New paper "A Tractable Multi-Leader Multi-Follower Peak-Load-Pricing Model with Strategic Interaction" by @GrimmVeronika, D. Nowak, L. Schewe, @schmaidt, G. Zöttl and me. This one is for people interested in #Optimization, #Game #Theory and #European #Gas #Markets 1/8

#Capacity #constrained #Cournot #games have been around for a while and are quite well understood. Often, e.g. in the #EntryExit system used in the European gas market, the capacities represent long-term investments, that need to be made a-priori. 2/8

The objective of every firm thus is to maximize the aggregated gain from one or more subsequent capacity-constrained Cournot games minus the initial cost for capacity expansion. Both parts of the objective function can depend on the decisions of the other firms. 3/8

This results in a bi-level #NashEquilibrium problem also known as multi-leader multi-follower problem (MLFG) or equilibrium problem with equilibrium constraints (EPEC). 4/8

Using our detailed analysis of the lower-level solution, we could reformulate the bi-level problem into a one-level #NashEquilibrium problem. However, the resulting objective functions are piecewise defined with both concave and nonconcave kinks at the boundaries. 5/8

#Nonsmooth and #nonconvex (here nonconcave) objective functions or constraints are a common challenge in the analysis of MLFGs, because #Nash #equilibria require global optima, but in the MLFG setting #stationarity is not sufficient to guarantee global optimality. 6/8

By deriving tailored #stationarity and #optimality conditions, we could develop a solution algorithm, that provably computes exactly the set of #Nash #equilibria of the MLFG. We find all equilibria and all nonoptional stationary points are eliminated. 7/8

If you are interested in the details how exactly this works, please have a look at our paper available at https://papers.ssrn.com/sol3/papers.cfm?abstract_id=3656965. And if you have questions, please let me know. 8/8