both players get a payoff of 0.

The game is defined by various stages, that can specify an active player and his actions, like offer, random moves of nature like autoAccept, or deterministically computed variables like payoff_1 or payoff_2 (the payoff variables have reserved names and must always be specified). In addition, one can explicitly specify which variables players observe in a stage and a condition specifying whether a stage is played or not. The corresponding fields can contain fixed values or formulas starting with ~ that reference to previously specified variables or parameters.

The following code assumes that players have inequality aversion preferences à la Fehr & Schmidt with an envy parameter of alpha=1 but no guilt (beta=0) and then solves for all pure strategy SPE of the game. The results in a table format:

game %>%
  game_set_preferences(pref_ineqAv(alpha=1, beta=0)) %>%
  game_solve() %>%
  eq_tables()

We see that the proposer offers 4 and every offer below 4 would be rejected. What happens for an auto accept probability of 90%?

game %>%
  game_change_param(autoAcceptProb = 0.9) %>%
  game_solve() %>%
  eq_tables()

While the responder's behavior does not change, the proposer will now only offer 0. Sure the offer will be rejected with 10% probability, but in 90% of cases the proposer gets the whole cake for herself.

Take a look at the different tutorials for more information about gtree.

skranz/gtree documentation built on March 27, 2021, 6:03 a.m.