We provide an analysis of the spatial dynamic behavioral outcome of a group of people gathered for a cocktail party when individual utility exhibits social interaction effects. There are N partygoers gathered in a square room. Our goal is to model the spatial dynamics of individual moves within the room during the party. For this purpose we represent the room space as a two dimensional array with individuals each occupying one cell. Each individual is assigned a unique identifying number to allow move tracking.
All individuals are aware of the others' locations.
At the same time we assume that agents are myopic in the sense that they look only one period ahead. Big negative number corresponds to the situation when a person does not like this individual, and positive number represents the case when a person likes this individual. Matrix L summarizes pre-existing friendship structure among individuals. In our model individuals exhibit time dependent preferences. The last term represents the temporal flow of utility derived from conversation.