Buy-or-Sell Auctions

Gustavo Passareli Giroud Joaquim.


Orientador: Leonardo Rezende.

Banca: Humberto Moreira. Leonardo Rezende. Vinicius Nascimento Carrasco.

n this paper we explore a situation where an auctioneer can conduct an auction and not inform the participants if this auction is going to be forward or reverse (or both). The bidders have affiliated private signals and place a single bid. If a bidder wins the forward (reverse) auction, he pays his bid minus (plus) a spread defined by the auctioneer. This distinguished design creates a "double sided Winner's course" phenomenon that reduces the expected profit of bidders. Considering that some agents may not participate in the auction due to this phenomenon, we fully characterize the continuum of pure strategy Bayes-Nash symmetric equilibra. The cardinality of equilibria and characteristics of the optimal bidding function vary with changes in the spread defined by the auctioneer. If the spread is greater than a threshold, then full participation is guaranteed and the equilibrium is unique. If the spread is zero, however, then there is no equilibrium where all agents have non-negative expected profits. Moreover, we characterize the effect of spread changes on payments, but the effect of revealing the type of auction being conducted (forward or reverse) is not always well defined and also depends on the value of the spread. Finally, we propose the problem that an auctioneer should solve (choosing the spread) if trying to minimize the dispersion of bids or, alternatively, maximize the expected profit.

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