Nashian game theory is incompatible with quantum physics

TL;DR

This paper proposes a novel game-theoretical framework for quantum measurement outcomes, challenging traditional Nash equilibrium approaches and suggesting non-Nashian game theory as more compatible with quantum physics.

Contribution

It introduces an original game-theoretical model translating quantum notions into decision theory, highlighting incompatibility of Nash equilibria with quantum phenomena like Bell inequality violations.

Findings

Nash equilibria conflict with Bell inequality violations

Game theory based on decision models can represent quantum measurement scenarios

Counterfactual dependencies are distinct from causation and correlation in quantum contexts

Abstract

We suggest to look at quantum measurement outcomes not through the lens of probability theory, but instead through decision theory. We introduce an original game-theoretical framework, model and algorithmic procedure where measurement scenarios are multiplayer games with a structure all observers agree on. Measurement axes and, newly, measurement outcomes are modeled as decisions with nature being an action-minimizing economic agent. We translate physical notions of causality, correlation, counterfactuals, and contextuality to particular aspects of game theory. We investigate the causal consistency of dynamic games with imperfect information from the quantum perspective and conclude that counterfactual dependencies should be distinguished from causation and correlation as a separate phenomenon of its own. Most significantly, we observe that game theory based on Nash equilibria stands in contradiction with a violation of Bell inequalities. Hence, we propose that quantum physics should be analyzed with non-Nashian game theory, the inner workings of which we demonstrate using our proposed model.