7,789 research outputs found
A betting interpretation for probabilities and Dempster-Shafer degrees of belief
There are at least two ways to interpret numerical degrees of belief in terms
of betting: (1) you can offer to bet at the odds defined by the degrees of
belief, or (2) you can judge that a strategy for taking advantage of such
betting offers will not multiply the capital it risks by a large factor. Both
interpretations can be applied to ordinary additive probabilities and used to
justify updating by conditioning. Only the second can be applied to
Dempster-Shafer degrees of belief and used to justify Dempster's rule of
combination.Comment: 20 page
Distributed Game Theoretic Optimization and Management of Multichannel ALOHA Networks
The problem of distributed rate maximization in multi-channel ALOHA networks
is considered. First, we study the problem of constrained distributed rate
maximization, where user rates are subject to total transmission probability
constraints. We propose a best-response algorithm, where each user updates its
strategy to increase its rate according to the channel state information and
the current channel utilization. We prove the convergence of the algorithm to a
Nash equilibrium in both homogeneous and heterogeneous networks using the
theory of potential games. The performance of the best-response dynamic is
analyzed and compared to a simple transmission scheme, where users transmit
over the channel with the highest collision-free utility. Then, we consider the
case where users are not restricted by transmission probability constraints.
Distributed rate maximization under uncertainty is considered to achieve both
efficiency and fairness among users. We propose a distributed scheme where
users adjust their transmission probability to maximize their rates according
to the current network state, while maintaining the desired load on the
channels. We show that our approach plays an important role in achieving the
Nash bargaining solution among users. Sequential and parallel algorithms are
proposed to achieve the target solution in a distributed manner. The
efficiencies of the algorithms are demonstrated through both theoretical and
simulation results.Comment: 34 pages, 6 figures, accepted for publication in the IEEE/ACM
Transactions on Networking, part of this work was presented at IEEE CAMSAP
201
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A tree formulation for signaling games
We provide a detailed presentation and complete analysis of the sender/receiver Lewis signaling game using a game theory extensive form, decision tree formulation. The analysis employs well established game theory ideas and concepts. We establish the existence of four perfect Bayesian equilibria in this game. We explain which equilibrium is the most likely to prevail. Our explanation provides an essential step for understanding the formation of a language convention. Further, we discuss the informational content of such signals and calibrate a more detailed definition of a true (“correct”) signal in terms of the payoffs of the sender and the receiver
Distributed Adaptive Networks: A Graphical Evolutionary Game-Theoretic View
Distributed adaptive filtering has been considered as an effective approach
for data processing and estimation over distributed networks. Most existing
distributed adaptive filtering algorithms focus on designing different
information diffusion rules, regardless of the nature evolutionary
characteristic of a distributed network. In this paper, we study the adaptive
network from the game theoretic perspective and formulate the distributed
adaptive filtering problem as a graphical evolutionary game. With the proposed
formulation, the nodes in the network are regarded as players and the local
combiner of estimation information from different neighbors is regarded as
different strategies selection. We show that this graphical evolutionary game
framework is very general and can unify the existing adaptive network
algorithms. Based on this framework, as examples, we further propose two
error-aware adaptive filtering algorithms. Moreover, we use graphical
evolutionary game theory to analyze the information diffusion process over the
adaptive networks and evolutionarily stable strategy of the system. Finally,
simulation results are shown to verify the effectiveness of our analysis and
proposed methods.Comment: Accepted by IEEE Transactions on Signal Processin
Probability in the Everett World: Comments on Wallace and Greaves
It is often objected that the Everett interpretation of QM cannot make sense
of quantum probabilities, in one or both of two ways: either it can't make
sense of probability at all, or it can't explain why probability should be
governed by the Born rule. David Deutsch has attempted to meet these
objections. He argues not only that rational decision under uncertainty makes
sense in the Everett interpretation, but also that under reasonable
assumptions, the credences of a rational agent in an Everett world should be
constrained by the Born rule. David Wallace has developed and defended
Deutsch's proposal, and greatly clarified its conceptual basis. In particular,
he has stressed its reliance on the distinguishing symmetry of the Everett
view, viz., that all possible outcomes of a quantum measurement are treated as
equally real. The argument thus tries to make a virtue of what has usually been
seen as the main obstacle to making sense of probability in the Everett world.
In this note I outline some objections to the Deutsch-Wallace argument, and to
related proposals by Hilary Greaves about the epistemology of Everettian QM.
(In the latter case, my arguments include an appeal to an Everettian analogue
of the Sleeping Beauty problem.) The common thread to these objections is that
the symmetry in question remains a very significant obstacle to making sense of
probability in the Everett interpretation.Comment: 17 pages; no figures; LaTe
Sequential Two-Player Games with Ambiguity
If players' beliefs are strictly non-additive, the Dempster-Shafer updating rule can be used to define beliefs off the equilibrium path. We define an equilibrium concept in sequential two-person games where players update their beliefs with the Dempster-Shafer updating rule. We show that in the limit as uncertainty tends to zero, our equilibrium approximates Bayesian Nash equilibrium by imposing context-dependent constraints on beliefs under uncertainty.
Coherent frequentism
By representing the range of fair betting odds according to a pair of
confidence set estimators, dual probability measures on parameter space called
frequentist posteriors secure the coherence of subjective inference without any
prior distribution. The closure of the set of expected losses corresponding to
the dual frequentist posteriors constrains decisions without arbitrarily
forcing optimization under all circumstances. This decision theory reduces to
those that maximize expected utility when the pair of frequentist posteriors is
induced by an exact or approximate confidence set estimator or when an
automatic reduction rule is applied to the pair. In such cases, the resulting
frequentist posterior is coherent in the sense that, as a probability
distribution of the parameter of interest, it satisfies the axioms of the
decision-theoretic and logic-theoretic systems typically cited in support of
the Bayesian posterior. Unlike the p-value, the confidence level of an interval
hypothesis derived from such a measure is suitable as an estimator of the
indicator of hypothesis truth since it converges in sample-space probability to
1 if the hypothesis is true or to 0 otherwise under general conditions.Comment: The confidence-measure theory of inference and decision is explicitly
extended to vector parameters of interest. The derivation of upper and lower
confidence levels from valid and nonconservative set estimators is formalize
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