Abstract: Keyword auction has become one of the main profit-seeking means for search engine, due to its highly-directed and non-invasive forms of presentation. Meanwhile, promoting commercial advertisements brings advertisers with high returns. With the continuous innovation of search engine's business model, keyword auction mechanisms are increasingly focusing on the quality weight of the advertisers. Driven by the search engine's auction rules and advertisers' own interests, the advertisers are willing to invest in extensive market research or optimizing webpage design to improve their performance level in order to get a better ranking in search engine results page and attract more click.
A theoretical model is developed to study advertisers' investment behavior and bidding strategies when advertisers' investment is introduced. Effort is defined as the various factors and resources invested by the advertisers, which is a continuous variable and endogenously determined. More specifically, advertisers can endogenously exert effort to improve their performance which is characterized by the capacity and the effect of advertisers and represented by the total hits. Obviously, this continuously changing effort will inevitably promote the clicks of advertisers, and bring time and financial costs.
In this way, the optimal decision on effort depends on the tradeoff between the increase in revenue and the investment cost.In this paper, a two-stage model is established which consists of endogenous effort in the process of investment. Moreover, according to the different performance levels of all advertisers in the initial state (measured by the amount of clicks the advertiser received over a certain period), they are divided into two types:high type (H-type) and low type (L-type). The type of advertiser can be known by the advertiser itself and the search engine, but not known to other advertisers. This model can be described as follows. Firstly, search engine announces the ranking rules. Next, the endogenous effort is introduced to analyze the optimal effort strategy of advertisers in the investment stage. Then, the equilibrium bidding strategies of two types of advertisers are explored in bidding stage. Subsequently, based on the advertisers' investment and bidding, search engine selects the winning advertiser based on the auction rules. We consider first-price, sealed-bid unit-price auction in symmetric independent private value model where advertises and search engine are both risk-neutral and there is no reserve price involved.
Using backward induction in game theory, advertisers' equilibrium bidding function is first derived in bidding stage, and then the equilibrium bidding function is plugged into investment stage to explore advertisers' investment behavior. The decision is examined on whether L-type advertisers are willing to change the type of advertiser through investment and the optimal effort decision of two types of advertisers. Moreover, how search engine's auction rules (quality weight of L-type advertisersω) affect the advertiser's effort on investment decision-making is under discussion.
The main findings of this paper are as following. In bidding stage, equilibrium bidding strategy of the two types of advertisers is analyzed. First of all, advertisers' investment behavior and bidding decisions are independent of each other. Then, the equilibrium bidding functions of two types of advertisers are monotonously increasing in their own valuation. In investment stage, the results show that when exerting the initial minimum effort, the marginal cost is greater than the marginal benefit, then this cutoff value will be existent and unique. And in case one, the optimal effort of the potential advertisers is always larger than the H-type advertisers', while in case two, the optimal effort of the two types of advertisers tend to coincide with the increase of the value. Meanwhile, search engine's auction rules (quality weight of L-type advertisersω) will affect the advertiser's effort on investment decision-making:the greater the quality weight which the search engine given to L-type advertisers, the higher the cutoff value is. At the same time, the optimal effort of the potential advertisers and the H-type advertiser is reduced.
Finally, the optimal effort of two types of advertisers and the influence of the auction rules on advertisers' optimal effort are analyzed by numerical examples. The number of advertisers and the probability that an advertiser is considered to be a high type are given. Let advertisers' valuation follows uniform distribution at[0,1]. The cost function and the click function with the effort are assumed respectively. The comparisons of the optimal effort of the two types of advertisers under two different situations is discussed under different parameter settings, and are illustrated by the diagram 1 and 2, which verifies the conclusions of Propositions 2 and 3. Meanwhile, under situation 2, different explicit values are set for quality weightω, and the impact of search engine auction rules on the cutoff-value v^* for L-type advertisers and the optimal effort of H-type advertisers are examined separately and illustrated by the diagram 3, where the conclusions of Corollary 1, 2, and 3 are also verified.
Our study is an important extension of keyword auction theory in the field of investment to promote theoretical advancement and provide practical reference. As the market of keyword adverting matures and becomes more standardized, search engine adopting a ranking mechanism which takes into account advertisers' endogenous effort exerted in the process of investment should be an important concert for promoting the virtuous circle of the keyword advertising industry.

Key words: keywords auction, competitive investment, equilibrium bidding strategy, optimal effort