30 research outputs found
Perfect Prediction in Minkowski Spacetime: Perfectly Transparent Equilibrium for Dynamic Games with Imperfect Information
The assumptions of necessary rationality and necessary knowledge of
strategies, also known as perfect prediction, lead to at most one surviving
outcome, immune to the knowledge that the players have of them. Solutions
concepts implementing this approach have been defined on both dynamic games
with perfect information and no ties, the Perfect Prediction Equilibrium, and
strategic games with no ties, the Perfectly Transparent Equilibrium.
In this paper, we generalize the Perfectly Transparent Equilibrium to games
in extensive form with imperfect information and no ties. Both the Perfect
Prediction Equilibrium and the Perfectly Transparent Equilibrium for strategic
games become special cases of this generalized equilibrium concept. The
generalized equilibrium, if there are no ties in the payoffs, is at most
unique, and is Pareto-optimal.
We also contribute a special-relativistic interpretation of a subclass of the
games in extensive form with imperfect information as a directed acyclic graph
of decisions made by any number of agents, each decision being located at a
specific position in Minkowski spacetime, and the information sets and game
structure being derived from the causal structure. Strategic games correspond
to a setup with only spacelike-separated decisions, and dynamic games to one
with only timelike-separated decisions.
The generalized Perfectly Transparent Equilibrium thus characterizes the
outcome and payoffs reached in a general setup where decisions can be located
in any generic positions in Minkowski spacetime, under necessary rationality
and necessary knowledge of strategies. We also argue that this provides a
directly usable mathematical framework for the design of extension theories of
quantum physics with a weakened free choice assumption.Comment: 25 pages, updated technical repor
Rumble: Data Independence for Large Messy Data Sets
This paper introduces Rumble, an engine that executes JSONiq queries on
large, heterogeneous and nested collections of JSON objects, leveraging the
parallel capabilities of Spark so as to provide a high degree of data
independence. The design is based on two key insights: (i) how to map JSONiq
expressions to Spark transformations on RDDs and (ii) how to map JSONiq FLWOR
clauses to Spark SQL on DataFrames. We have developed a working implementation
of these mappings showing that JSONiq can efficiently run on Spark to query
billions of objects into, at least, the TB range. The JSONiq code is concise in
comparison to Spark's host languages while seamlessly supporting the nested,
heterogeneous data sets that Spark SQL does not. The ability to process this
kind of input, commonly found, is paramount for data cleaning and curation. The
experimental analysis indicates that there is no excessive performance loss,
occasionally even a gain, over Spark SQL for structured data, and a performance
gain over PySpark. This demonstrates that a language such as JSONiq is a simple
and viable approach to large-scale querying of denormalized, heterogeneous,
arborescent data sets, in the same way as SQL can be leveraged for structured
data sets. The results also illustrate that Codd's concept of data independence
makes as much sense for heterogeneous, nested data sets as it does on highly
structured tables.Comment: Preprint, 9 page