  We develop extensions to auction theory results that are useful in real life
scenarios.
  1. Since valuations are generally positive we first develop approximations
using the log-normal distribution. This would be useful for many finance
related auction settings since asset prices are usually non-negative.
  2. We formulate a positive symmetric discrete distribution, which is likely
to be followed by the total number of auction participants, and incorporate
this into auction theory results.
  3. We develop extensions when the valuations of the bidders are
interdependent and incorporate all the results developed into a final combined
realistic setting.
  4. Our methods can be a practical tool for bidders and auction sellers to
maximize their profits. The models developed here could be potentially useful
for inventory estimation and for wholesale procurement of financial instruments
and also non-financial commodities.
  All the propositions are new results and they refer to existing results which
are stated as Lemmas.
