The family of c-bisection auctions: efficiency and running time

In this paper we analyze the performance of a recently proposed sequential auction, called the c-bisection auction, that can be used for a sale of a single indivisible object. We discuss the running time and the e±ciency in the ex-post equilibrium of the auction. We show that by changing the parameter c of the auction we can trade o® e±ciency against running time. Moreover, we show that the auction that gives the desired level of e±ciency in expectation takes the same number of rounds for any number of players.computer science applications;

Inefficiency of equilibria in query auctions with continuous valuations

We show that, when bidders have continuous valuations, any ex post equilibrium in an ex post individually rational query auction can only be ex post efficient when the running timeof the auction is infinite for almost all realizations of valuations of the bidders. We also show that this result applies to the general class of bisection auctions. In contrast we show that, when we allow for inefficient allocations with arbitrarily small probability, there is a query auction (to be more specific, a bisection auction) that attains this level of approximate efficiency in equilibrium, while additionally the running time of the auction in equilibrium is finite for all realizations of valuations.mathematical economics;

Inefficiency of equilibria in query auctions with continuous valuations

We show that, when bidders have continuous valuations, any ex post equilibrium in an ex post individually rational query auction can only be ex post efficient when the running time of the auction is infinite for almost all realizations of valuations of the bidders. In contrast we show that, when we allow for inefficient allocations with arbitrarily small probability, there is a query auction (to be more specific, a bisection auction) that attains this level of approximate efficiency in equilibrium, while additionally the running time of the auction in equilibrium is finite for all realizations of valuations

Inefficiency of equilibria in query auctions with continuous valuations

Query auctions are iterative auctions in which bidders have to select in each round an action from a finite set. We show that, when bidders have continuous valuations, any ex post equilibrium in an ex post individually rational query auction can only be ex post efficient when the running time of the auction is infinite for almost all realizations of valuations of thebidders. Thus, when valuations are drawn from a continuous probability distribution, efficiency can only be bought at the expense of a running time that is infinite with probability one. For two bidders we even show this to be true when we only require efficiency with probability one.mathematical economics;

Computing the communication costs of item allocation

Multiagent systems require techniques for effectively allocating resources or tasks to among agents in a group. Auctions are one method for structuring communication of agents’ private values for the resource or task to a central decision maker. Different auction methods vary in their communication requirements. This paper makes three contributions to the understanding the types of group decision making for which auctions are appropriate methods. First, it shows that entropy is the best measure of communication bandwidth used by an auction in messages bidders send and receive. Second, it presents a method for measuring bandwidth usage; the dialogue trees used for this computation are a new and compact representation of the probability distribution of every possible dialogue between two agents. Third, it presents new guidelines for choosing the best auction, guidelines which differ significantly from recommendations in prior work. The new guidelines are based on detailed analysis of the communication requirements of Sealed-bid, Dutch, Staged, Japanese, and Bisection auctions. In contradistinction to previous work, the guidelines show that the auction that minimizes bandwidth depends on both the number of bidders and the sample space from which bidders’ valuations are drawn.Engineering and Applied Science

The communication complexity of private value single item auctions

In this paper we present a new auction, the bisection auction, that can be used for the sale of a single indivisible object. We discuss the issue concerning the information revelation requirement of this auction and the associated amount of data that needs to be transmitted. We show that in the truthtelling equilibrium the bisection auction is economical in its demand for information on the valuations of the players. It requires the players to transmit less information bits to the auctioneer than the Vickrey and English auctions. In particular, we prove that for integer valuations uniformly distributed on the interval [0,L) the bisection auction of n players requires in expectation transmission of at most 2n + log L information bits by the players. Compared with the corresponding number in the Vickrey auction which is n log L, and in the English auction which is on average at least (1/3) nL, the bisection auction turns out to be the best performer.mathematical economics;