34 research outputs found
The Blackwell relation defines no lattice
Blackwell's theorem shows the equivalence of two preorders on the set of
information channels. Here, we restate, and slightly generalize, his result in
terms of random variables. Furthermore, we prove that the corresponding partial
order is not a lattice; that is, least upper bounds and greatest lower bounds
do not exist.Comment: 5 pages, 1 figur
Strategic Payments in Financial Networks
In their seminal work on systemic risk in financial markets, Eisenberg and Noe [Larry Eisenberg and Thomas Noe, 2001] proposed and studied a model with n firms embedded into a network of debt relations. We analyze this model from a game-theoretic point of view. Every firm is a rational agent in a directed graph that has an incentive to allocate payments in order to clear as much of its debt as possible. Each edge is weighted and describes a liability between the firms. We consider several variants of the game that differ in the permissible payment strategies. We study the existence and computational complexity of pure Nash and strong equilibria, and we provide bounds on the (strong) prices of anarchy and stability for a natural notion of social welfare. Our results highlight the power of financial regulation - if payments of insolvent firms can be centrally assigned, a socially optimal strong equilibrium can be found in polynomial time. In contrast, worst-case strong equilibria can be a factor of ?(n) away from optimal, and, in general, computing a best response is an NP-hard problem. For less permissible sets of strategies, we show that pure equilibria might not exist, and deciding their existence as well as computing them if they exist constitute NP-hard problems
Quantifying unique information
We propose new measures of shared information, unique information and
synergistic information that can be used to decompose the multi-information of
a pair of random variables with a third random variable . Our
measures are motivated by an operational idea of unique information which
suggests that shared information and unique information should depend only on
the pair marginal distributions of and . Although this
invariance property has not been studied before, it is satisfied by other
proposed measures of shared information. The invariance property does not
uniquely determine our new measures, but it implies that the functions that we
define are bounds to any other measures satisfying the same invariance
property. We study properties of our measures and compare them to other
candidate measures.Comment: 24 pages, 2 figures. Version 2 contains less typos than version