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120000
LWA
LWLR
QR
SearchMin
SearchMax
100000
80000
60000
40000
20000
0
0
50
100
150
200
Storage Cost
Fig. 2. Several different estimates for the correspondence between storage costs and aggregate
day-0 purchases in equilibrium. Estimates from three learning methods are shown, along with an
interval estimate from the best-first search algorithm. SearchMin is the minimum day-0 level for
a profile with -bound less than 2.5M, and SearchMax is the corresponding maximum.
also evidence that high levels of day-0 procurement were a rational response by agents
to the new specification. The minimum prediction of any method for the storage cost
setting used in the final round was approximately 38000, and the maximum was consid-
erably higher at approximately 60000. The observed levels during the tournament were
somewhat above even the high estimate given by our methods, but it seems clear that
undesirably high levels of early purchasing are rational.
We also considered whether any setting of storage costs could have resulted in a de-
sirable outcome for day-0 purchasing. To test this, we attempted to find a setting that
would yield equilibrium outcomes with aggregate procurement less than 23600 (still
higher than we would want in practice). Linear extrapolation of the SearchMax line
predicts that this should occur for a storage cost setting of 320%. However, further sim-
ulations resulted in an estimated outcome range of 31860-38940 for this profile, only
slightly lower than the estimates for storage costs of 200%. There appears to be very
little benefit to additional increases of storage costs beyond 200%. Furthermore, agent
profits were almost always negative for storage costs of 320%, so additional increases
would be undesirable even if day-0 procurement could eventually be reduced to accept-
able levels.
Our analysis suggests that the changes to the game rules did have the desired effect to
some extent, but that this effect was not as large as anticipated. In games as complex as
TAC/SCM it is very difficult to asses the effects of potential rule changes. In principle,
the techniques used here provide ways of gathering additional data to assess the impact
of design decisions in games with important strategic interactions.
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