Motivated by recent progress on pricing in the AI literature, we study
marketplaces that contain multiple vendors offering identical or similar
products and unit-demand buyers with different valuations on these vendors. The
objective of each vendor is to set the price of its product to a fixed value so
that its profit is maximized...
The profit depends on the vendor's price itself
and the total volume of buyers that find the particular price more attractive
than the price of the vendor's competitors. We model the behaviour of buyers
and vendors as a two-stage full-information game and study a series of
questions related to the existence, efficiency (price of anarchy) and
computational complexity of equilibria in this game. To overcome situations
where equilibria do not exist or exist but are highly inefficient, we consider
the scenario where some of the vendors are subsidized in order to keep prices
low and buyers highly satisfied.