Modeling television commercial advertisement markets: To zap or not to zap, that is the question for sponsors of TV programs

We propose a simple probabilistic model of zapping process of television viewers. Our model might be regarded as a `theoretical platform´ to investigate the human collective behavior in the macroscopic scale through the zapping action of each viewer at the microscopic level. The stochastic process of audience measurements as macroscopic quantities such as television program rating point or the so-called gross rating point (GRP for short) are reconstructed using the microscopic modeling of each viewer´s decision making. Assuming that each viewer decides the television station to watch by means of three factors, namely, physical constraints on television controllers, exogenous information such as advertisement of program by television station, and endogenous information given by `word-of-mouth communication´ through the past market history, we shall construct an aggregation probability of Gibbs-Boltzmann-type with the energy function. We discuss the possibility for the ingredients of the model system to exhibit the collective behavior due to not exogenous but endogenous information.