Mathematical Modeling of Competition in Sponsored Search Market

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.Comment: A short version would appear at 2010 Workshop on the Economics of Networks, Systems, and Computation (NetEcon '10

Effective Dynamics, Big Bounces and Scaling Symmetry in Bianchi Type I Loop Quantum Cosmology

The detailed formulation for loop quantum cosmology (LQC) in the Bianchi I model with a scalar massless field has been constructed. In this paper, its effective dynamics is studied in two improved strategies for implementing the LQC discreteness corrections. Both schemes show that the big bang is replaced by the big bounces, which take place up to three times, once in each diagonal direction, when the area or volume scale factor approaches the critical values in the Planck regime measured by the reference of the scalar field momentum. These two strategies give different evolutions: In one scheme, the effective dynamics is independent of the choice of the finite sized cell prescribed to make Hamiltonian finite; in the other, the effective dynamics reacts to the macroscopic scales introduced by the boundary conditions. Both schemes reveal interesting symmetries of scaling, which are reminiscent of the relational interpretation of quantum mechanics and also suggest that the fundamental spatial scale (area gap) may give rise to a temporal scale.Comment: 19 pages, 6 figures, 1 table; one reference added; version to appear in PR

Stagger Lee : how violent nostalgia created an American folk song standard

“Stagger” Lee Shelton (1865-1912) was an African-American carriage driver and sometime-pimp from Missouri. He became immortalized in song as a folklore antihero after murdering a drinking partner following a political argument gone bad in a St Louis saloon on Christmas day, 1895. Sentenced to 25 years in prison, Shelton died in Missouri State Penitentiary after violating his parole with a subsequent conviction for assault and robbery. The song, Stack-a-Lee was first documented in 1897, becoming well known in African American communities along the lower Mississippi River over the following decade as Stagolee, Stagger Lee, Stack OLee and other variants. Two versions were published in the Journal of American Folklore in 1911, with notable recordings entering the charts in the 1920s and beyond. Stagger Lee embodies the archetype of a violent and dangerous antihero as his story is retold, and reimagined or referenced in film, becoming a potent symbol of racial conflict in the United States.In both music and cinematic reincarnations, Stagger Lee seems to have an enduring popularity, partly due to the changing nature of his story, which ensures his tale remains up-to-date (it was most recently adapted to a musical in 2015). This article considers how and why this paean to violence, with its fetishistic vision of extreme masculinity, has become something of a standard in the American folk canon