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ultimatum(formulas, data, subset, na.action, minOffer = 0, maxOffer, offertol = sqrt(.Machine$double.eps), s1 = NULL, s2 = NULL, outcome = c("both", "offer"), boot = 0, bootreport = TRUE, profile, method = "BFGS", ..., reltol = 1e-12)Formula object
with two right-hand sides. See "Details" and the examples below.data to use in fitting.offertol of
minOffer/maxOffer will be considered to be at the
minimum/maximum. (This is used to prevent floating-point problems and
need not be changed in most applications.)NULL (the
default), the parameter will be estimated.NULL (the
default), the parameter will be estimated.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.maxLik)maxLik).optim). Use of values higher than the default is discouraged.c("game", "ultimatum"). For details on
the game class, see egame12. The ultimatum
class is just for use in the generation of predicted values (see
predProbs) and profiling (see profile.game).
. 1 . / \ . / \ . / \ y in [0, Q] . / \ . --------- . /\ 2 . / \ . / \ . / \ . Q - y R1 . y R2Q refers to the maximum feasible offer (the argument
maxOffer).The two equations on the right-hand side of formulas refer to Player
1's and Player 2's reservation values respectively. The left-hand side
should take the form offer + acceptance, where outcome
contains the numeric value of the offer made and acceptance is an
indicator for whether it was accepted. (If outcome is set to
"offer", the acceptance indicator can be omitted. See below for more.)
The outcome argument refers to whether the outcome of interest is
just the level of the offer made, or both the level of the offer and whether
it was accepted. If acceptance was unobserved, then outcome should
be set to "offer". If so, the estimates for Player 2's reservation value
should be interpreted as Player 1's expectations about these parameters. It
may also be useful to set outcome to "offer" even if acceptance data
are available, for the purpose of comparing the strategic model to other
models of offer levels (as in Ramsay and Signorino 2009). If an acceptance
variable is specified but outcome is set to "offer", the acceptance
data will be used for starting values but not in the actual fitting.
Numerical instability is not uncommon in the statistical ultimatum game, especially when the scale parameters are being estimated.
data(data_ult)
## Model formula:
f1 <- offer + accept ~ x1 + x2 + x3 + x4 + w1 + w2 | z1 + z2 + z3 + z4 + w1 + w2
## ^^^^^^^^^^^^^^^^^^^^^^^^^^^ ^^^^^^^^^^^^^^^^^^^^^^^^^^^
## R1 R2
m1 <- ultimatum(f1, data = data_ult, maxOffer = 15)
summary(m1)
## Estimating offer size only
f2 <- update(Formula(f1), offer ~ .)
m2 <- ultimatum(f2, data = data_ult, maxOffer = 15, outcome = "offer")
summary(m2)
## Fixing scale terms
m3 <- ultimatum(f1, data = data_ult, maxOffer = 15, s1 = 5, s2 = 1)
summary(m3)
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