Dr. Ghislain Fourny

Generalization of superrationality to non-symmetric games

Generalization of superrationality to dynamic games (solving Grandfather's paradoxes)

We live in a world where AI/ML technology is getting better every day at predicting the action of human beings, leading to increasingly interdependent decisions. Yet, the discipline that is dedicated to the modelling of what rational agents should or would do, game theory, is commonly based on a strong assumption of free choice in which agents are by essence unpredictable: in the Nash paradigm, economic agents optimize their decisions by freezing what everybody else does and unilaterally considering their possible decisions. This motivates investigating decision models with different assumptions about predictability.

I am investigating what happens if, instead, we assume that rational agents are perfectly predictable, an idea that Prof. J.-P. Dupuy (Stanford) coined in the 1990s. Free choice can be reconciled with predictability with a fixpoint framework in which a decision is entangled with its always correct prediction, and this decision must be immune to its prediction in terms of causality. In other words, the correct prediction of a decision must trigger a chain of events that causes this very decision to be taken (self-fulfilling prophecy). This kind of thinking is similar to what the Director of a central bank tries to avoid on a macroscopic level: saying too boldly that the economy is doing well may lead to a market crash, contradicting their prediction, since interest rate hikes would then be expected by the public.

I co-designed the corresponding non-Nashian equilibrium concepts and algorithms for games in both extensive and normal form. As predicted in a conjecture by Prof. Dupuy, notably, Pareto optimal outcomes are always reached. Concretely, this means that, unlike in the Nash paradigm, it is rational to be honest and not betray other agents. Philosophically, the underlying concept is that of a Kantian categorical imperative urging to avoid Grandfather's paradoxes.

Future directions of research include investigating the feasibility of programming robots and artificial intelligences with non-Nashian algorithms, to investigate their implications for cooperation in AI systems.

Generalization of game theory to special relativity

Non-Nashian decision models for quantum foundations

Another direction of research is the link with quantum theory: indeed, the core assumption behind the inherent non-determinism of quantum theory is the same one as that of the Nash paradigm, namely, the free choice of the physicist who unpredictably picks a measurement axis. It is used, for example, in combination with the Kochen-Specker impossibility theorem.

However, this strong free choice assumption seems to be in contradiction with some findings of the neuroscience community, indicating that a human may only have a veto right on their decisions.

I am thus building a model that weakens the free choice assumption in quantum physics, along the same lines as in non-Nashian game theory, namely, that the correct prediction of an agent's action could be entangled with their action, and nevertheless causing it to happen. This decision model is based firstly on a generalization of game theory to special relativity to account for spacelike and timelike separated choices of measurement axes and of measurement outcomes -- in a structure compatible with and familiar to the quantum foundations community. Secondly, this decision model can be seen as a big game between experimenters and the universe, who both maximize their utility (e.g., principle of least action), leading to a deterministic resolution predicting an outcome for each experiment, without probabilities. In this framework, our work examines the incompatibility of Nash equilibria with contextuality and develops non-Nashian alternatives. From an abstract perspective, in this model, our actual world can be seen as the unique solution to a fixpoint equation.

The next phase is to instantiate these models into theories by playing with the parameters.

RumbleDB

The latest technological developments in the area of Big Data have come at the cost of more complexity, making efficient querying costly and, in spite of the field of data science's being by essence interdisciplinary, not easily accessible to non-IT-savvy-users. While the database community invests a lot of efforts into the performance aspects of such systems, usability and productivity are also important research questions.

I believe that we need to come back to the fundamental ideas laid out by Edgar Codd in 1970, namely data independence, in his founding paper on relational databases: use natural, simple querying languages that hide away all the complexity and storage details of a system. Such languages must be functional, declarative and tailored to the data shapes at hand: tables (SQL), trees, cubes or graphs.

With this line of reasoning, I co-designed the functional JSONiq language during my doctoral studies to query arborescent documents, which correspond to heterogeneous, denormalized datasets commonly found on the Web as JSON or XML. The language has been implemented by several query engines. In order to build on the shoulders of giants and learn from past experience, 95% of the language is directly inherited from the XQuery standard, itself designed at the World Wide Web Consortium by some of the same people who designed the SQL language, and involving major industry players.

I am now working on the implementation of JSONiq on top of large-scale clusters such as Spark, in a project called RumbleDB. The JSONiq expressions are seamlessly mapped to Spark constructs, hiding the complexity of Spark to the end user and making it accessible to non-Computer Scientists.

Further investigation includes making JSONiq accessible to the Machine Learning community with the same goal in mind.