A bounded rational agent-based model of consumer choice

In a bottom-up approach, agent-based models have been extensively used in finance and economics in order to understand how macro-level phenomena can emerge from myriads of micro-level behaviours of individual agents. Moreover, in the absence of (big) data there is still the need to test economic theories and understand how macro-level laws can be materialized as the aggregate of a multitude of interactions of discrete agents. We exemplify how we can solve this problem in a particular instance: We introduce an agent-based method in order to generate data with Monte Carlo and then we interpolate the data with machine learning methods in order to derive multi-parametric demand functions. In particular, the model we construct is implemented in a simulated economy with 1000 consumers and two products, where each consumer is characterized by a unique set of preferences and available income. The demand for each product is determined by a stochastic process, incorporating the uncertainty in consumer preferences. By interpolating the data for the demands for various scenarios and types of consumers we derive poly-parametric demand functions. These demand functions are partially in tension with classical demand theory since on certain occasions they imply that the demand of a product increases as its price increases. Our proposed method of generating data from discrete agents with Monte Carlo and of interpolating the data with machine learning methods can be easily generalized and applied to the assessment of economic theories and to the derivation of economic laws in a bottom-up approach.