Is Knowledge Power? On the (Im)possibility of Learning from Strategic Interactions

TL;DR

This paper investigates whether agents in strategic environments can learn to achieve their optimal outcomes through repeated interactions, revealing that information asymmetry often prevents uninformed players from reaching their Stackelberg value.

Contribution

The study introduces a game-theoretic framework analyzing learning algorithms in strategic interactions, highlighting limitations in achieving optimal outcomes under information asymmetry.

Findings

Perfect knowledge by one player leads to persistent informational gaps.

No PNE guarantees partially informed players achieve Stackelberg value.

Repeated interactions alone are insufficient for uninformed players to learn optimal strategies.

Abstract

When learning in strategic environments, a key question is whether agents can overcome uncertainty about their preferences to achieve outcomes they could have achieved absent any uncertainty. Can they do this solely through interactions with each other? We focus this question on the ability of agents to attain the value of their Stackelberg optimal strategy and study the impact of information asymmetry. We study repeated interactions in fully strategic environments where players' actions are decided based on learning algorithms that take into account their observed histories and knowledge of the game. We study the pure Nash equilibria (PNE) of a meta-game where players choose these algorithms as their actions. We demonstrate that if one player has perfect knowledge about the game, then any initial informational gap persists. That is, while there is always a PNE in which the informed agent achieves her Stackelberg value, there is a game where no PNE of the meta-game allows the partially informed player to achieve her Stackelberg value. On the other hand, if both players start with some uncertainty about the game, the quality of information alone does not determine which agent can achieve her Stackelberg value. In this case, the concept of information asymmetry becomes nuanced and depends on the game's structure. Overall, our findings suggest that repeated strategic interactions alone cannot facilitate learning effectively enough to earn an uninformed player her Stackelberg value.