Budgetary Effects on Pricing Equilibrium in Online Markets

Following the work of Babaioff et al, we consider the pricing game with strategic vendors and a single buyer, modeling a scenario in which multiple competing vendors have very good knowledge of a buyer, as is common in online markets. We add to this model the realistic assumption that the buyer has a fixed budget and does not have unlimited funds. When the buyer's valuation function is additive, we are able to completely characterize the different possible pure Nash Equilibria (PNE) and in particular obtain a necessary and sufficient condition for uniqueness. Furthermore, we characterize the market clearing (or Walresian) equilibria for all submodular valuations.