Binomial coefficients have been used for centuries in a variety of fields and accumulated numerous definitions. In this paper, we introduce new way defining binomial as repeated sums ones. A multitude coefficient identities will be shown order to prove definition. Using definition, simplify some particular such the Harmonic sum Binomial-Harmonic sum. We derive formulae simplifying general <i...

We study a model of two-round, …rst-price, sealed bid auctions with two bidders and two identical items. We assume that both bidders want to purchase both items and the bidder’s valuation for the object remains the same in both rounds. After the conclusion of the …rst round, the winner and the winning bid are publicly announced. The bidders use this information to update their beliefs about the...

This paper considers a first price common value auction with one-sided private information among bidders. An object is rented each period to the highest bidder without revealing the bids made in previous periods. The paper extends single crossing arguments used in static games to show the existence of equilibrium in this repeated auction. The model predicts that bidders bid more aggressively in...