3,729 research outputs found
Quantized VCG Mechanisms for Polymatroid Environments
Many network resource allocation problems can be viewed as allocating a
divisible resource, where the allocations are constrained to lie in a
polymatroid. We consider market-based mechanisms for such problems. Though the
Vickrey-Clarke-Groves (VCG) mechanism can provide the efficient allocation with
strong incentive properties (namely dominant strategy incentive compatibility),
its well-known high communication requirements can prevent it from being used.
There have been a number of approaches for reducing the communication costs of
VCG by weakening its incentive properties. Here, instead we take a different
approach of reducing communication costs via quantization while maintaining
VCG's dominant strategy incentive properties. The cost for this approach is a
loss in efficiency which we characterize. We first consider quantizing the
resource allocations so that agents need only submit a finite number of bids
instead of full utility function. We subsequently consider quantizing the
agent's bids
Almost Budget Balanced Mechanisms with Scalar Bids For Allocation of a Divisible Good
This paper is about allocation of an infinitely divisible good to several
rational and strategic agents. The allocation is done by a social planner who
has limited information because the agents' valuation functions are taken to be
private information known only to the respective agents. We allow only a scalar
signal, called a bid, from each agent to the social planner. Yang and Hajek
[Jour. on Selected Areas in Comm., 2007] as well as Johari and Tsitsiklis
[Jour. of Oper. Res., 2009] proposed a scalar strategy Vickrey-Clarke-Groves
(SSVCG) mechanism with efficient Nash equilibria. We consider a setting where
the social planner desires minimal budget surplus. Example situations include
fair sharing of Internet resources and auctioning of certain public goods where
revenue maximization is not a consideration. Under the SSVCG framework, we
propose a mechanism that is efficient and comes close to budget balance by
returning much of the payments back to the agents in the form of rebates. We
identify a design criterion for {\em almost budget balance}, impose feasibility
and voluntary participation constraints, simplify the constraints, and arrive
at a convex optimization problem to identify the parameters of the rebate
functions. The convex optimization problem has a linear objective function and
a continuum of linear constraints. We propose a solution method that involves a
finite number of constraints, and identify the number of samples sufficient for
a good approximation.Comment: Accepted for publication in the European Journal of Operational
Research (EJOR
Competition and Cooperation in Divisible Good Auctions: An Experimental Examination
An experimental approach is used to examine the performance of three different multi-unit auction designs: discriminatory, uniform-price with fixed supply, and uniform-price with endogenous supply. We find that the strategies of the individual bidders and the aggregate demand curves are inconsistent with theoretically identified equilibrium strategies. The discriminatory auction is found to be more susceptible to collusion than are the uniform-price auctions, and so contrary to theoretical predictions and previous experimental results, the discriminatory auction provides the lowest average revenue. Consistent with theoretical predictions, bidder demands are more elastic with reducible supply or discriminatory pricing than in the uniform-price auction with fixed supply. Despite a lack of a priori differences across bidders, the discriminatory auction results in significantly more symmetric allocations.Divisible good, Auctions, Experimental economics
Efficiency of scalar-parameterized mechanisms
We consider the problem of allocating a fixed amount of an infinitely divisible resource among multiple
competing, fully rational users. We study the efficiency guarantees that are possible when we restrict to
mechanisms that satisfy certain scalability constraints motivated by large scale communication networks;
in particular, we restrict attention to mechanisms where users are restricted to one-dimensional strategy
spaces. We first study the efficiency guarantees possible when the mechanism is not allowed to price differen-
tiate. We study the worst-case efficiency loss (ratio of the utility associated with a Nash equilibrium to the
maximum possible utility), and show that the proportional allocation mechanism of Kelly (1997) minimizes
the efficiency loss when users are price anticipating. We then turn our attention to mechanisms where price
differentiation is permitted; using an adaptation of the Vickrey-Clarke-Groves class of mechanisms, we con-
struct a class of mechanisms with one-dimensional strategy spaces where Nash equilibria are fully efficient.
These mechanisms are shown to be fully efficient even in general convex environments, under reasonable
assumptions. Our results highlight a fundamental insight in mechanism design: when the pricing flexibility
available to the mechanism designer is limited, restricting the strategic flexibility of bidders may actually
improve the efficiency guarantee.National Science FoundationArmy Research OfficeDARPA - Next Generation Internet InitiativeNational Science Foundation Graduate Research Fellowshi
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