The Pricing War Continues: On Competitive Multi-Item Pricing


  • Omer Lev The Hebrew University
  • Joel Oren University of Toronto
  • Craig Boutilier University of Toronto
  • Jeffrey Rosenschein The Hebrew University



Game theory, Equilibrium, Price of anarchy, Price of stability


We study a game with \emph{strategic} vendors (the agents) who own multiple items and a single buyer with a submodular valuation function. The goal of the vendors is to maximize their revenue via pricing of the items, given that the buyer will buy the set of items that maximizes his net payoff.% (valuation minus the prices). We show this game may not always have a pure Nash equilibrium, in contrast to previous results for the special case where each vendor owns a single item. We do so by relating our game to an intermediate, discrete game in which the vendors only choose the available items, and their prices are set exogenously afterwards. We further make use of the intermediate game to provide tight bounds on the price of anarchy for the subset games that have pure Nash equilibria; we find that the optimal PoA reached in the previous special cases does not hold, but only a logarithmic one. Finally, we show that for a special case of submodular functions, efficient pure Nash equilibria always exist.




How to Cite

Lev, O., Oren, J., Boutilier, C., & Rosenschein, J. (2015). The Pricing War Continues: On Competitive Multi-Item Pricing. Proceedings of the AAAI Conference on Artificial Intelligence, 29(1).



AAAI Technical Track: Game Theory and Economic Paradigms