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A looming revolution: Implications of self-generation for the risk exposure of retailers. ESRI WP597, September 2018
Managing the risk associated with uncertain load has always been a challenge for retailers in electricity markets. Yet
the load variability has been largely predictable in the past, especially when aggregating a large number of consumers. In
contrast, the increasing penetration of unpredictable, small-scale electricity generation by consumers, i.e. self-generation,
constitutes a new and yet greater volume risk. Using value-at-risk metrics and Monte Carlo simulations based on German
historical loads and prices, the contribution of decentralized solar PV self-generation to retailers’ load and revenue risks is
assessed. This analysis has implications for the consumers’ welfare and the overall efficiency of electricity markets
When Can Limited Randomness Be Used in Repeated Games?
The central result of classical game theory states that every finite normal
form game has a Nash equilibrium, provided that players are allowed to use
randomized (mixed) strategies. However, in practice, humans are known to be bad
at generating random-like sequences, and true random bits may be unavailable.
Even if the players have access to enough random bits for a single instance of
the game their randomness might be insufficient if the game is played many
times.
In this work, we ask whether randomness is necessary for equilibria to exist
in finitely repeated games. We show that for a large class of games containing
arbitrary two-player zero-sum games, approximate Nash equilibria of the
-stage repeated version of the game exist if and only if both players have
random bits. In contrast, we show that there exists a class of
games for which no equilibrium exists in pure strategies, yet the -stage
repeated version of the game has an exact Nash equilibrium in which each player
uses only a constant number of random bits.
When the players are assumed to be computationally bounded, if cryptographic
pseudorandom generators (or, equivalently, one-way functions) exist, then the
players can base their strategies on "random-like" sequences derived from only
a small number of truly random bits. We show that, in contrast, in repeated
two-player zero-sum games, if pseudorandom generators \emph{do not} exist, then
random bits remain necessary for equilibria to exist
Randomness Extraction in AC0 and with Small Locality
Randomness extractors, which extract high quality (almost-uniform) random
bits from biased random sources, are important objects both in theory and in
practice. While there have been significant progress in obtaining near optimal
constructions of randomness extractors in various settings, the computational
complexity of randomness extractors is still much less studied. In particular,
it is not clear whether randomness extractors with good parameters can be
computed in several interesting complexity classes that are much weaker than P.
In this paper we study randomness extractors in the following two models of
computation: (1) constant-depth circuits (AC0), and (2) the local computation
model. Previous work in these models, such as [Vio05a], [GVW15] and [BG13],
only achieve constructions with weak parameters. In this work we give explicit
constructions of randomness extractors with much better parameters. As an
application, we use our AC0 extractors to study pseudorandom generators in AC0,
and show that we can construct both cryptographic pseudorandom generators
(under reasonable computational assumptions) and unconditional pseudorandom
generators for space bounded computation with very good parameters.
Our constructions combine several previous techniques in randomness
extractors, as well as introduce new techniques to reduce or preserve the
complexity of extractors, which may be of independent interest. These include
(1) a general way to reduce the error of strong seeded extractors while
preserving the AC0 property and small locality, and (2) a seeded randomness
condenser with small locality.Comment: 62 page
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