# On the Importance of Correlations in Rational Choice: A Case for Non-Nashian Game Theory

## TL;DR

This paper advocates for a non-Nashian approach to game theory that incorporates correlations between agents' decisions, challenging the independence assumption of traditional Rational Choice Theory and proposing the Perfect Prediction Equilibrium as a viable alternative.

## Contribution

It introduces a consistent alternative to Nash equilibrium based on correlated decisions, and advocates for the development of non-Nashian game theory frameworks.

## Key findings

- Correlations between decisions can explain observed rational behavior.
- The Perfect Prediction Equilibrium offers a meaningful complement to Nash equilibrium.
- Misconceptions about non-Nashian equilibria are addressed.

## Abstract

The Nash equilibrium paradigm, and Rational Choice Theory in general, rely on agents acting independently from each other. This note shows how this assumption is crucial in the definition of Rational Choice Theory. It explains how a consistent Alternate Rational Choice Theory, as suggested by Jean-Pierre Dupuy, can be built on the exact opposite assumption, and how it provides a viable account for alternate, actually observed behavior of rational agents that is based on correlations between their decisions. The end goal of this note is three-fold: (i) to motivate that the Perfect Prediction Equilibrium, implementing Dupuy's notion of projected time and previously called "projected equilibrium", is a reasonable approach in certain real situations and a meaningful complement to the Nash paradigm, (ii) to summarize common misconceptions about this equilibrium, and (iii) to give a concise motivation for future research on non-Nashian game theory.