Mathematical modeling of competition in sponsored search market

Abstract

Sponsored search mechanisms have drawn much attention from both academic community and industry in recent years since the seminal papers of [3] and [4]. 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 <i>competitive</i> market. We study the competition between two search engines as a three-stage dynamic game and prove the existence of Nash equilibrium prices when allowing advertisers to participate in both advertising systems simultaneously. To compare the expected revenues and social welfare under competition and monopoly, we carry out extensive simulation under common parameter setting of participants. Our results can provide useful insight in regulating the sponsored search market and protecting the interests of advertisers and end users.