Game Development Reference
In-Depth Information
FIGURE 5.6
When cutting the cake, if it is assumed that the Decider will always take a
larger piece, the only way the Cutter does not get a smaller piece is if they are equal.
U
LTIMATUM
G
AME
Admittedly, the cake example in the previous section would be much simpler if we
didn't allow the other person to select which piece he wanted. However, there is an-
other popular twist on asymmetrical decision theory that is in a similar vein. In this
scenario, often referred to as the Ultimatum Game, there are still two differing
roles—the Giver (similar to the Cutter) and the Decider. Once again, the Giver is
in charge of dividing and distributing a finite amount between himself and another
person. As much as I would like to continue using confection as our medium of
exchange, I find that this example works better with money.
Let's assume that we, as the Giver, have been entrusted with $100 to distribute
between ourselves and another person (the Decider). We are told that we propose
to give a non-zero amount to the other person (the titular ultimatum). Whatever
we don't give to that person, we will be allowed to keep for ourselves, with one
major caveat: The Decider can select to accept or refuse our offering. If the Decider
keeps his cut, we (as the Giver) get to keep ours as well. If the Decider turns down
the offer for whatever reason, we do
not
get to keep our share of the money either.
In effect, the Decider is electing that
neither
of us will get anything at all. The $100
is returned to the mysterious source from whence it came.
This game has been used often in psychological studies, with interesting results.
People's actions differ significantly from those that would be dictated by using sim-
ple mathematics alone.
To determine where things go awry, we first need to analyze the decision fac-
ing the Giver. Theoretically, we must select a value that the Decider will accept. The
reason for this is plainly obvious. If the Decider is displeased with our offering, he
will reject us, and we will get nothing. (Does it sound like we need a volcano and a
small farm animal in this example?) However, if we please the Decider, we will get
to keep whatever is left. Mathematically, the problem is, how do we get the most
that we can out of the $100 without risking getting nothing at all?
