egame123: Strategic model with 3 players, 4 terminal nodes
In games: Statistical Estimation of Game-Theoretic Models

Description Usage Arguments Details Value Author(s) Examples

Fits a strategic model with three players and four terminal nodes, as in the game illustrated below in "Details".

egame123(formulas, data, subset, na.action, link = c("probit", "logit"),
  type = c("agent", "private"), startvals = c("sbi", "unif", "zero"),
  fixedUtils = NULL, sdformula = NULL, sdByPlayer = FALSE, boot = 0,
  bootreport = TRUE, profile, method = "BFGS", ...)

`formulas`	a list of eight formulas, or a `Formula` object with eight right-hand sides. See "Details" and "Examples".
`data`	a data frame.
`subset`	an optional logical vector specifying which observations from `data` to use in fitting.
`na.action`	how to deal with `NA`s in `data`. Defaults to the `na.action` setting of `options`. See `na.omit`
`link`	whether to use a probit (default) or logit link structure,
`type`	whether to use an agent-error ("agent", default) or private-information ("private") stochastic structure.
`startvals`	whether to calculate starting values for the optimization from statistical backwards induction ("sbi", default), draw them from a uniform distribution ("unif"), or to set them all to 0 ("zero")
`fixedUtils`	numeric vector of values to fix for u11, u13, u15, u16, u23, u25, u26, and u36. `NULL` (the default) indicates that these should be estimated with regressors, not fixed.
`sdformula`	an optional list of formulas or a `Formula` containing a regression equation for the scale parameter. See `egame12` for details.
`sdByPlayer`	logical: if scale parameters are being estimated (i.e., `sdformula` or `fixedUtils` is non-`NULL`), should a separate one be estimated for each player? This option is ignored unless `fixedUtils` or `sdformula` is specified.
`boot`	integer: number of bootstrap iterations to perform (if any).
`bootreport`	logical: whether to print status bar during bootstrapping.
`profile`	output from running `profile.game` on a previous fit of the model, used to generate starting values for refitting when an earlier fit converged to a non-global maximum.
`method`	character string specifying which optimization routine to use (see `maxLik`)
`...`	other arguments to pass to the fitting function (see odemaxLik).

The model corresponds to the following extensive-form game:

.     1
.     /\
.    /  \
.   /    \ 2
.  u11   /\
.       /  \
.      /    \
.    u13     \ 3
.    u23     /\
.           /  \
.          /    \
.         u15   u16
.         u25   u26
.         0     u36

For additional details on any of the function arguments or options, see egame12. The only difference is that the right-hand side of formulas must have eight components (rather than four) in this case.

Ways to specify the dependent variable in egame123:

Numeric vector y containing 4 unique values, corresponding to the outcomes (in order from left to right) as labeled in the game tree above.
Factor y, where y has four levels, corresponding in order to the outcomes as labeled above.
Indicator variables y1 + y2 + y3, where y1 indicates whether Player 1 moves left or right, y2 indicates Player 2's move, and y3 indicates Player 3's move. Non-observed values of y2 and y3 (where the game ended before the move could be made) should be set to 0, not NA, to ensure that observations are not dropped when na.action = na.omit.

An object of class c("game", "egame123"). See egame12 for a description of the game class.

Brenton Kenkel (brenton.kenkel@gmail.com)

data("data_123")

## Model formula:
f1 <- y ~ x1 + x2 | 0 | x3 | x4 + x5 | 0 | x6 | x7 | x8
##    ^   ^^^^^^^   ^   ^^   ^^^^^^^   ^   ^^   ^^   ^^
##    y     u11    u13  u15    u16    u23  u25  u26  u36

m1 <- egame123(f1, data = data_123, link = "probit", type = "private")
summary(m1)

## Dummy specification of the dependent variable
f2 <- update(Formula(f1), a1 + a2 + a3 ~ .)
m2 <- egame123(f2, data = data_123, link = "probit", type = "private")
summary(m2)