
The timing of the game is as follows: First, media platforms choose their advertising
levels a
1
and a
2
and the search engine chooses x. In the second stage, the advertising mar-
ket clears—that is, p
0
, p
1
, and p
2
equalize demand and supply for each outlet. In the third
stage, consumers decide whether or not to use the search engine. Finally, those con-
sumers who use the search engine type in a query and visit the media platform suggested
by the search engine.
When deciding whether or not to use the search engine, a consumer knows x and has
an expectation about the advertising levels on the media platforms, denoted by a
i
e
. The
expected utility of a