4,614 research outputs found
(Non-)Equivalence of Universal Priors
Ray Solomonoff invented the notion of universal induction featuring an aptly
termed "universal" prior probability function over all possible computable
environments. The essential property of this prior was its ability to dominate
all other such priors. Later, Levin introduced another construction --- a
mixture of all possible priors or `universal mixture'. These priors are well
known to be equivalent up to multiplicative constants. Here, we seek to clarify
further the relationships between these three characterisations of a universal
prior (Solomonoff's, universal mixtures, and universally dominant priors). We
see that the the constructions of Solomonoff and Levin define an identical
class of priors, while the class of universally dominant priors is strictly
larger. We provide some characterisation of the discrepancy.Comment: 10 LaTeX pages, 1 figur
Robust Mechanism Design
The mechanism design literature assumes too much common knowledge of the environment among the players and planner. We relax this assumption by studying implementation on richer type spaces. We ask when ex post implementation is equivalent to interim (or Bayesian) implementation for all possible type spaces. The equivalence holds in the case of separable environments; examples of separable environments arise (1) when the planner is implementing a social choice function (not correspondence); and (2) in a quasilinear environment with no restrictions on transfers. The equivalence fails in general, including in some quasilinear environments with budget balance. In private value environments, ex post implementation is equivalent to dominant strategies implementation. The private value versions of our results offer new insights into the relation between dominant strategy implementation and Bayesian implementation.Mechanism design, Common knowledge, Universal type space, Interim equilibrium, Ex-post equilibrium, Dominant strategies
A structural Markov property for decomposable graph laws that allows control of clique intersections
We present a new kind of structural Markov property for probabilistic laws on
decomposable graphs, which allows the explicit control of interactions between
cliques, so is capable of encoding some interesting structure. We prove the
equivalence of this property to an exponential family assumption, and discuss
identifiability, modelling, inferential and computational implications.Comment: 10 pages, 3 figures; updated from V1 following journal review, new
more explicit title and added section on inferenc
Design of Multidimensional Franchise Auctions by an Ignorant Principal
The paper’s main aim is to identify under which conditions the criterion of prior-independent optimality is applicable in the design of multidimensional franchise auctions. We first establish an impossibility result for second-score auctions by showing that in single-crossing environments necessary and sufficient condition for score functions to be optimal in this sense is that bidders have equal variable cost functions. Then we show that the result is not confined to the second-score format but holds for any scoring auction under stochastic independence. Therefore, a regulator who has no information at all about firms’ costs cannot in such circumstances avail himself of prior-independent optimality as choice criterion. Conversely, if variable cost functions are equal across potential contractors, as is likely in certain public services markets, and the regulator knows it, it is possible for him to implement a prior-independent optimum by scoring bids according to the social welfare function under various auction formats, including first- and second-score auctions. This simple prescription however no longer applies if the regulator is ignorant about market demand too. In this case a fully rational choice of the score function is precluded, though it may be possible to make a reasonable one: a brief discussion of this point closes the paper.
Mutual Absolute Continuity of Multiple Priors
This note provides a behavioral characterization of mutually absolutely continuous multiple priors.Mutual absolute continuity, Multiple priors
Coherent Price Systems and Uncertainty-Neutral Valuation
We consider fundamental questions of arbitrage pricing arising when the
uncertainty model is given by a set of possible mutually singular probability
measures. With a single probability model, essential equivalence between the
absence of arbitrage and the existence of an equivalent martingale measure is a
folk theorem, see Harrison and Kreps (1979). We establish a microeconomic
foundation of sublinear price systems and present an extension result. In this
context we introduce a prior dependent notion of marketed spaces and viable
price systems. We associate this extension with a canonically altered concept
of equivalent symmetric martingale measure sets, in a dynamic trading framework
under absence of prior depending arbitrage. We prove the existence of such sets
when volatility uncertainty is modeled by a stochastic differential equation,
driven by Peng's G-Brownian motions
Bayesian games with a continuum of states
We show that every Bayesian game with purely atomic
types has a measurable Bayesian equilibrium when the common knowl-
edge relation is smooth. Conversely, for any common knowledge rela-
tion that is not smooth, there exists a type space that yields this common
knowledge relation and payoffs such that the resulting Bayesian game
will not have any Bayesian equilibrium. We show that our smoothness
condition also rules out two paradoxes involving Bayesian games with
a continuum of types: the impossibility of having a common prior on
components when a common prior over the entire state space exists, and
the possibility of interim betting/trade even when no such trade can be
supported
ex ante
On the Empirical Consequences of the AdS/CFT Duality
We provide an analysis of the empirical consequences of the AdS/CFT duality
with reference to the application of the duality in a fundamental theory,
effective theory and instrumental context. Analysis of the first two contexts
is intended to serve as a guide to the potential empirical and ontological
status of gauge/gravity dualities as descriptions of actual physics at the
Planck scale. The third context is directly connected to the use of AdS/CFT to
describe real quark-gluon plasmas. In the latter context, we find that neither
of the two duals are confirmed by the empirical data.Comment: 15 pages + abstract, references. Submitted to "Beyond Spacetime"
volum
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