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.