Information Technology Reference
In-Depth Information
Each of the three graphs given in the figure relates to different possible divi-
sions,
d
of
X
∗
(marked next to it), depicting the expected profit of the auctioneer
in the equilibrium resulting in the specific cost of information on the horizontal
axis. In this example the resulting equilibrium is always based on pure strategies
(i.e.,
p,p
i
∈{
) and the points of discontinuity in the curve represent the
transition from one equilibrium to another. In particular, for
C
values in which
the curve decreases, the equilibrium is based on always purchasing the informa-
tion (though not necessarily disclosing all subsets). This happens when the cost
of purchasing the information justifies its purchase, i.e., for relatively small
C
values. The non-decreasing part of the curve is associated with an equilibrium
in which the information is essentially not purchased.
As can be seen from the figure, for any cost of purchasing the information
0
.
9
<C<
1
.
1, the auctioneer is better off not allowing the information provider
to distinguish between all values: the division
d
=
0
,
1
}
{{
x
1
}
,
{
x
2
}
,
{
x
3
}
,
{
x
4
}}
is
dominated by
d
=
and
d
=
.The
explanation for this interesting phenomenon lies in the different costs of the
transition between equilibria due to stability considerations. With fully distin-
guishable values, it is possible that a desired solution which yields the auctioneer
a substantial expected profit is not stable (e.g., in our case when 0
.
9
<C<
1
.
1
the solution is that the information is not purchased at all), whereas with inac-
curate information the solution is stable and holds as the equilibrium.
In particular, in our example, when the information provider acts fully strate-
gically, i.e., sets the price of information to the maximum possible price for
which the information will still be purchased (the
C
valueinwhichtheequi-
librium changes from purchase to not purchase the information, marked with
circles in the graphs) the auctioneer will gain (and the information provider will
essentially lose) from restricting the information provider's ability to distinguish
between values. For example, with
{{x
1
}, {x
2
,x
3
}, {x
4
}}
the information will be
priced at
C
=0
.
4 yielding the auctioneer an expected profit of 47
.
6 (compared
to
C
=1
.
1 and a profit of 46
.
8 in the “fully distinguishable” case).
{{
x
1
}
,
{
x
2
,x
3
}
,
{
x
4
}}
{{
x
1
,x
2
}
,
{
x
3
,x
4
}}
5 Related Work
Auctions are an effective means of trading and allocating goods whenever the
seller is unsure about buyers' (bidders') exact valuations of the sold item [24,25].
The advantage of many auction mechanism variants in this context is in the
ability to effectively extract the bidders' valuations [23,32], resulting in the most
ecient allocation. Due to its many advantages, this mechanism is commonly
used and researched and over the years has evolved to support various settings
and applications such as on-line auctions [22,27,19,37,36], matching agents in
dynamic two-sided markets [5], resource allocation [31,30,7] and even for task
allocation and joint exploration [15,26]. In this context great emphasis has been
placed on studying bidding strategies [40,38,3], the use of software agents to
represent humans in auctions [6], combinatorial auctions [39] and the develop-
ment of auction protocols that are truthful [5,8,7,2] and robust (e.g., against
false-name bids in combinatorial auctions [41]).
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