On Substitutability and Complementarity in Discrete Choice Models

In this paper, we propose the concepts of substitutability and complementarity in discrete choice models. These concepts concern whether the choice probability of one alternative in a choice model increases or decreases with the utility of another alternative, and they play important roles in capturing certain practical choice patterns, such as the halo effect. We study conditions on discrete choice models that will lead to substitutability and complementarity. Particularly, we show that the random utility model only allows substitutability between different alternatives, while the representative agent model and the welfare-based choice model allow more flexible substitutability/complementarity patterns. We also present ways of constructing choice models that exhibit complementary property.

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