Simultaneous pooled auctions

Suppose a seller wants to sell k similar or identical objects and there are n > k potential buyers. Suppose that each buyer wants only one object. In this case, we suggest the use of a simultaneous auction that would work as follows. Players are asked to submit sealed bids for one object. The individual with the highest bid chooses an object first; the individual with the second-highest bid chooses the next object; and this process continues until the individual with the kth highest bid receives the last object. Each individual pays the equivalent to his or her bid. When objects are identical, we show that the proposed auction generates the same revenue as a first-price sealed-bid sequential auction. When objects are perfectly correlated, there is no known solution for sequential auctions, whereas we can characterize bidding strategies in the proposed auction. Moreover, the proposed auction is optimal (given an appropriately chosen reserve price), and it may be easier and cheaper to run than a sequential auction.

Abstract types and distributions in independent private value auctions

In this note, in an independent private values auction framework, I discuss the relationship between the set of types and the distribution of types. I show that any set of types, finite dimensional or not, can be extended to a larger set of types preserving incentive compatibility constraints, expected revenue and bidder’s expected utilities. Thus for example we may convexify a set of types making our model amenable to the large body of theory in economics and mathematics that relies on convexity assumptions. An interesting application of this extension procedure is to show that although revenue equivalence is not valid in general if the set of types is not convex these mechanism have underlying distinct allocation mechanism in the extension. Thus we recover in these situations the revenue equivalence.

Pure strategy equilibria of multidimensional and non-monotonic auctions

We give necessary and sufficient conditions for the existence of symmetric equilibrium without ties in interdependent values auctions, with multidimensional independent types and no monotonic assumptions. In this case, non-monotonic equilibria might happen. When the necessary and sufficient conditions are not satisfied, there are ties with positive probability. In such case, we are still able to prove the existence of pure strategy equilibrium with an all-pay auction tie-breaking rule. As a direct implication of these results, we obtain a generalization of the Revenue Equivalence Theorem. From the robustness of equilibrium existence for all-pay auctions in multidimensional setting, an interpretation of our results can give a new justification to the use of tournaments in practice.

Teoria de Leilões com Aplicação ao Mercado de Petróleo Brasileiro

O processo de reforma que ocorreu na indústria petrolífera a partir da década de 1990, associada à transferência de serviços de utilidade pública para o setor privado, trouxe mudanças importantes para a economia. Neste contexto, a intensificação do uso de leilões, para a privatização das empresas públicas e para a concessão de direitos de exploração de seus serviços assumiu um papel de grande relevância na economia brasileira. A discussão sobre o desenho de leilão adotado para a venda de blocos petrolíferos é fundamental, pois representa o ponto inicial desta nova política. Sendo assim, este trabalho aborda os principais aspectos que fundamentam a escolha de um formato apropriado de leilão, detalhando as peculiaridades da indústria petrolífera e, finalmente, discutindo os resultados obtidos.

Uma análise dos leilões de partilha de produção do pré-sal através de simulação computacional

O presente trabalho consiste na aplicação da simulação computacional como método de aprofundamento do estudo de mecanismos de leilões aplicados na alocação do direito de exploração das reservas de petróleo da camada do pré-sal. A camada do pré-sal está localizada na costa brasileira e apresenta um grande potencial em termos de reserva de óleo e gás. A função lance aplicada para os participantes criados computacionalmente foi estimada com base em dados experimentais e segue uma função exponencial. A simulação possibilita reproduzir o modelo de leilão considerando todas as características e parâmetros dos experimentos sem incorrer no custo da realização de novas sessões de leilão com participantes reais. Os leilões estudados foram o leilão de valores privados de 1° preço e o leilão de valores privados de 2° preço. Através dos resultados obtidos identificou-se que o leilão de valores privados de 1° preço é menos arriscado que o leilão de valores privados de 2° preço; no leilão com simetria, o Princípio de Equivalência de Receita é válido; a eficiência observada é menor em leilões assimétricos; o leilão de 2° preço comparado com o de 1° preço apresenta um tradeoff entre a eficiência e a receita do governo; e que considerando o aprendizado dos participantes, não se observam alterações significativas nas estatísticas analisadas à medida que os participantes se tornam mais experientes.

Equivalence of piecewise-linear approximation and Lagrangian relaxation for network revenue management

The network revenue management (RM) problem arises in airline, hotel, media,and other industries where the sale products use multiple resources. It can be formulatedas a stochastic dynamic program but the dynamic program is computationallyintractable because of an exponentially large state space, and a number of heuristicshave been proposed to approximate it. Notable amongst these -both for their revenueperformance, as well as their theoretically sound basis- are approximate dynamic programmingmethods that approximate the value function by basis functions (both affinefunctions as well as piecewise-linear functions have been proposed for network RM)and decomposition methods that relax the constraints of the dynamic program to solvesimpler dynamic programs (such as the Lagrangian relaxation methods). In this paperwe show that these two seemingly distinct approaches coincide for the network RMdynamic program, i.e., the piecewise-linear approximation method and the Lagrangianrelaxation method are one and the same.

On the tractability of the piecewise-linear approximation for general discrete-choice network revenue management

The choice network revenue management (RM) model incorporates customer purchase behavioras customers purchasing products with certain probabilities that are a function of the offeredassortment of products, and is the appropriate model for airline and hotel network revenuemanagement, dynamic sales of bundles, and dynamic assortment optimization. The underlyingstochastic dynamic program is intractable and even its certainty-equivalence approximation, inthe form of a linear program called Choice Deterministic Linear Program (CDLP) is difficultto solve in most cases. The separation problem for CDLP is NP-complete for MNL with justtwo segments when their consideration sets overlap; the affine approximation of the dynamicprogram is NP-complete for even a single-segment MNL. This is in contrast to the independentclass(perfect-segmentation) case where even the piecewise-linear approximation has been shownto be tractable. In this paper we investigate the piecewise-linear approximation for network RMunder a general discrete-choice model of demand. We show that the gap between the CDLP andthe piecewise-linear bounds is within a factor of at most 2. We then show that the piecewiselinearapproximation is polynomially-time solvable for a fixed consideration set size, bringing itinto the realm of tractability for small consideration sets; small consideration sets are a reasonablemodeling tradeoff in many practical applications. Our solution relies on showing that forany discrete-choice model the separation problem for the linear program of the piecewise-linearapproximation can be solved exactly by a Lagrangian relaxation. We give modeling extensionsand show by numerical experiments the improvements from using piecewise-linear approximationfunctions.

Equivalence between Redfield- and master-equation approaches for a time-dependent quantum system and coherence control

We present a derivation of the Redfield formalism for treating the dissipative dynamics of a time-dependent quantum system coupled to a classical environment. We compare such a formalism with the master equation approach where the environments are treated quantum mechanically. Focusing on a time-dependent spin-1/2 system we demonstrate the equivalence between both approaches by showing that they lead to the same Bloch equations and, as a consequence, to the same characteristic times T(1) and T(2) (associated with the longitudinal and transverse relaxations, respectively). These characteristic times are shown to be related to the operator-sum representation and the equivalent phenomenological-operator approach. Finally, we present a protocol to circumvent the decoherence processes due to the loss of energy (and thus, associated with T(1)). To this end, we simply associate the time dependence of the quantum system to an easily achieved modulated frequency. A possible implementation of the protocol is also proposed in the context of nuclear magnetic resonance.

Equivalence between hot tensile and creep testing data for Kanthal A1 alloy

Hot tensile and creep tests were carried out on Kanthal A1 alloy in the temperature range from 600 to 800 degrees C. Each of these sets of data were analyzed separately according to their own methodologies, but an attempt was made to find a correlation between them. A new criterion proposed for converting hot tensile data to creep data, makes possible the analysis of the two kinds of results according to usual creep relations like: Norton, Monkman-Grant, Larson-Miller and others. The remarkable compatibility verified between both sets of data by this procedure strongly suggests that hot tensile data can be converted to creep data and vice-versa for Kanthal A1 alloy, as verified previously for other metallic materials.