seq_form() defines a sequential-form game and creates an object of "sequential_form" class.

seq_form(
  players = NULL,
  s1 = NULL,
  s2 = NULL,
  payoffs1,
  payoffs2,
  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
)

Arguments

players

A character vector of the name (label) for the players.

s1

A character vector of pure strategies for Player 1 (row player). Required only when the players have discrete-choice strategies.

s2

A character vector of pure strategies for Player 2 (column player). Required only when the players have discrete-choice strategies.

payoffs1

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.

payoffs2

The payoff of Player 2. See the explanation of payoffs1 for detail.

discretize

A logical value. Set this TRUE to evaluate payoff functions at some discrete values of strategies s1 and s2. Default is FALSE.

discrete_points

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 strategy par1_lim and par2_lim. Instead of setting this parameter, you can specify arbitrary points to use by setting s1 and s2.

symmetric

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.

byrow

A logical value. If TRUE, payoffs will be lined up by row. Default is FALSE. Only used when both s1 and s2 are provided.

pars

A character vector of parameters that are selected by players 1 and 2, respectively. Only used when payoffs1 and payoffs2 are specified as a function (either as a character string or as an R function).

par1_lim

A numeric vector of length 2, which defines the range of parameters from which Player 1 chooses her strategy.

par2_lim

A numeric vector of length 2, which defines the range of parameters from which Player 2 chooses his strategy.

cons1

A named list of parameters contained in payoffs1 that should be treated as constants, if any.

cons2

A named list of parameters contained in payoffs2 that should be treated as constants, if any.

cons_common

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.

Value

An object of "sequential_form" class, which defines a sequential-form game (an extensive form game with a leader and a follower).

Details

Create an object of 'sequential_form' class, which can be passed to functions in order to find solutions of the game.

Author

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

Examples

g1 <- seq_form(
  players = c("Leader", "Follower"),
  s1 = c("R", "S", "P"),
  s2 = c("R", "S", "P"),
  payoffs1 = c(0, -1, 1, 1, 0, -1, -1, 1, 0),
  payoffs2 = c(0, 1, -1, -1, 0, 1, 1, -1, 0))