  We study the price competition in a duopoly with an arbitrary number of
buyers. Each seller can offer multiple units of a commodity depending on the
availability of the commodity which is random and may be different for
different sellers. Sellers seek to select a price that will be attractive to
the buyers and also fetch adequate profits. The selection will in general
depend on the number of units available with the seller and also that of its
competitor - the seller may only know the statistics of the latter. The setting
captures a secondary spectrum access network, a non-neutral Internet, or a
microgrid network in which unused spectrum bands, resources of ISPs, and excess
power units constitute the respective commodities of sale. We analyze this
price competition as a game, and identify a set of necessary and sufficient
properties for the Nash Equilibrium (NE). The properties reveal that sellers
randomize their price using probability distributions whose support sets are
mutually disjoint and in decreasing order of the number of availability. We
prove the uniqueness of a symmetric NE in a symmetric market, and explicitly
compute the price distribution in the symmetric NE.
