Auction theory adaptations for real life applications

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.