Nonatomic discrete choice game model with taste heterogeneity of agents

Abstract

We consider a discrete choice game model in which the agent's disutility is determined only by how the numbers of agents' choices are distributed over them. Its equilibrium is defined in the aggregate choices of agents so that taste heterogeneity is modeled through randomized parameters. This enables us to estimate the joint density of parameters from a collective choice data. The joint density is estimated by a biquadratic inverse optimization that matches observed choices to the equilibrium condition expressed in a set-valued best-response function. The model is capacitated with an arbitrary disutility function continuous in attributes and measurable in taste parameters. We observed that the proposed equilibrium defined as an aggregate choice of agents with such a disutility is actually equivalent to nonatomic Nash equilibrium defined in agent-specific variational inequality. In a comparison test on a massive metro route choice data, we demonstrate the proposed model is a good alternative to existing non-game choice models. An extended test also instantiates the advantage of the general disutility capable of formulating application-dependent choice behaviors of agents.