game theory can’t talk about how agents reach equilibria, only what they do once they’re already there.
This overstates a limitation of game theory. Branches such as learning in games and evolutionary game theory explicitly study how agents’ behavior changes over time and when play converges to equilibrium.
Full reasoning
The quoted sentence is too broad as a factual description of game theory.
Modern game theory includes entire subfields devoted to how equilibrium is reached, not just what happens once equilibrium is assumed. For example:
- The Journal of Economic Perspectives article “Whither Game Theory? Towards a Theory of Learning in Games” argues that models of learning are part of extending and improving game theory’s predictive power, and emphasizes understanding the speed with which learning takes place.
- Standard summaries of learning in games describe it as studying the processes by which players interact and reach equilibria, and the MIT literature on learning and equilibrium says this theory examines how, which, and what kind of equilibria can arise from long-run nonequilibrium processes of learning, adaptation, or imitation.
So while some classical equilibrium analysis is static, it is inaccurate to say that game theory can’t talk about how agents reach equilibria. A more accurate formulation would be that some traditional equilibrium models abstract away from the path to equilibrium, while other well-established parts of game theory study that path directly.
3 sources
- Whither Game Theory? Towards a Theory of Learning in Games - American Economic Association
Abstract: "Game theory has been a huge success in economics... we argue that models of learning are a promising route for improving and widening game theory's predictive power... We emphasize in particular the need for better understanding of the speed with which learning takes place."
- Cambridge University Press excerpt on Learning in Games
"Learning (in the context of games) refers to the process that game-theoretic decision makers can use to interact and reach the sought equilibria" and to understand "when, or whether, play might converge to equilibrium."
- Learning and Equilibrium (MIT Economics)
"The theory of learning in games provides a foundation for equilibrium analysis by examining how, which, and what kind of equilibria can arise as a consequence of a long-run nonequilibrium process of learning, adaptation, and/or imitation."