Strategic Teaching and Learning in Games

TL;DR

This paper demonstrates that no universal uncoupled learning heuristic exists that is both evolutionarily stable and capable of leading players to Nash equilibrium or related solution concepts in all finite games, highlighting the strategic importance of teaching.

Contribution

It proves the impossibility of universally stable uncoupled learning heuristics and emphasizes the strategic role of teaching in game-theoretic settings.

Findings

No uncoupled learning heuristic is evolutionarily stable in all finite games.

Players can strategically teach opponents to secure better payoffs.

Impossibility persists across various classes of games and solution concepts.

Abstract

It is known that there are uncoupled learning heuristics leading to Nash equilibrium in all finite games. Why should players use such learning heuristics and where could they come from? We show that there is no uncoupled learning heuristic leading to Nash equilibrium in all finite games that a player has an incentive to adopt, that would be evolutionary stable or that could "learn itself". Rather, a player has an incentive to strategically teach such a learning opponent in order secure at least the Stackelberg leader payoff. The impossibility result remains intact when restricted to the classes of generic games, two-player games, potential games, games with strategic complements or 2x2 games, in which learning is known to be "nice". More generally, it also applies to uncoupled learning heuristics leading to correlated equilibria, rationalizable outcomes, iterated admissible outcomes, or minimal curb sets. A possibility result restricted to "strategically trivial" games fails if some generic games outside this class are considered as well.