Estimating heterogeneous agent preferences by inverse optimization in a randomized nonatomic game

We consider an externality game in which nonatomic agents choose from a finite set of alternatives and disutility is determined only by the number of agents choosing each alternative. The equilibrium is defined with respect to the agents’ choices so that taste heterogeneity, modeled through randomized parameters, can be estimated from collective choice data. The joint density of the taste parameters is computed by a biquadratic inverse optimization process that matches observed choices to the equilibrium condition associated with a set-valued best-response function, and hence imposes no prior assumptions on the taste parameters. The model is capacitated with disutility generalized into an arbitrary function that is continuous in attributes and measurable in taste parameters. The existence of an equilibrium under such a disutility model is established by observing that, in an externality game, the proposed aggregate equilibrium is actually equivalent to the agent-specific Nash equilibrium previously established by Schmeidler (J Stat Phys 7(4):295–300, 1973). In a comparison test on intensive metro route-choice data, we demonstrate that the proposed model is a good alternative to existing nongame choice models. An extended test also demonstrates the advantage of the general disutility model in describing agents choice behaviors in other contexts.