solve_nfg: Find equilibria of a normal-form game
In yukiyanai/rgamer: rgamer: Learn Game Theory Using R

solve_nfg

R Documentation

Find equilibria of a normal-form game

Description

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

Usage

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"`.

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.

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).

Author(s)

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)

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)

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)

yukiyanai/rgamer documentation built on June 14, 2024, 7:38 p.m.