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holdings, and marginal flight values. On a high level, the strategy is designed to defer
purchase of flights that are not quickly increasing, allowing for flexibility in avoiding
expensive hotels as hotel price information is revealed.
The flight purchase strategy can be described in the form of a decision tree as de-
picted in Figure 1. First, Walverine compares the expected perturbation ( E [ Δ ]) with
a threshold T 1, deferring purchase if the prices are not expected to increase by T 1 or
more. If T 1 is exceeded, Walverine next compares the expected perturbation with a
second higher threshold, T 2, and if the prices are expected to increase by more than T 2
Walverine purchases all units for that flight that are in the optimal package.
E[6v] < T1?
YN
E[6v] > T2?
DELAY
YN
Reducible trip AND
#clients > T3?
BUY
YN
First ticket AND
surplus > T4?
BUY
YN
BUY
DELAY
Fig. 1. Decision tree for deciding whether to delay flight purchases
If T 1 <E [ Δ ] <T 2, the Walverine flight delay strategy is designed to take into
account the potential benefit of avoiding travel on high demand days. Walverine checks
whether the flight constitutes one end of a reducible trip: one that spans more than
a single day. If the trip is not reducible, Walverine buys all the flights. If reducible,
Walverine considers its own demand (defined by the optimal package) for the day that
would be avoided through shortening the trip, equivalent to the day of an inflight, and
the day before an outflight. If our own demand for that day is T 3 or fewer, Walverine
purchases all the flights. Otherwise (reducible and demand greater than T 3), Walverine
delays the purchases, except possibly for one unit of the flight instance, which it will
purchase if its marginal surplus exceeds another threshold, T 4.
Though the strategy described above is based on sound calculations and tradeoff
principles, it is difficult to justify particular settings of threshold parameters without
making numerous assumptions and simplifications. Therefore we treat these as strategy
parameters, to be explored empirically, along with the other Walverine parameters.
2.2
Bid Shading
The Walverine optimal shading algorithm [1] identifies, for each hotel auction, the bid
value maximizing expected utility based on a model of other agents' marginal value
distributions. Because this optimization is based on numerous simplifications and ap-
proximations, we include several parameters to control its use.
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