A marketing game: Consumer choice and the Ising model

In this paper we present an outline for a marketing/consumer choice problem using graphical games and Markov random fields. We consider a simple marketing scenario and cast it as a coordination game on a network. We consider Glauber dynamics for the strategy update dynamics and then consider the corresponding equilibrium Ising distribution. The parameters of the network are the interaction and marketing strengths, the former being the exponential parameters on statistics describing the relative strategies of the players on the network, the latter being the exponential parameters applied to the strategies of the players, representing an external field. We discuss how marketers for the two brands can estimate the network parameter from data and thereby estimate not only the interaction strengths, but also his opponent´s marketing strength. Connecting an equilibrium Gibbs distribution with the set of typical configurations, we discuss how marketers can then use understanding of the interaction and marketing strengths to select a new marketing strength to help drive the current configuration into the typical set for a new equilibrium Gibbs distribution. We briefly discuss the possible influence of phase transitions on this approach.