23 research outputs found
SLA-mechanisms for electricity trading under volatile supply and varying criticality of demand (Extended Abstract)
The increasing adoption of renewable power generation makes volatile quantities of electricity available, the delivery of which cannot be guaranteed, if sold. However, if not sold, the electricity might need to be curtailed, thus foregoing potential profits. In this paper we adapt service level agreements (SLAs) for the future smart electricity grid, where generation will primarily depend on volatile and istributed renewable power sources, and where buyers' ability to cope with uncertainty may vary significantly. We propose a contracting framework through SLAs to allocate uncertain power generation to buyers of varying preferences. These SLAs comprise quantity, reliability and price. We define a characterization of the value degradation of tolerant and critical buyers with regards to the uncertainty of electricity delivery (generalizing the Value of Lost Load, VoLL). We consider two mechanisms (sequential second-price auction and VCG) that allocate SLAs based on buyer bids. We further study the incentive compatibility of the proposed mechanisms, and show that both mechanisms ensure that no buyer has an incentive to misreport its valuation. We experimentally compare their performance and demonstrate that VCG dominates alternative allocations, while vastly improves the efficiency of the proposed system when compared to a baseline allocation considering only the VoLL. This article lays the ground work for distributed energy trading under uncertainty, thereby contributing an essential component to the future smart grid
Welfare guarantees for proportional allocations
According to the proportional allocation mechanism from the network
optimization literature, users compete for a divisible resource -- such as
bandwidth -- by submitting bids. The mechanism allocates to each user a
fraction of the resource that is proportional to her bid and collects an amount
equal to her bid as payment. Since users act as utility-maximizers, this
naturally defines a proportional allocation game. Recently, Syrgkanis and
Tardos (STOC 2013) quantified the inefficiency of equilibria in this game with
respect to the social welfare and presented a lower bound of 26.8% on the price
of anarchy over coarse-correlated and Bayes-Nash equilibria in the full and
incomplete information settings, respectively. In this paper, we improve this
bound to 50% over both equilibrium concepts. Our analysis is simpler and,
furthermore, we argue that it cannot be improved by arguments that do not take
the equilibrium structure into account. We also extend it to settings with
budget constraints where we show the first constant bound (between 36% and 50%)
on the price of anarchy of the corresponding game with respect to an effective
welfare benchmark that takes budgets into account.Comment: 15 page
On the Efficiency of the Walrasian Mechanism
Central results in economics guarantee the existence of efficient equilibria
for various classes of markets. An underlying assumption in early work is that
agents are price-takers, i.e., agents honestly report their true demand in
response to prices. A line of research in economics, initiated by Hurwicz
(1972), is devoted to understanding how such markets perform when agents are
strategic about their demands. This is captured by the \emph{Walrasian
Mechanism} that proceeds by collecting reported demands, finding clearing
prices in the \emph{reported} market via an ascending price t\^{a}tonnement
procedure, and returns the resulting allocation. Similar mechanisms are used,
for example, in the daily opening of the New York Stock Exchange and the call
market for copper and gold in London.
In practice, it is commonly observed that agents in such markets reduce their
demand leading to behaviors resembling bargaining and to inefficient outcomes.
We ask how inefficient the equilibria can be. Our main result is that the
welfare of every pure Nash equilibrium of the Walrasian mechanism is at least
one quarter of the optimal welfare, when players have gross substitute
valuations and do not overbid. Previous analysis of the Walrasian mechanism
have resorted to large market assumptions to show convergence to efficiency in
the limit. Our result shows that approximate efficiency is guaranteed
regardless of the size of the market
Draft Auctions
We introduce draft auctions, which is a sequential auction format where at
each iteration players bid for the right to buy items at a fixed price. We show
that draft auctions offer an exponential improvement in social welfare at
equilibrium over sequential item auctions where predetermined items are
auctioned at each time step. Specifically, we show that for any subadditive
valuation the social welfare at equilibrium is an -approximation
to the optimal social welfare, where is the number of items. We also
provide tighter approximation results for several subclasses. Our welfare
guarantees hold for Bayes-Nash equilibria and for no-regret learning outcomes,
via the smooth-mechanism framework. Of independent interest, our techniques
show that in a combinatorial auction setting, efficiency guarantees of a
mechanism via smoothness for a very restricted class of cardinality valuations,
extend with a small degradation, to subadditive valuations, the largest
complement-free class of valuations. Variants of draft auctions have been used
in practice and have been experimentally shown to outperform other auctions.
Our results provide a theoretical justification
On the Complexity of Computing an Equilibrium in Combinatorial Auctions
We study combinatorial auctions where each item is sold separately but
simultaneously via a second price auction. We ask whether it is possible to
efficiently compute in this game a pure Nash equilibrium with social welfare
close to the optimal one.
We show that when the valuations of the bidders are submodular, in many
interesting settings (e.g., constant number of bidders, budget additive
bidders) computing an equilibrium with good welfare is essentially as easy as
computing, completely ignoring incentives issues, an allocation with good
welfare. On the other hand, for subadditive valuations, we show that computing
an equilibrium requires exponential communication. Finally, for XOS (a.k.a.
fractionally subadditive) valuations, we show that if there exists an efficient
algorithm that finds an equilibrium, it must use techniques that are very
different from our current ones
On Simultaneous Two-player Combinatorial Auctions
We consider the following communication problem: Alice and Bob each have some
valuation functions and over subsets of items,
and their goal is to partition the items into in a way that
maximizes the welfare, . We study both the allocation
problem, which asks for a welfare-maximizing partition and the decision
problem, which asks whether or not there exists a partition guaranteeing
certain welfare, for binary XOS valuations. For interactive protocols with
communication, a tight 3/4-approximation is known for both
[Fei06,DS06].
For interactive protocols, the allocation problem is provably harder than the
decision problem: any solution to the allocation problem implies a solution to
the decision problem with one additional round and additional bits of
communication via a trivial reduction. Surprisingly, the allocation problem is
provably easier for simultaneous protocols. Specifically, we show:
1) There exists a simultaneous, randomized protocol with polynomial
communication that selects a partition whose expected welfare is at least
of the optimum. This matches the guarantee of the best interactive, randomized
protocol with polynomial communication.
2) For all , any simultaneous, randomized protocol that
decides whether the welfare of the optimal partition is or correctly with probability requires
exponential communication. This provides a separation between the attainable
approximation guarantees via interactive () versus simultaneous () protocols with polynomial communication.
In other words, this trivial reduction from decision to allocation problems
provably requires the extra round of communication