Find equilibria of a normal-form game — solve

solve_nfg() finds Nash equilibria of a normal-form game.

solve_nfg(
  game,
  mixed = FALSE,
  show_table = TRUE,
  mark_br = TRUE,
  cons1 = NULL,
  cons2 = NULL,
  cons_common = NULL,
  precision = 1,
  plot = TRUE,
  mark_NE = FALSE,
  quietly = FALSE,
  color_palette = "Set1"
)

Arguments

game: A "normal_form" class object created by normal_form().
mixed: A logical value. If TRUE, mixed-strategy NE will be searched. Default is FALSE.
show_table: A logical value. If TRUE, the payoff matrix of the game will be displayed. Default is TRUE.
mark_br: A logical value. If TRUE, the best response to each of the opponent's strategy is marked. Default is TRUE.
cons1: A named list of parameters contained in game$payoff$payoffs1 that should be treated as constants, if any.
cons2: A named list of parameters contained in game$payoff$payoffs2 that should be treated as constants, if any.
cons_common: A named list of parameters contained in game$payoff$payoffs1 and game$payoff$payoffs2 that should be treated as constants, if any. If cons1 and cons2 are exactly same, you can specify cons_common instead of specifying both cons1 and cons2.
precision: A natural number specifying the precision of numerical approximation. The value n approximately means that the approximation is correct up to the Nth decimal place. The default value is 1.
plot: A logical value to determine whether the figure of the best response correspondences will be displayed. Default is TRUE.
mark_NE: A logical value to control if the NE (if any) will be marked in the best response plot, which will be displayed (only displayed when plot = TRUE). Default is FALSE.
quietly: A logical value that determines whether the equilibrium will be kept in the returned list without being printed on screen. Default is FALSE.
color_palette: A color palette to be used. Default is "Set1".

Value

A list containing Nash equilibria (if any), the payoff matrix of the game (if available), and the plot of best response correspondence (if available).

Details

This function finds Nash equilibria of a normal-form game by solve_nfg_matrix, solve_nfg_char, or solve_nfg_fcn depending on type of a "normal_form" object defined by normal_form.

Author

Yoshio Kamijo and Yuki Yanai yanai.yuki@kochi-tech.ac.jp

Examples

game1 <- normal_form(
  s1 = c("T", "B"),
  s2 = c("L", "R"),
  payoffs1 = c(4, 2, 3, 1),
  payoffs2 = c(4, 3, 2, 1))
s1 <- solve_nfg(game1, show_table = FALSE)
#> Pure-strategy NE: [T, L]

game2 <- normal_form(
  payoffs1 = "-x1^2 + (28 - x2) * x1",
  payoffs2 = "-x2^2 + (28 - x1) * x2",
  par1_lim = c(0, 30),
  par2_lim = c(0, 30),
  pars = c("x1", "x2"))
s2 <- solve_nfg(game2)
#> approximated NE: (9.3, 9.3)
#> The obtained NE might be only a part of the solutions.
#> Please examine br_plot (best response plot) carefully.


fx <- function(x, y) -x^2 + (28 - y) * x
fy <- function(x, y) -y^2 + (28 - x) * y
game3 <- normal_form(
    payoffs1 = fx,
    payoffs2 = fy,
    pars = c("x", "y"),
    par1_lim = c(0, 40),
    par2_lim = c(0, 40))
s3 <- solve_nfg(game3)
#> approximated NE: (9.3, 9.3)
#> The obtained NE might be only a part of the solutions.
#> Please examine br_plot (best response plot) carefully.