The model corresponds to the following extensive-form
game, described in Ramsay and Signorino (2009):
. 1
. / \
. / \
. / \ y in [0, Q]
. / \
. ---------
. /\ 2
. / \
. / \
. / \
. Q - y R1
. y R2
Q 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.