Affiliation, equilibrium existence and the revenue ranking of auctions

We consider private value auctions where bidders’ types are dependent, a case usually treated by assuming affiliation. We show that affiliation is a restrictive assumption in three senses: topological, measure-theoretic and statistical (affiliation is a very restrictive characterization of positive dependence). We also show that affiliation’s main implications do not generalize for alternative definitions of positive dependence. From this, we propose new approaches to the problems of pure strategy equilibrium existence in first-price auctions (PSEE) and the characterization of the revenue ranking of auctions. For equilibrium existence, we slightly restrict the set of distributions considered, without loss of economic generality, and offer a complete characterization of PSEE. For revenue ranking, we obtain a characterization of the expected revenue differences between second and first price auctions with general dependence of types

Corrigendum to "existence of equilibrium in single and double private value actions"

This is a corrigendum to Theorem 15 of Jackson and Swinkels (2005) [Existence of Equilibrium in Single and Double Private Value Auctions, Econometrica, 73, 93-140], which proves the existence of equilibrium with positive probability of trade for private value auctions

Science with the World Space Observatory - Ultraviolet

The World Space Observatory-Ultraviolet (WSO-UV) will provide access to the UV range during the next decade. The instrumentation on board will allow to carry out high resolution imaging, high sensitivity imaging, high resolution (R~55000) spectroscopy and low resolution (R~2500) long slit spectroscopy. In this contribution, we briefly outline some of the key science issues that WSO-UV will address during its lifetime. Among them, of special interest are: the study of galaxy formation and the intergalactic medium; the astronomical engines; the Milky Way formation and evol ution, and the formation of the Solar System and the atmospheres of extrasolar p lanets.Comment: Just one text file (aigomezdecastro.tex). To be published in the proceeding of the conference: "New Quest in Stellar Astrophysics II: UV properties of evolved stellar populations" held in Puerto Vallarta - Mexico, in april 200

Equilibria Existence in Regular Discontinuous Games

Many conditions have been introduced to weaken the continuity re- quirements for equilibrium existence in games. We introduce a new con- dition, called regularity, that is simple and easy to verify. It is implied both by Reny's better-reply security and Simon and Zame's endogenous sharing rule method. Regularity implies that the limits of epsilon-equilibria are equilibria. Since this condition is weak, it is yet not enough to ensure pure strategy equilibrium existence, but we are able to identify extra conditions that, together with regularity, are sufficient for equilibrium existence. One is the marginal continuity property introduced by Prokopovych (2008), while the second is the well behavior of a sequence of approximating con- tinuous functions. In this way, we provide new equilibrium existence re- sults for discontinuous games under conditions that are simpler and easier to check than most of the available alternatives.

CORRIGENDUM TO "EXISTENCE OF EQUILIBRIUM IN SINGLE AND DOUBLE PRIVATE VALUE ACTIONS"

This is a corrigendum to Theorem 15 of Jackson and Swinkels (2005) [Existence of Equilibrium in Single and Double Private Value Auctions, Econometrica, 73, 93-140], which proves the existence of equilibrium with positive probability of trade for private value auctions.

Pure strategy equilibria of single and double auctions with interdependent values

We prove the existence of monotonic pure strategy equilibrium for many types of asymmetric auctions with n bidders and unitary demands, interdependent values and independent types. The assumptions require monotonicity only in the own bidder's type. The payments can be a function of all bids. Thus, we provide a new equilibrium existence result for asymmetrical double auctions and a small number of bidders. The generality of our setting requires the use of special tie-breaking rules. We present a reasonable counterexample for interdependent values auctions that shows that sometimes all equilibria are trivial, that is, they have zero probability of trade. Nevertheless, we give sufficient conditions for non-trivial equilibrium existence

Affiliation, equilibrium existence and the revenue ranking of auctions

We consider private value auctions where bidders’ types are dependent, a case usually treated by assuming affiliation. We show that affiliation is a restrictive assumption in three senses: topological, measure-theoretic and statistical (affiliation is a very restrictive characterization of positive dependence). We also show that affiliation’s main implications do not generalize for alternative definitions of positive dependence. From this, we propose new approaches to the problems of pure strategy equilibrium existence in first-price auctions (PSEE) and the characterization of the revenue ranking of auctions. For equilibrium existence, we slightly restrict the set of distributions considered, without loss of economic generality, and offer a complete characterization of PSEE. For revenue ranking, we obtain a characterization of the expected revenue differences between second and first price auctions with general dependence of types.

Cyclic and ruled Lagrangian surfaces in complex Euclidean space

We study those Lagrangian surfaces in complex Euclidean space which are foliated by circles or by straight lines. The former, which we call cyclic, come in three types, each one being described by means of, respectively, a planar curve, a Legendrian curve of the 3-sphere or a Legendrian curve of the anti de Sitter 3-space. We also describe ruled Lagrangian surfaces. Finally we characterize those cyclic and ruled Lagrangian surfaces which are solutions to the self-similar equation of the Mean Curvature Flow. Finally, we give a partial result in the case of Hamiltonian stationary cyclic surfaces

Beyond the soft photon approximation in radiative production and decay of charged vector mesons

We study the effects of model-dependent contributions and the electric quadrupole moment of vector mesons in the decays $V^- \to P^-P^0\gamma$ and $\tau^- \to \nu V^-\gamma$. Their interference with the amplitude originating from the radiation due to electric charges vanishes for photons emitted collinearly to the charged particle in the final state. This brings further support to our claim in previous works, that measurements of the photon energy spectrum for nearly collinear photons in those decays are suitable for a first measurement of the magnetic dipole moment of charged vector mesons.Comment: 13 pages, 2 eps figures, Latex. Accepted for publication in Journal of Physics G: Nuclear and Particle Physics(2001