Competitive Uncapacitated Lot- Sizing Game

A game merging the lot-sizing problem with a Cournot competition model is for the first time theoretically studied. Each player is a producer 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 game is potential with possibly multiple pure Nash equilibria. 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 constant production and no inventory costs, we prove that a pure Nash equilibrium can be computed in polynomial time.