Analysis

In this section we interpret the optimal placement strategy and examine the sensitivity of the placement strategy to exogenous factors and factors that the information search engine can control. We examine the case where 46#46, omitting the less interesting case of high 42#42 which always results in the boundary solution 52#52. Consider the effect of users' disutility (13#13) for paid placement. The level of bias is controllable by search engine. Hence it's useful to examine the sensitivity of placement strategy and fees to 13#13. If users were indifferent to paid placement (58#58), the search engine would maximize its placement revenues without regard for the effect on users. A disutility 13#13 forces the search engine to tradeoff between placement and advertising revenues. Proposition  elaborates on this.

Proposition 1   There exists a threshold 59#59 such that when 13#13 is below 60#60, the search engine can improve profits by increasing its bias, and when 61#61, an increase in the bias causes the search engine's profits to decrease.  

62#62
An implication of this result is that there exists an optimal bias 60#60 for some functional forms. The next result describes how the search engine's optimal fraction of paid placement changes with the extent of bias.

Proposition 2   When 63#63, then an increase in 13#13 leaves 35#35 unchanged at zero. When 64#64, an increase in 13#13 causes a decrease in the optimal fraction of paid placements.

This result can be easily seen from Eq.  and Lemma  . The change of the search engine's revenue will be determined by proposition . One of the controllable factors of the information search engine is its quality of service, which is determined by the size of the database, the algorithms, and the user interface. Hence the search engine can improve quality via investments in these areas. Intuitively, search engine could give up some placement revenues, improve q, attract more customers and get more advertisement revenues. What is the trade-off between the search engine's quality and the placement revenue?

Proposition 3   An increase in the search engine's quality q allows it to increase the fraction of paid placement (level of independence 35#35 goes down), increasing its placement revenues and total profits. The search engine's market coverage increases as well, hence an increase in q increases surplus for all players.

65#65
In general, to increase placement revenues, the search engine must increase its fraction of paid placement, but this increases users' disutility and reduces demand and advertising revenues. An increase in q, however, compensates for the increased disutility from increased paid placement. Hence the search engine is able to increase its placement revenues and yet increase total profits. Finally, we consider the impact of per user profit. How do changes in a affect the search engine's paid placement strategy?

Proposition 4   An increase in the per user profit a allows the search engine to increase its degree of independence, so that the fraction of paid placements 66#66 decreases while the placement fee 12#12 increases. As a result, the search engine increase its market coverage 8#8 and total profits 34#34.

67#67
To understand this result, consider the search engine's tradeoff between its two revenue sources. As a increases, the potential for advertising revenue increases, hence a partial sacrifice of revenues brought by users imposes a greater cost on the getekeeper. Therefore, it reduces its level of paid placement in order to provide greater utility to users, and captures a greater percentage of potential advertising revenues.