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