  Sponsored search mechanisms have drawn much attention from both academic
community and industry in recent years since the seminal papers of [13] and
[14]. However, most of the existing literature concentrates on the mechanism
design and analysis within the scope of only one search engine in the market.
In this paper we propose a mathematical framework for modeling the interaction
of publishers, advertisers and end users in a competitive market. We first
consider the monopoly market model and provide optimal solutions for both ex
ante and ex post cases, which represents the long-term and short-term revenues
of search engines respectively. We then analyze the strategic behaviors of end
users and advertisers under duopoly and prove the existence of equilibrium for
both search engines to co-exist from ex-post perspective. To show the more
general ex ante results, we carry out extensive simulations under different
parameter settings. Our analysis and observation in this work can provide
useful insight in regulating the sponsored search market and protecting the
interests of advertisers and end users.
