300 research outputs found
Communication Complexity of Cake Cutting
We study classic cake-cutting problems, but in discrete models rather than
using infinite-precision real values, specifically, focusing on their
communication complexity. Using general discrete simulations of classical
infinite-precision protocols (Robertson-Webb and moving-knife), we roughly
partition the various fair-allocation problems into 3 classes: "easy" (constant
number of rounds of logarithmic many bits), "medium" (poly-logarithmic total
communication), and "hard". Our main technical result concerns two of the
"medium" problems (perfect allocation for 2 players and equitable allocation
for any number of players) which we prove are not in the "easy" class. Our main
open problem is to separate the "hard" from the "medium" classes.Comment: Added efficient communication protocol for the monotone crossing
proble
Additive Stable Solutions on Perfect Cones of Cooperative Games
Closed kernel systems of the coalition matrix turn out to correspond to cones of games on which the core correspondence is additive and on which the related canonical barycentric solution is additive, stable and continuous. Different perfect cones corresponding to closed kernel systems are described.cooperative games;core;barycenter of the core;perfect cone of games
Nash Social Welfare Approximation for Strategic Agents
The fair division of resources is an important age-old problem that has led
to a rich body of literature. At the center of this literature lies the
question of whether there exist fair mechanisms despite strategic behavior of
the agents. A fundamental objective function used for measuring fair outcomes
is the Nash social welfare, defined as the geometric mean of the agent
utilities. This objective function is maximized by widely known solution
concepts such as Nash bargaining and the competitive equilibrium with equal
incomes. In this work we focus on the question of (approximately) implementing
the Nash social welfare. The starting point of our analysis is the Fisher
market, a fundamental model of an economy, whose benchmark is precisely the
(weighted) Nash social welfare. We begin by studying two extreme classes of
valuations functions, namely perfect substitutes and perfect complements, and
find that for perfect substitutes, the Fisher market mechanism has a constant
approximation: at most 2 and at least e1e. However, for perfect complements,
the Fisher market does not work well, its bound degrading linearly with the
number of players.
Strikingly, the Trading Post mechanism---an indirect market mechanism also
known as the Shapley-Shubik game---has significantly better performance than
the Fisher market on its own benchmark. Not only does Trading Post achieve an
approximation of 2 for perfect substitutes, but this bound holds for all
concave utilities and becomes arbitrarily close to optimal for Leontief
utilities (perfect complements), where it reaches for every
. Moreover, all the Nash equilibria of the Trading Post mechanism
are pure for all concave utilities and satisfy an important notion of fairness
known as proportionality
Cases in Cooperation and Cutting the Cake
Cooperative game;sharing problem
Statistical Multiplexing and Traffic Shaping Games for Network Slicing
Next generation wireless architectures are expected to enable slices of
shared wireless infrastructure which are customized to specific mobile
operators/services. Given infrastructure costs and the stochastic nature of
mobile services' spatial loads, it is highly desirable to achieve efficient
statistical multiplexing amongst such slices. We study a simple dynamic
resource sharing policy which allocates a 'share' of a pool of (distributed)
resources to each slice-Share Constrained Proportionally Fair (SCPF). We give a
characterization of SCPF's performance gains over static slicing and general
processor sharing. We show that higher gains are obtained when a slice's
spatial load is more 'imbalanced' than, and/or 'orthogonal' to, the aggregate
network load, and that the overall gain across slices is positive. We then
address the associated dimensioning problem. Under SCPF, traditional network
dimensioning translates to a coupled share dimensioning problem, which
characterizes the existence of a feasible share allocation given slices'
expected loads and performance requirements. We provide a solution to robust
share dimensioning for SCPF-based network slicing. Slices may wish to
unilaterally manage their users' performance via admission control which
maximizes their carried loads subject to performance requirements. We show this
can be modeled as a 'traffic shaping' game with an achievable Nash equilibrium.
Under high loads, the equilibrium is explicitly characterized, as are the gains
in the carried load under SCPF vs. static slicing. Detailed simulations of a
wireless infrastructure supporting multiple slices with heterogeneous mobile
loads show the fidelity of our models and range of validity of our high load
equilibrium analysis
How to Charge Lightning: The Economics of Bitcoin Transaction Channels
Off-chain transaction channels represent one of the leading techniques to
scale the transaction throughput in cryptocurrencies. However, the economic
effect of transaction channels on the system has not been explored much until
now.
We study the economics of Bitcoin transaction channels, and present a
framework for an economic analysis of the lightning network and its effect on
transaction fees on the blockchain. Our framework allows us to reason about
different patterns of demand for transactions and different topologies of the
lightning network, and to derive the resulting fees for transacting both on and
off the blockchain.
Our initial results indicate that while the lightning network does allow for
a substantially higher number of transactions to pass through the system, it
does not necessarily provide higher fees to miners, and as a result may in fact
lead to lower participation in mining within the system.Comment: An earlier version of the paper was presented at Scaling Bitcoin 201
- …