# equiprice_agenda

# EQUIPRICE scientific agenda

The EQUIPRICE project seeks to build an innovative economic toolbox (ranging from modelling, computation, inference, and empirical applications) for the study of equilibrium models with gross substitutes, with applications to models of matching with or without transfers, trade flows on networks, multinomial choice models, as well as hedonic and dynamic pricing models. While under-emphasized in general equilibrium theory, equilibrium models with gross substitutes are very relevant to these problems as each of these problems can be recast as such.

Thus far, almost any tractable empirical model of these problems typically required making the strong assumption of quasi-linear utilities, leading to a predominance of models with transferable utility in applied work. The current project seeks to develop a new paradigm to move beyond the transferable utility framework to the imperfectly transferable utility one, where the agent’s utilities are no longer quasi-linear.

The mathematical structure of gross substitutes will replace the structure of convexity underlying in models with transferable utility.

To investigate this class of models, one builds a general framework embedding all the models described above, the “equilibrium flow problem.” The gross substitute property is properly generalized and properties (existence of an equilibrium, uniqueness, lattice structure) are derived. Computational algorithms that rely on gross substitutability are designed and implemented. The econometrics of the problem is addressed (estimation, inference, model selection). Applications to various fields such as labor economics, family economics, international trade, urban economics, industrial organization, etc. are investigated.

The project touches upon other disciplines. It will propose new ideas in applied mathematics, offer new algorithms of interest in computer science and machine learning, and provide new methods in other social sciences (like sociology, demography and geography).

## Seven scientific challenges

**Challenge 1.** How to build a single framework to be able to reformulate matching models with or without (or with imperfect) transfers, hedonic models, models of multinomial choice, and models of international trade as problems of competitive equilibrium with gross substitutes?

**Challenge 2.** How to extend the framework investigated in challenge 1 to handle dynamic, Markov versions of these problems (both in the finite-horizon and stationary case)?

**Challenge 3.** How to extend the notion of gross substitutes to allow for the possibility of indifference between preferred alternatives, i.e. consider the case of set-valued excess demand / supply?

**Challenge 4.** Build and analyze a set of algorithms for the equilibrium problem with gross substitutes to handle the problems described in the previous Challenges.

**Challenge 5.** Implement these algorithms into a compiled, parallelized software library.

**Challenge 6.** Develop a novel inferential theory based on minimax regret estimation for the estimation of equilibrium models with Gross Substitutes, to handle inference in the previous problems.

**Challenge 7.** In the minimax regret estimation framework of challenge 6, extend the estimation and inference theory to handle sparsity constraints.

**EQUIPRICE: Equilibrium methods for Resource Allocation and Dynamic Pricing. European Research Council consolidator grant (ERC-CoG) No. 866274, 2020-2025.**