A general theory of equilibrium behavior

TL;DR

This paper develops a comprehensive mathematical framework for understanding equilibrium behavior in vector fields and noncooperative games, revealing new structural insights and atypical equilibria, inspired by computational complexity challenges in game theory.

Contribution

It introduces a general theory of equilibrium behavior in vector fields, uncovering previously unknown structural properties and atypical equilibria, extending beyond traditional game theory concepts.

Findings

Reveals significant structure in vector fields related to equilibrium behavior

Identifies atypical, previously unknown equilibrium phenomena

Provides a unifying mathematical framework for diverse equilibrium concepts

Abstract

Economists were content with the concept of the Nash equilibrium as game theory's solution concept until Daskalakis, Goldberg, and Papadimitriou showed that finding a Nash equilibrium is most likely a computationally hard problem, a result that set off a deep scientific crisis. Motivated, in part, by their result, in this paper, we propose a general theory of equilibrium behavior in vector fields (and, therefore, also noncooperative games). Our line of discourse is to show that these universal in nature mathematical objects are endowed with significant structure, which we probe to unearth atypical, previously unidentified, equilibrium behavior.