What is non-Nashian Game Theory?

In classical game theory and economics, we make a fundamental assumption: agents can make their decisions independently of each other.

This translates to a reasoning along the lines of “If I were to make this decision instead, the other agent would still have acted in the same way.” This is also often known as “free choice”, in its strong version. A decision is fully independent from anything not in the future, and from what other people are doing.

Yet, in the real world, there are dependencies between our actions. If we acted differently, then other people would probably also act differently.

This book aims at giving an introduction to non-Nashian game theory, in which the fundamental Nashian assumption of independence is dropped. I like to call this subfield of game theory “Non-Nashian Game Theory” as a positive tribute to the work of John Nash, in the same way as we call “Non-Euclidean Geometry” the subfield of geometry in which Euclid’s axiom is dropped.

The book is based on published research papers in various journals, and on preprints, but is written in way that should be easier and smoother to read for a broader audience.

As it turns out, free choice is also one of the assumptions underlying all known impossibility theorems in quantum theory. In other words, a deterministic extension of quantum theory as envisioned by Albert Einstein can only be achieved if we reconsider our definition of free choice.

This book also offers an introduction to our deterministic extension model of quantum theory, which is based on viewining quantum experiments as a game between observers (who decides on the measurement settings) and Nature (which can be seen as an economic agent that minimizes action to decide on the measurement outcomes).