normal_form() defines a normal-form game and
creates an object of "normal_form" class.
normal_form(
players = NULL,
s1 = NULL,
s2 = NULL,
payoffs1 = NULL,
payoffs2 = NULL,
cells = NULL,
discretize = FALSE,
discrete_points = c(6, 6),
symmetric = FALSE,
byrow = FALSE,
pars = NULL,
par1_lim = NULL,
par2_lim = NULL,
cons1 = NULL,
cons2 = NULL,
cons_common = NULL
)A character vector of the name (label) for the players.
A character vector of pure strategies for Player 1 (row player). Required only when the player has discrete-choice strategies.
A character vector of pure strategies for Player 2 (column player). Required only when the player has discrete-choice strategies.
The payoff of Player1. This argument can be specified in three different ways. First, it can be a numeric vector of payoffs. Second, it can be a character string of the payoff function (e.g., payoffs1 = "x^2 - y"). Third, it can be an R function of payoff.
The payoff of Player 2. See the explanation of
payoffs1 for detail.
A list of vectors to specify the payoff for each cell. Each element of the list should be a numeric vector of two players' payoffs.
A logical value. Set this TRUE to evaluate payoff
functions at some discrete values of strategies s1 and s2.
Default is FALSE.
A numeric vector of length 2 to set how many discrete
points should be used to discretize the game defined by payoff functions.
Default is c(6, 6), which shows equally spaced 6 values from the
range of the strategies par1_lim and par2_lim. Instead of
setting this parameter, you can specify the vectors of arbitrary
strategies by setting s1 and s2.
A logical value. Set this TRUE when the payoffs for
two players are symmetric as in the prisoners' dilemma. Then, payoffs1 is
recycled for payoffs2. Default is FALSE.
A logical value. If TRUE, payoffs will be lined up by
row. Default is FALSE. Only used when both s1 and s2
are provided.
A character vector of parameters that are selected by players 1
and 2, respectively. Only used when payoffs1 and payoffs2
are specified by payoff functions (either as character strings or R
functions).
A numeric vector of length 2, which defines the range of parameters from which Player 1 chooses her strategy.
A numeric vector of length 2, which defines the range of parameters from which Player 2 chooses his strategy.
A named list of parameters contained in payoffs1 that
should be treated as constants, if any.
A named list of parameters contained in payoffs2 that
should be treated as constants, if any.
A named list of parameters contained in payoffs1
and payoffs2 that should be treated as constants, if any. If
cons1 and cons2 are exactly same, you can specify
cons_common instead of both cons1 and cons2.
An object of "normal_form" class, which defines a normal-form (or strategic-form) game.
Creates an object of "normal_form" class, which can be passed to functions in order to find solutions of the game.
game1 <- normal_form(
s1 = c("T", "B"),
s2 = c("L", "R"),
payoffs1 = c(4, 2, 3, 1),
payoffs2 = c(4, 3, 2, 1),
players = c("Row Player", "Column Player"))
game1b <- normal_form(
s1 = c("T", "B"),
s2 = c("L", "R"),
cells = list(c(4, 4),
c(2, 3),
c(3, 2),
c(1, 1)),
players = c("Row Player", "Column Player"))
game2 <- normal_form(
players = c("A", "B"),
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"))
fx <- function(x, y, a, b) -x^a + (b - y) * x
fy <- function(x, y, s, t) -y^s + (t - x) * y
game3 <- normal_form(
payoffs1 = fx,
payoffs2 = fy,
pars = c('x', 'y'),
par1_lim = c(0, 30),
par2_lim = c(0, 30))
if (FALSE) {
## This throws an error because payoffs1 and payoffs2 are in different forms.
game4 <- normal_form(
payoffs1 = fx,
payoffs2 = "-y^2 + (28 - x) * y",
pars = c('x', 'y'),
par1_lim = c(0, 30),
par2_lim = c(0, 30)
)
}