TY - GEN
T1 - The pricing war continues
T2 - 29th AAAI Conference on Artificial Intelligence, AAAI 2015 and the 27th Innovative Applications of Artificial Intelligence Conference, IAAI 2015
AU - Lev, Omer
AU - Oren, Joel
AU - Boutilier, Craig
AU - Rosenschein, Jeffrey S.
N1 - Publisher Copyright:
Copyright © 2015, Association for the Advancement of Artificial Intelligence (www.aaai.org). All rights reserved.
PY - 2015/6/1
Y1 - 2015/6/1
N2 - We study a game with 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. 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.
AB - We study a game with 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. 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.
UR - http://www.scopus.com/inward/record.url?scp=84959889009&partnerID=8YFLogxK
M3 - Conference contribution
AN - SCOPUS:84959889009
T3 - Proceedings of the National Conference on Artificial Intelligence
SP - 972
EP - 978
BT - Proceedings of the 29th AAAI Conference on Artificial Intelligence, AAAI 2015 and the 27th Innovative Applications of Artificial Intelligence Conference, IAAI 2015
PB - AI Access Foundation
Y2 - 25 January 2015 through 30 January 2015
ER -