Antitrust legislation of many countries admits horizontal agreements between market participants as illegal per se not only in case of price fixing, market sharing, but also in case of bid-riggings. This paper has presented a review and an academic assessment of market participants behavior at auctions by bidding. Such behavior creates incentives to collude and to sustain a collusion but with some features which are suitable for auctions. These suitable features for auctions are in detail described in the paper of R. Preston Mcafee and John Mcmillan “Bidding Ring”. In order to collude, the bidders must resolve their asymmetric-information problem: they must have some way of selecting a winner and a winning bid. So the main characteristic of auction by bidding is asymmetric information. The knowledge is non-uniform distributed between the parties to the contract: the seller does not know a demand of auction by bidding participants. Otherwise the seller would know what price it is worth to set.
In our paper we used these features and the conditions of collusion’ sustainability to give academic assessment of market participants behavior at the auctions by bidding. We showed that the cartel sustainability in the conditions of e-auction corresponds to balance of profit and expected fine imposed in the case of cartel detection but not corresponds to discount factor as an indicator of “cartel sustainability”. The cases of Russian antitrust practice which are devoted to the auction by bidding in the pharmaceutical market gave us an opportunity to show how the firms use the price strategies to keep the prices at the rate which give them to earn monopoly profits.
There is by now a large literature arguing that auctions with a variety of after-market interactions may not yield an efficient allocation of the objects for sale, especially when the bidders impose strong negative externalities upon each other. In this note, we argue that these inefficiencies can be avoided by asking bidders prior to the auction to submit any publicly observable payment they would like to make. These payments, so-called flexible entry fees, do not affect the allocation decision of the auctioneer. We show that auctions with flexible entry fees have a fully revealing equilibrium where bidders signal their type before the auction itself takes place.
We consider certain spaces of functions on the circle, which naturally appear in harmonic analysis, and superposition operators on these spaces. We study the following question: which functions have the property that each their superposition with a homeomorphism of the circle belongs to a given space? We also study the multidimensional case.
We consider the spaces of functions on the m-dimensional torus, whose Fourier transform is p -summable. We obtain estimates for the norms of the exponential functions deformed by a C1 -smooth phase. The results generalize to the multidimensional case the one-dimensional results obtained by the author earlier in “Quantitative estimates in the Beurling—Helson theorem”, Sbornik: Mathematics, 201:12 (2010), 1811 – 1836.
We consider the spaces of function on the circle whose Fourier transform is p-summable. We obtain estimates for the norms of exponential functions deformed by a C1 -smooth phase.