Solution concepts in game theory—like the Nash equilibrium and its refinements—are used in two key ways. Normatively, they proscribe how rational agents ought to behave. Descriptively, they propose how agents actually behave when interactions settle into equilibrium. The Nash equilibrium[1] underpins much of modern game theory and its applications in economics, political science, and evolutionary biology.

Here, we focus on the descriptive use of the concept in game theory. To do so, our first question must be: when should we expect players to play Nash equilibrium strategies in practice?

It turns out that trying to understand the theoretical conditions under which agents might play the Nash equilibrium of a game has led theorists down two very different paths:

1. High Rationality Road (Epistemic Game Theory): Model the (sometimes infinite) hierarchy of beliefs of hyper-rational agents. Each agent reasons not just about the game, but about the others’ beliefs [...]

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Outline:

(01:57) What is a Nash equilibrium?

(03:58) The High Rationality Road (Epistemic Game Theory)

(05:20) The Low Rationality Road (Evolutionary Game Theory)

(07:53) The Replicator Dynamics

(09:55) Example of an Error of Omission for Weak Nash

(10:03) Nash Equilibria

(10:30) Stability Under Replicator Dynamics

(11:22) Example of an Error of Commission for Strict Nash

(11:31) Nash Equilibria

(12:15) Stability Under Replicator Dynamics

(13:18) The Evolutionarily Stable Strategy (ESS)

(14:25) Revisiting the Examples

(15:25) Even ESS Falls Short: Cycles, Spirals, and Chaos

(18:59) Deeper Reading

(19:39) Recap and Conclusion: Beyond Static Equilibria

The original text contained 15 footnotes which were omitted from this narration.

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Narrated by TYPE III AUDIO.

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