We study the strategical behaviour of firms facing a lot-sizing problem with Cournot competition. Each player is a firm with her own production facility, modeled as an uncapacitated lot-sizing problem (i.e., production incurs set-up and variable costs and inventories are allowed). A Cournot competition is played in each time period (market) with each player deciding the quantity of product to place on it. The market price of that product in each time period depends on the total quantity placed in the market. We show that this is a potential game with possibly multiple pure Nash equilibria. We then investigate the plausibility of these equilibria to predict the game outcome by evaluating the difficulty of computing them. If the game has a single period, we prove that an equilibrium can be found in polynomial time, but it is weakly NP-hard to find an optimal pure Nash equilibrium (with respect to a given equilibrium refinement). If the game has no variable production and inventory costs, we prove that a pure Nash equilibrium can be computed in polynomial time.
Nota bibliográficaFunding Information:
Part of this work was performed while the first author was in the Faculty of Sciences University of Porto and INESC TEC. First author thanks the support of Institute for data valorisation (IVADO) through the IVADO fellowship , the Portuguese Foundation for Science and Technology ( FCT ) through a PhD grant number SFRH/BD/79201/2011 (POPH/FSE program), the ERDF European Regional Development Fund through the Operational Programme for Competitiveness and Internationalisation - COMPETE 2020 Programme within project POCI-01-0145-FEDER-006961 , and National Funds through the FCT (Portuguese Foundation for Science and Technology ) as part of project UID/EEA/50014/2013 .
Third author supported by the FSR Incoming Post-doctoral Fellowship of the Catholic University of Louvain (UCL), funded by the French Community of Belgium .
Third author supported by the FSR Incoming Post-doctoral Fellowship of the Catholic University of Louvain (UCL), funded by the French Community of Belgium.
© 2018 Elsevier B.V.
- Cournot competition
- Lot-sizing problem
- Nash equilibria
- Potential game