Identification using Revealed Preferences in Linearly Separable Models

Revealed preference arguments are commonly used when identifying models of both single-agent decisions and non-cooperative games. We develop general identification results for a large class of models that have a linearly separable payoff structure. Our model allows for both discrete and continuous choice sets. It incorporates widely studied models such as discrete and hedonic choice models, auctions, school choice mechanisms, oligopoly pricing and trading games. We characterize the identified set and show that point identification can be achieved either if the choice set is sufficiently rich or if a variable that shifts preferences is available. Our identification results also suggests an estimation approach. Finally, we implement this approach to estimate values in a combinatorial procurement auction for school lunches in Chile.