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disjoint subsets, each composed of values which the information provider cannot
distinguish between.
Limiting the information provider's ability to distinguish between values may
seem non-intuitive in the sense that it limits the auctioneer's strategy space when
it comes to disclosing this information to bidders, if it is purchased. Nevertheless,
in many settings the strategy of constraining the information provider's input
can actually play into the hands of the auctioneer and improve her expected
profit. This phenomenon is illustrated in Figure 1, which depicts the auction-
eer's expected profit (vertical axis) as a function of the information purchasing
cost (horizontal axis), for several possible divisions of
X
∗
into subsets of non-
distinguishable values. The setting used for this example is given in the table
below the graph. It is based on three bidders, where each can be of four different
types. The first column of the table depicts the different bidder types and the
second column gives their probability. Similarly, the second and third rows depict
the different possible values of
X
(denoted
x
1
,
x
2
,
x
3
and
x
4
) and their proba-
bilities. The remaining values are the valuations that bidders of different types
assign different possible values of the parameter
X
. For example, if a bidder is
of type 3, then her valuation of
x
2
is 59.
Fig. 1.
The auctioneer's expected profit as a function of the information purchasing
cost for different divisions of
X
∗
into subsets of non-distinguishable values
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