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Post-tournament analysis showed that aggressive early procurement was a rational strat-
egy despite the potential for negative profits, but that the presence of a preemptive agent
could potentially improve profits for the entire field by knocking the agents out of the
undesirable equilibrium [3].
While these strategic interactions were interesting, the extreme emphasis on early
procurement detracted from other research problems, including factory scheduling [4],
optimizing customer bids [5], and dynamically managing inventory in response to new
information. The random order in which suppliers considered requests also introduced
a “lottery effect,” where these random outcomes had a strong effect on the overall out-
come of the game [6]. Several changes were made to the specification for the 2004
competition; these were intended to reduce the incentives for day-0 procurement. The
changes included modifications to the supplier pricing policy, segmentation of the cus-
tomer markets, and the addition of storage costs.
3.2
Early Procurement in TAC-04/SCM
During the TAC-04/SCM qualifying round day-0 procurement remained very high, de-
spite the rule changes. In response, the GameMaster increased storage costs fivefold for
the remaining rounds. Even this did not dampen the day-0 purchasing; the number of
components ordered based on day-0 requests actually increased by 14% from 2003 to
2004 (in games with no blocking strategies). This sequence of events raises questions
about the impact of the rule changes (especially storage costs) on agent behavior. Do
higher storage costs actually reduce incentives for early procurement, as suggested by
intuitive arguments? Was the high level of early procurement observed in TAC-04/SCM
a rational response to the new rules? Could any level of storage costs have reduced day-
0 procurement to an acceptable level?
We address these questions with a systematic exploration of the relationship be-
tween storage costs and day-0 procurement. Conceptually, each setting of storage costs
induces a different game between the agents. Game theory suggests that stable pro-
files (e.g. Nash equilibria) are likely to be played when rational, self-interested agents
compete in games. In general, we model the strategic interactions between a mecha-
nism designer and participants as a two-stage game. The designer moves first by setting
the mechanism parameter θ (e.g. storage costs), and all the participants observe θ and
move simultaneously thereafter (e.g. selecting a day-0 procurement quantity). We refer
to game between the participants in the second stage as the game Γ θ induced by θ :
Γ θ =[ I,
{
S i }
,
{
u i ( s, θ )
}
] .
Here I is the set of participants, S i the set of strategies for each participant, and u i (
·
)
the utility function for each participant. Suppose the goal of the designer is to optimize
some welfare function W ( · ).Let
{s ( θ ) }
be the set of Nash equilibria of Γ θ .Herewe
define W ( s ( θ ) )=inf {W ( s, θ ): s ∈{s ( θ ) }}
. Alternatively, if one has a probabil-
ity distribution over the Nash equilibria given θ , it may be natural to take the expectation
of W instead: W ( s ( θ ) )= E s∈s [ W ( s, θ )] . 3
If there are no Nash equilibria of Γ θ (a
3
For example, such a distribution could be derived from analysis of evolutionary dynamics, as
in [7].
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