886 research outputs found
Auctions with Severely Bounded Communication
We study auctions with severe bounds on the communication allowed: each
bidder may only transmit t bits of information to the auctioneer. We consider
both welfare- and profit-maximizing auctions under this communication
restriction. For both measures, we determine the optimal auction and show that
the loss incurred relative to unconstrained auctions is mild. We prove
non-surprising properties of these kinds of auctions, e.g., that in optimal
mechanisms bidders simply report the interval in which their valuation lies in,
as well as some surprising properties, e.g., that asymmetric auctions are
better than symmetric ones and that multi-round auctions reduce the
communication complexity only by a linear factor
Fraction auctions: the tradeoff between effciency and running time
This paper studies the sales of a single indivisible object where bidders have continuous valuations. In Grigorieva et al. [13] it was shown that, in this setting, query auctions necessarily allocate inefficiently in equilibrium. In this paper we propose a new sequential auction, called the c-fraction auction. We show c-fraction auctions guarantee approximate efficiency at any desired level of accuracy, independent of the number of bidders. We discuss the running time and the efficiency in the ex-post equilibrium of the auction. We show that by changing the parameter c of the auction we can trade off efficiency against running time.operations research and management science;
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
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;
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;
Fraction auctions : the tradeoff between efficiency and running time
This paper studies the sales of a single indivisible object where bidders have continuous valuations. In grigorieva et al. [14] it was shown that, in this setting, query auctions necessarily allocate inefficiently in equilibrium. In this paper we propose a new sequential auction, called the c-fraction auction. We show the existence of an ex-post equilibrium, called bluff equilibrium, in which bidders behave truthfully except for particular constellations of observed bids at which it is optimal to pretend a slightly higher valuation. We show c-fraction auctions guarantee approximate efficiency at any desired level of accuracy, independent of the number of bidders, when bidders choose to play the bluff equilibrium. We discuss the running time and the efficiency in the bluff equilibrium. We show that by changing the parameter c of the auction we can trade off efficiency against running time
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
Computational Efficiency Requires Simple Taxation
We characterize the communication complexity of truthful mechanisms. Our
departure point is the well known taxation principle. The taxation principle
asserts that every truthful mechanism can be interpreted as follows: every
player is presented with a menu that consists of a price for each bundle (the
prices depend only on the valuations of the other players). Each player is
allocated a bundle that maximizes his profit according to this menu. We define
the taxation complexity of a truthful mechanism to be the logarithm of the
maximum number of menus that may be presented to a player.
Our main finding is that in general the taxation complexity essentially
equals the communication complexity. The proof consists of two main steps.
First, we prove that for rich enough domains the taxation complexity is at most
the communication complexity. We then show that the taxation complexity is much
smaller than the communication complexity only in "pathological" cases and
provide a formal description of these extreme cases.
Next, we study mechanisms that access the valuations via value queries only.
In this setting we establish that the menu complexity -- a notion that was
already studied in several different contexts -- characterizes the number of
value queries that the mechanism makes in exactly the same way that the
taxation complexity characterizes the communication complexity.
Our approach yields several applications, including strengthening the
solution concept with low communication overhead, fast computation of prices,
and hardness of approximation by computationally efficient truthful mechanisms
On The Fastest Vickrey Algorithm
We investigate the algorithmic performance of Vickrey-Clarke-Groves mechanisms in the single item case. We provide a formal definition of a Vickrey algorithm for this framework, and give a number of examples of Vickrey algorithms. We consider three performance criteria, one corresponding to a Pareto criterion, one corresponding to worst case analysis, and a third criterion related to first-order stochastic dominance. We show that Pareto optimal Vickrey algorithms do not exist and that worst case analysis is of no use in discriminating between Vickrey algorithms. For the case of two bidders, we show the bisection auction to be optimal according to the third criterion. The bisection auction istherefore optimal in a very strong sense.operations research and management science;
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