Single-Leader-Radner-Equilibrium: A New Approach for a Class of Bilevel Problems Under Uncertainty

Bilevel problems with several followers, often called Single-Leader-Multi-Follower problems, have been proved to be very useful for modeling hierarchical interactions between agents in economics, industry, etc. When uncertainty must be taken into account, a classical approach is to use stochastic bilevel optimization. In this work, we introduce an alternative approach intrinsically integrating at the same time uncertain future and time-dependent decision processes. It is called Single-Leader-Radner-Equilibrium (SLRE) and is characterized by a hierarchical structure with one leader and several followers competing to reach a Radner equilibrium. A variational reformulation of the quasiconcave SLRE model (that is, where the objective function of the followers is only quasiconcave) is proposed and used to prove the existence of an optimistic solution of the quasiconcave SLRE. Finally, thanks to these developments we present a new approach of optimal design of eco-industrial parks.