152 research outputs found
Online Ascending Auctions for Gradually Expiring Items
In this paper we consider online auction mechanisms for the allocation of M items that are identical to each other except for the fact that they have different expiration times, and each item must be allocated before it expires. Players arrive at different times, and wish to buy one item before their deadline. The main difficulty is that players act "selfishly" and may mis-report their values, deadlines, or arrival times. We begin by showing that the usual notion of truthfulness (where players follow a single dominant strategy) cannot be used in this case, since any (deterministic) truthful auction cannot obtain better than an M-approximation of the social welfare. Therefore, instead of designing auctions in which players should follow a single strategy, we design two auctions that perform well under a wide class of selfish, "semi-myopic", strategies. For every combination of such strategies, the auction is associated with a different algorithm, and so we have a family of "semi-myopic" algorithms. We show that any algorithm in this family obtains a 3-approximation, and by this conclude that our auctions will perform well under any choice of such semi-myopic behaviors. We next turn to provide a game-theoretic justification for acting in such a semi-myopic way. We suggest a new notion of "Set-Nash" equilibrium, where we cannot pin-point a single best-response strategy, but rather only a set of possible best-response strategies. We show that our auctions have a Set-Nash equilibrium which is all semi-myopic, hence guarantees a 3-approximation. We believe that this notion is of independent interest
Redesigning Bitcoin's fee market
The security of the Bitcoin system is based on having a large amount of
computational power in the hands of honest miners. Such miners are incentivized
to join the system and validate transactions by the payments issued by the
protocol to anyone who creates blocks. As new bitcoins creation rate decreases
(halving every 4 years), the revenue derived from transaction fees start to
have an increasingly important role. We argue that Bitcoin's current fee market
does not extract revenue well when blocks are not congested. This effect has
implications for the scalability debate: revenue from transaction fees may
decrease if block size is increased.
The current mechanism is a "pay your bid" auction in which included
transactions pay the amount they suggested. We propose two alternative auction
mechanisms: The Monopolistic Price Mechanism, and the Random Sampling Optimal
Price Mechanism (due to Goldberg et al.). In the monopolistic price mechanism,
the miner chooses the number of accepted transactions in the block, and all
transactions pay exactly the smallest bid included in the block. The mechanism
thus sets the block size dynamically (up to a bound required for fast block
propagation and other security concerns). We show, using analysis and
simulations, that this mechanism extracts revenue better from users, and that
it is nearly incentive compatible: the profit due to strategic bidding relative
to honest biding decreases as the number of bidders grows. Users can then
simply set their bids truthfully to exactly the amount they are willing to pay
to transact, and do not need to utilize fee estimate mechanisms, do not resort
to bid shading and do not need to adjust transaction fees (via replace-by-fee
mechanisms) if the mempool grows.
We discuss these and other properties of our mechanisms, and explore various
desired properties of fee market mechanisms for crypto-currencies
Ascending auctions and Walrasian equilibrium
We present a family of submodular valuation classes that generalizes gross
substitute. We show that Walrasian equilibrium always exist for one class in
this family, and there is a natural ascending auction which finds it. We prove
some new structural properties on gross-substitute auctions which, in turn,
show that the known ascending auctions for this class (Gul-Stacchetti and
Ausbel) are, in fact, identical. We generalize these two auctions, and provide
a simple proof that they terminate in a Walrasian equilibrium
Approximating Generalized Network Design under (Dis)economies of Scale with Applications to Energy Efficiency
In a generalized network design (GND) problem, a set of resources are
assigned to multiple communication requests. Each request contributes its
weight to the resources it uses and the total load on a resource is then
translated to the cost it incurs via a resource specific cost function. For
example, a request may be to establish a virtual circuit, thus contributing to
the load on each edge in the circuit. Motivated by energy efficiency
applications, recently, there is a growing interest in GND using cost functions
that exhibit (dis)economies of scale ((D)oS), namely, cost functions that
appear subadditive for small loads and superadditive for larger loads.
The current paper advances the existing literature on approximation
algorithms for GND problems with (D)oS cost functions in various aspects: (1)
we present a generic approximation framework that yields approximation results
for a much wider family of requests in both directed and undirected graphs; (2)
our framework allows for unrelated weights, thus providing the first
non-trivial approximation for the problem of scheduling unrelated parallel
machines with (D)oS cost functions; (3) our framework is fully combinatorial
and runs in strongly polynomial time; (4) the family of (D)oS cost functions
considered in the current paper is more general than the one considered in the
existing literature, providing a more accurate abstraction for practical energy
conservation scenarios; and (5) we obtain the first approximation ratio for GND
with (D)oS cost functions that depends only on the parameters of the resources'
technology and does not grow with the number of resources, the number of
requests, or their weights. The design of our framework relies heavily on
Roughgarden's smoothness toolbox (JACM 2015), thus demonstrating the possible
usefulness of this toolbox in the area of approximation algorithms.Comment: 39 pages, 1 figure. An extended abstract of this paper is to appear
in the 50th Annual ACM Symposium on the Theory of Computing (STOC 2018
A Note on the Incompatibility of Strategy-proofness and Pareto-optimality in Quasi-linear Settings with Public Budget Constraints
We show that any deterministic mechanism, for allocating identical items that are complements to budget-constrained bidders, cannot simultaneously satisfy individual-rationality, strategy-proofness, Pareto-efficiency, and no-positive-transfers. This holds even for two bidders, two items, and commonly-known budgets, and generalizes to richer settings
Option Values in Sequential Auctions with Time-Varying Valuations
We investigate second-price sequential auctions of unit-demand bidders with time-variable valuations under complete information. We describe how a bidder figures willingness to pay by calculating option values, and show that when bidders bid their option value, and a condition of consistency is fulfilled, a subgame-perfect equilibrium is the result. With no constraints on valuations, equilibria are not necessarily efficient, but we show that when bidder valuations satisfy a certain constraint, an efficient equilibrium always exists. This result may be extended to a model with arrivals of bidders. We show how the equilibrium allocation, bids, and bidder utilities are calculated in the general case. We prove constructively that a pure subgame-perfect equilibrium always exists, and show how all pure equilibria can be found by the method of option value
Optimal Lower Bounds for Anonymous Scheduling Mechanisms
We consider the problem of designing truthful mechanisms on m unrelated machines, to minimize some optimization goal. Nisan and Ronen [Nisan, N., A. Ronen. 2001. Algorithmic mechanism design. Games Econom. Behav. 35 166–196] consider the specific goal of makespan minimization, and show a lower bound of 2, and an upper bound of m. This large gap inspired many attempts that yielded positive results for several special cases, but very partial success for the general case: the lower bound was slightly increased to 2.61 by Christodoulou et al. [Christodoulou, G., E. Koutsoupias, A. Kovács. 2010. Mechanism design for fractional scheduling on unrelated machines. ACM Trans. Algorithms (TALG) 6(2) 1–18] and Koutsoupias and Vidali [Koutsoupias, E., A. Vidali. 2007. A lower bound of 1+phi for truthful scheduling mechanisms. Proc. 32nd Internat. Sympos. Math. Foundations Comput. Sci. (MFCS)], while the best upper bound remains unchanged. In this paper we show the optimal lower bound on truthful anonymous mechanisms: no such mechanism can guarantee an approximation ratio better than m. Moreover, our proof yields similar optimal bounds for two other optimization goals: the sum of completion times and the lp norm of the schedule.United States-Israel Binational Science FoundationIsrael. Ministry of ScienceGoogle Inter-University Center for Electronic Markets and Auction
VCG Under Sybil (False-name) Attacks -- a Bayesian Analysis
VCG is a classical combinatorial auction that maximizes social welfare.
However, while the standard single-item Vickrey auction is false-name-proof, a
major failure of multi-item VCG is its vulnerability to false-name attacks.
This occurs already in the natural bare minimum model in which there are two
identical items and bidders are single-minded. Previous solutions to this
challenge focused on developing alternative mechanisms that compromise social
welfare. We re-visit the VCG auction vulnerability and consider the bidder
behavior in Bayesian settings. In service of that we introduce a novel notion,
termed the granularity threshold, that characterizes VCG Bayesian resilience to
false-name attacks as a function of the bidder type distribution. Using this
notion we show a large class of cases in which VCG indeed obtains Bayesian
resilience for the two-item single-minded setting.Comment: This is an extended version of an article to appear in AAAI-2020.
Supporting code for generating the article's figures can be found at
https://github.com/yotam-gafni/vcg_bayesian_fn
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