Also for this kind of problem, a computational model would constitute a better methodology. Movies come in several types unknown to the potential spectator. M heterogeneous agents are arranged on a circle. Deciding of going to the movie theater or not is a random choice. Neighbors are assumed to do the same.
Agent have rational expectations so that .
If we now assume that then the story becomes interesting. Each location will have a different demand depending on the parameter representing their cultural background. We propose to use an agent based computational model at this point, in order to understand how the equilibrium solution changes. The equation , which determines the static equilibrium in heterogeneous case becomes very difficult to solve numerically when the number of agents is large. Constructing a Gibbs Sampler is a possible way out.