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

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

Kuhn Poker Description

Wikipedia describes the Kuhn Poker game in conventional poker terms as follows:

• Each player antes 1.

• Each player is dealt one of the three cards, and the third is put aside unseen.

• Player one can check or bet 1.

• If player one checks then player two can check or bet 1.
  • If player two checks there is a showdown for the pot of 2 (i.e. the higher card wins 1 from the other player).
  • If player two bets then player one can fold or call.
  • If player one folds then player two takes the pot of 3 (i.e. winning 1 from player 1).
  • If player one calls there is a showdown for the pot of 4 (i.e. the higher card wins 2 from the other player).
• If player one bets then player two can fold or call.
  • If player two folds then player one takes the pot of 3 (i.e. winning 1 from player 2).
  • If player two calls there is a showdown for the pot of 4 (i.e. the higher card wins 2 from the other player).

Specifying as gtree game

library(gtree)
game = new_game(
  gameId = "KuhnPoker",
  params = list(numPlayers=2),
  options = make_game_options(verbose=1),
  stages = list(
    stage("dealCards",
      nature = list(
        natureMove("pl1_card", 1:3),
        natureMove("pl2_card", ~setdiff(1:3, pl1_card))
      )
    ),
    stage("pl1CheckBet",
      player=1,
      observe = c("pl1_card"),
      actions = list(
        action("cb1",c("check","bet"))
      )
    ),
    stage("pl2CheckBet",
      player=2,
      condition = ~ cb1 == "check",
      observe = c("pl2_card","cb1"),
      actions = list(
        action("cb2",c("check","bet"))
      )
    ),
    stage("pl2FoldCall",
      player=2,
      condition = ~ cb1 == "bet",
      observe = c("pl2_card","cb1"),
      actions = list(
        action("fc2",c("fold","call"))
      )
    ),
    stage("pl1FoldCall",
      player=1,
      condition = ~ is_true(cb1 == "check" & cb2=="bet"),
      observe = c("cb2"),
      actions = list(
        action("fc1",c("fold","call"))
      )
    ),
    stage("PayoffStage",
      player=1:2,
      compute=list(
        folder ~ case_distinction(
          is_true(fc1 == "fold"),1,
          is_true(fc2 == "fold"),2,
          0
        ),
        winner ~ case_distinction(
          folder == 1,2,
          folder == 2,1,
          folder == 0, (pl2_card > pl1_card) +1
        ),
        gave1 ~ 1 + 1*(is_true(cb1 == "bet") | is_true(fc1 == "call")),
        gave2 ~ 1 + 1*(is_true(cb2 == "bet") | is_true(fc2 == "call")),
        pott ~ gave1 + gave2,
        payoff_1 ~ (winner == 1)*pott - gave1,
        payoff_2 ~ (winner == 2)*pott - gave2
      )
    )
  )
) 

To check whether we have correctly specified the game, let us take a look at the outcomes:

game %>% get_outcomes()

Looking at the number of pure strategy profiles the game seems tractable for numerical analysis

game %>%
  game_print_size_info()

Solving Kuhn Poker

Let us now solve the game using the gambit-logit solver, which is the default solver for finding a mixed strategy equilibrium:

game %>%
  game_gambit_solve(mixed=TRUE) %>%
  eq_tables()

game %>% 
  eq_expected_outcomes() %>% 
  select(payoff_1,payoff_2, cb1, fc1, cb2,fc2)

Loss Averse Players

What if players become inequality averse?

game %>%
  game_set_preferences(pref_ineqAv(alpha=1, beta=0.5)) %>%
  game_gambit_solve(mixed=TRUE) %>%
  eq_tables()

game %>% 
  eq_expected_outcomes() %>% 
  select(payoff_1,payoff_2, cb1, fc1, cb2,fc2)

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