Technical Note - A Monge Sequence-Based Approach to Characterize the Competitive Newsvendor Problem

Replicating cash flows of multiple agents in game-theoretic settings tends to be a challenging task. In this paper, we consider the competitive newsvendor game where multiple newsvendors choose inventory levels before demand arrival and the unmet demand of each newsvendor spills over to multiple other newsvendors. We show that this spillover behavior and the resulting cash flows of each newsvendor can be replicated within a transportation problem after assigning artificial costs on spillover behavior. This replication provides an opportunity to study structural properties of the problem, as well as determine the equilibrium of the game. This paradigm of using artificial costs within an optimization framework to replicate agents’ cash flows can be used in many other games as well.