English auctions and the Stolper-Samuelson theorem

We prove that the English auction (with bidders that need not be ex ante identical and may have interdependent valuations) has an efficient ex post equilibrium. We establish this result for environments where it has not been previously obtained. We also prove two versions of the Stolper-Samuelson theorem, one for economies with n goods and n factors, and one for non-square economies. Similar assumptions and methods underlie these seemingly unrelated results.English auctions, Stolper-Samuelson, single crossing

Comparative Statics, English Auctions, and the Stolper-Samuelson Theorem

Changes in the parameters of an $n$-dimensional system of equations induce changes in its solutions. For a class of such systems, we determine the qualitative change in solutions given certain qualitative changes in parameters. Our methods and results are elementary yet useful. They highlight the existence of a common thread, our ``own effect'' assumption, in formally diverse areas of economics. We discuss several applications; among them, we establish the existence of efficient equilibria in English auctions with interdependent valuations, and a version of the Stolper-Samuelson Theorem for an $n \times n$ trade model.effficient auctions, international trade theory, implicit function theorem

Comparative Statics, English Auctions, and the Stolper-Samuelson Theorem

Changes in the parameters of an n-dimensional system of equations induce changes in its solutions. For a class of such systems, we determine the qualitative change in solutions given certain qualitative changes in parameters. Our methods and results are elementary yet useful. They highlight the existence of a common thread, our "own effect" assumption, in formally diverse areas of economics. We discuss several applications; among them, we establish the existence of efficient equilibria in English auctions with interdependent valuations, and a version of the Stolper-Samuelson Theorem for an nxn trade model

Promoting Entry and Efficiency via Reserve Prices

Reserve prices are used by sellers to modify the allocation induced by standard auctions. The existing literature has shown that, if the number of bidders is fixed, a reserve price can be used to increase expected revenues. This comes at the expense of efficiency when the auctioned good goes unsold. Instead, when the number of bidders is not fixed, a reserve price may discourage entry. The reduction in the number of bidders caused by the reserve price in this situation is detrimental for both revenues and efficiency. This work shows that a different conclusion may emerge when potential entrants arrive sequentially and face the risk of incurring losses conditional on winning the object on sale. In fact, we show that reserve prices may lead to more entry and raise the efficiency. Applications characterized by the presence of an incumbent who is better informed about some common characteristics of the object for sale may yield the type of features that are needed for our different conclusion to hold

Asymmetric English Auctions Revisited

I introduce a property of player's valuations that ensures the existence of an ex post efficient equilibrium in asymmetric English auctions. The use of this property has the advantage of yielding an ex post efficient equilibrium without assuming differentiability of valuations or that signals are drawn from a density. These technical, non economic, assumptions have been ubiquitous in the study of (potentially) asymmetric English auctions. Therefore, my work highlights the economic content of what it takes to obtain efficient ex post equilibria. I generalize prior work by Echenique and Manelli (2006) and by Birulin and Izmalkov (2003). Relative to Krishna (2003), I weaken his single crossing properties, drop his differentiability and densities assumptions, but I assume that one player's valuation is weakly increasing in other players' signals, while he uses a different assumption (neither stronger nor weaker).Efficiency; English Auctions; ex-post equilibrium

Nuclear Weapons and National Prestige

Leaders and historians see prestige as important, but international relations theorists have neglected the concept, in part for lack of a clear definition. It is proposed that a party "holds prestige" when group members generally believe that the party has a certain desirable quality, and this situation gives the party perceived power in the group. The definition gains support from a survey of international affairs writings on the sources of prestige. Prestige is strategically important when a party wants support from others who would rather join the side that more of the others are joining. Some general ways of acquiring prestige are discussed. Compared to achieving social progress, building and testing nuclear weapons is better at bearing prestige because it has distinct borders separating success and failure, because it is salient and because it involves the symbolism of power. In some cases when prestige is a factor, one can better demonstrate one’s ability to perform an accomplishment by refraining from doing it. The analysis yields suggestions for reducing nuclear proliferation.prestige, nuclear weapons, common knowledge, signaling, countersignaling, global games, symbolism

Ascending auctions: some impossibility results and their resolutions with final price discounts

When bidders are not substitutes, we show that there is no standard ascend-ing auction that implements a bidder-optimal competitive equilibrium under truthful bidding. Such an impossibility holds also in environments where the Vickrey payoff vector is a competitive equilibrium payoff and is thus stronger than de Vries, Schummer and Vohra s [On ascending Vickrey auctions for het-erogeneous objects, J. Econ. Theory, 132, 95-118] impossibility result with regards to the Vickrey payoff vector under general valuations. Similarly to Mishra and Parkes [Ascending price Vickrey auctions for general valuations, J. Econ. Theory, 132, 335-366], the impossibility can be circumvented by giving price discounts to the bidders from the final vector of prices. Nevertheless, the similarity is misleading: the solution we propose satisfies a minimality infor-mation revelation property that fails to be satisfied in any ascending auction that implements the Vickrey payoffs for general valuations. We investigate related issues when strictly positive increments have to be used under general continuous valuations.ascending auctions ; combinatorial auctions ; bidder-optimal competitive equilibrium ; non-linear pricing ; Vickrey payoffs ; increments

Asymmetric English Auctions Revisited

I introduce a property of player's valuations that ensures the existence of an ex post efficient equilibrium in asymmetric English auctions. The use of this property has the advantage of yielding an ex post efficient equilibrium without assuming differentiability of valuations or that signals are drawn from a density. These technical, non economic, assumptions have been ubiquitous in the study of (potentially) asymmetric English auctions. Therefore, my work highlights the economic content of what it takes to obtain efficient ex post equilibria. I generalize prior work by Echenique and Manelli (2006) and by Birulin and Izmalkov (2003). Relative to Krishna (2003), I weaken his single crossing properties, drop his differentiability and densities assumptions, but I assume that one player's valuation is weakly increasing in other players' signals, while he uses a different assumption (neither stronger nor weaker)

Second Best Efficiency in Auctions

We characterize the incentive compatible allocation that maximizes the expected social surplus in a single-unit sale when the efficient allocation is not implementable. This allocation may involve no selling when it is efficient to sell. We then show that the English auction always implements the second best allocation when there are only two bidders, but not with more than two. Our model employs a unidimensional type space with independent types and allocative externalities, but captures some features of models with multidimensional types.Efficiency, auctions, mechanism design