First-Price auction symmetric equlibria with a general distribution

In this paper I obtain the mixed strategy symmetric equilibria of the first-price auction for any distribution. The equilibrium is unique. The solution turns out to be a combination of absolutely continuous distributions case and the discrete distributions case.

First-price auction symmetric equilibria with a general distribution

In this paper I obtain the mixed strategy symmetric equilibria of the first-price auction for any distribution. The equilibrium is unique. The solution turns out to be a combination of absolutely continuous distributions case and the discrete distributions case.

An auction theoretical approach to fiscal wars

I examine a situation where a firm has to choose to locate a new factory in one of several jurisdictions and it depends on the private information held by each jurisdiction. Jurisdiction compete for the location of the new factory. This competition may take the form of expenditures already incurred on infraestructure, commitments to spend on infraestructure, tax incentives or even cash payments. The model combines two elements that are usually considered separately; competition is desirable because we want the factory to be located in the jurisdiction that values it the most, but competition in itself is wasteful. I show that expected total amount paid to the firm under a large family of arrangements. Moreover, I show that the ex-ante optimal mechanism that guarantees that the firm chooses the jurisdiction with the highest value for the factory, minimizes the total expected payment to the firm, and balances the budget in an ex-ante sense - can be implemented by running a standard auction and subsidizing participation.

Why do bidders drop out from a sequential auction

In actual sequential auctions, 1) bidders typically incur a cost in continuing from one sale to the next, and 2) bidders decide whether or not to continue. To investigate the question "why do bidders drop out," we define a sequential auction model with continuation costs and an endogenously determined number of bidders at each sale, and we characterize the equilibria in this model. Simple examples illustrate the effect of several possible changes to this model.

Optimal auction with a general distribution: virtual valuation without densities

We characterize the optimal auction in an independent private values framework for a completely general distribution of valuations. We do this introducing a new concept: the generalized virtual valuation. To show the wider applicability of this concept we present two examples showing how to extend the classical models of Mussa and Rosen and Baron and Myerson for arbitrary distributions

What really matters in auction design

The most important issues in auction design are the traditional concerns of competition policy preventing collusive, predatory, and entry-deterring behaviour. Ascending and uniform-price auctions are particularly vulnerable to these problems, and the Anglo-Dutch auction a hybrid of the sealed-bid and ascending auctions may often perform better. Effective anti-trust policy is also critical. However, everything depends on the details of the context; the circum- stances of the recent U.K. mobile-phone license auction made an ascending format ideal, but this author (and others) correctly predicted the same for- mat would fail in the Netherlands and elsewhere. Auction design is not one size Þts all . We also discuss the 3G spectrum auctions in Germany, Italy, Austria and Switzerland, and football TV-rights, TV franchise and other radiospectrum auctions, electricity markets, and takeover battles.

Auctions with options for re-auction

We examine the role of seller bidding and reserve prices in an infinitely repeated independent-private-value (IPV) ascending-price auction. The seller has a single object that she values at zero. At the end of any auction round, she may either sell to the highest bidder or pass-in the object and hold a new auction next period. New bidders are drawn randomly in each round. The ability to re-auction motivates a notion of reserve price as the option value of retaining the object for re-auctioning. Even in the absence of a mechanism with which to commit to a reserve price, the optimal “secret” reserve is shown to exceed zero. However, despite the infinite repetition, there may be significant value to the seller from a binding reserve price commitment: the optimal binding reserve is higher than the optimal “secret” reserve, and may be substantially so, even with very patient players. Furthermore, reserve price commitments may even be socially preferable at high discount factors. We also show that the optimal “phantom” bidding strategy for the seller is revenue-equivalent to a commitment to an optimal public reserve price.

Auction econometrics by least squares

This paper proposes a method to structurally estimate an auction model using a variation of OLS, under commonly held assumptions in both auction theory and econometrics. In spite of its computational simplicity, the method applies to a wide variety of environments, including interdependent values in general, and certain forms of endogenous participation and bidder asymmetry. Furthermore, it can be used for hypotheses testing about the shape of the valuation distribution, valuation interdependence, or existence of bidder asymmetry.

Mid-auction information acquisition

This paper studies a model of a sequential auction where bidders are allowed to acquire further information about their valuations of the object in the middle of the auction. It is shown that, in any equilibrium where the distribution of the final price is atornless, a bidder's best response has a simple characterization. In particular, the optimal information acquisition point is the same, regardless of the other bidders' actions. This makes it natural to focus on symmetric, undominated equilibria, as in the Vickrey auction. An existence theorem for such a class of equilibria is presented. The paper also presents some results and numerical simulations that compare this sequential auction with the one-shot auction. 8equential auctions typically yield more expected revenue for the seller than their one-shot counterparts. 80 the possibility of mid-auction information acquisition can provide an explanation for why sequential procedures are more often adopted.

Leilões 3G europeus e brasileiros: uma sugestão a fertilização

Atualmente, o leilão de espectro tem sido evento de considerável relevância para o mercado de telecomunicações. As cifras alcançadas nos leilões, a oportunidade que eles representam para as empresas interessadas em explorar o mercado de telecomunicações, e o interesse do governo em alocar de forma eficiente este recurso, trouxeram notoriedade e magnitude para este mecanismo de seleção. Com o advento de novas tecnologias de comunicação móvel, detentoras de características inovadoras que permitem preencher cada vez mais a cesta de necessidades do consumidor, e a partir da alocação destas tecnologias a distintas faixas de espectro, tornou-se necessário, a determinação do mecanismo de escolha mais adequado daquele que será o gestor do recurso que permitirá a oferta desses serviços ao mercado: o espectro de freqüência. Com o intuito de se avaliar esse cenário, e os distintos papéis de seus participantes, busca-se nesse trabalho, através da análise do mais recente conjunto de leilões realizados para alocação deste recurso, o leilão das licenças 3G na Europa, compreender os pormenores envolvidos desde a elaboração até o desfecho deste processo. Objetiva-se, por fim, enriquecer o debate sobre esse tema ao discutir-se o cenário brasileiro. O trabalho ao analisar os leilões europeus nos permite identificar que as regras do leilão, como comentado por diversos autores, não são diretamente transplantáveis entre diferentes ambientes. Afinal dentro do ambiente homogêneo caracterizado pelo continente europeu, apesar da semelhança entre os diversos modelos de leilão utilizados, o sucesso obtido em países como Reino Unido e Alemanha, não foi repassado aos demais, ao compararmos o preço pago per capta. Entretanto, o espectro tem seu valor altamente conectado à disponibilidade tecnológica de sua utilização, logo, espectro sem tecnologia adequada para seu uso é observado como de valor privado aproximadamente zero pelos participantes. Esse fenômeno foi caracterizado pelo baixo valor atribuído ao espectro não pareado. Apesar de valor ser relativamente nulo, não é zero, pois a aquisição do direito de uso do espectro pode representar um "hedge" para ser utilizado, senão hoje, quando a tecnologia estiver disponível. Porém sendo o espectro recurso escasso, a alocação deste para tecnologia ainda indisponível pode ser considerado ineficiente. Observa-se, também, que o "incumbent" tende a valorizar mais uma licença, porém não se conseguiu determinar se isso ocorre devido a maior quantidade de informação que este detém sobre o mercado, ou devido à tentativa de manter o "status quo" do oligopólio atual. Baseado no comentado anteriormente e nos resultados dos leilões torna-se evidente que caso o entrante não seja protegido, como o "incumbent" valoriza mais a licença este sempre pagará mais por esta. E caso, o entrante tenha esta certeza, este não virá participar do leilão, o que na maior parte dos casos inviabilizaria o leilão pois haveriam tantas licenças quanto participantes. Ao analisar-se o caso brasileiro identifica-se a presença de um jogo nacional e um subjogo regional, onde os participantes podem ser simultaneamente "incumbents" para uma região, porém entrantes em outra.

Optimal auctions with multidimensional types and the desirability of exclusion

Within the context of a single-unit, independent private values auction model, we show that if bidder types are multidimensional, then under the optimal auction exclusion of some bidder types will occur. A second contribution of the paper is methodological in nature. In particular, we identify conditions under which an auction model with multidimensional types can be reduced to a model with one dimensional types without loss of generality. Reduction results of this type have achieved the status of folklore in the mechanism design literature. Here, we provide a proof of the reduction result for auctions.

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.