An Introduction to Auction Theory by Flavio M. Menezes

By Flavio M. Menezes

The sensible significance of public sale concept is well known. certainly, economists were well-known for his or her contribution to the layout of numerous auction-like mechanisms, similar to the U. S. Federal Communications fee spectrum auctions, the 3G auctions in Europe and past, and the public sale markets for electrical energy markets all over the world. furthermore, public sale idea is now noticeable as an immense section of an economist's education. for instance, the various extra celebrated effects from the single-object public sale concept at the moment are often taught in complex undergraduate and first-year graduate classes at the economics of data. The strategies and insights won from the learn of public sale concept supply an invaluable start line in the event you are looking to enterprise into the economics of knowledge, mechanism layout, and regulatory economics. This e-book presents a step by step, self-contained remedy of the idea of auctions. the purpose is to supply an introductory textbook that might enable scholars and readers with a calculus heritage to paintings via the entire simple effects. assurance comprises: the fundamental independent-private-model; the consequences of introducing correlation in valuations on equilibrium behaviour and the seller's anticipated profit; mechanism layout; and the idea of multi-object auctions. The paperback variation of the textual content encompasses a new bankruptcy which acts as a consultant to present advancements in public sale conception.

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In the oral auction—represented by the button auction—bidder 1 is the last pressing the button, while bidder 2 takes his hand off the button when the price reaches v2 . Bidder 1’s profits are equal to v1 − v2 , while bidders 2, . . , n earn zero profits. Note that the choice of players 1 and 2 was completely arbitrary. Thus, the same profile of strategies in both auctions yields the same profits for all players. That is, oral auctions and second-price auctions are strategically equivalent. 14). 3 Revenue Equivalence Among the four types of auctions considered above, first- and second-price, Dutch, and English auctions, which one generates the highest expected revenue for the seller?

As mentioned in Chapter 2, our viewpoint when comparing auctions is that of the seller or from an analyst that does not have information about individuals’ types. Moreover, we focus on settings where the identity of an individual bidder is not particularly relevant. That is, we assume that bidders are ex-ante symmetric. In order to introduce the notion of symmetry we need the following definition. Definition 4 A permutation of the set S is a bijection σ : S → S. We can now define the notion of a symmetric function.

For example, if n = 3, u(a, b, c) is symmetric if u(a, b, c) = u(a, c, b) = u(b, a, c) = u(b, c, a) = u(c, a, b) = u(c, b, a) for every (a, b, c) ∈ [0, v¯]3 . We will apply this concept to the distribution of types. For example, exchanging the types of bidders 1 and 2 in a vector (x1 , x2 , x3 , . . , xn ) is of no consequence, that is, f (x1 , x2 , x3 , . . , xn ) = f (x2 , x1 , x3 , . . , xn ). This assumption is stated below along with some regularity restrictions. Symmetry The density f is symmetric, strictly positive and continuous.

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