Observability, Dominance, and Induction in Learning Models

TL;DR

This paper explores how learning models in game theory relate to concepts like dominance and induction, emphasizing the importance of extensive form representation for understanding players' feedback and decision-making.

Contribution

It clarifies the relationship between learning models, dominance, and extensive form representations, highlighting the limitations of normal form analysis in dynamic strategic settings.

Findings

Weakly dominated strategies can serve as experiments for learning.

Normal form analysis may overlook information conveyed by extensive form.

Playing extensive form is equivalent to augmented normal form with terminal node partitions.

Abstract

Learning models do not in general imply that weakly dominated strategies are irrelevant or justify the related concept of "forward induction," because rational agents may use dominated strategies as experiments to learn how opponents play, and may not have enough data to rule out a strategy that opponents never use. Learning models also do not support the idea that the selected equilibria should only depend on a game's normal form, even though two games with the same normal form present players with the same decision problems given fixed beliefs about how others play. However, playing the extensive form of a game is equivalent to playing the normal form augmented with the appropriate terminal node partitions so that two games are information equivalent, i.e., the players receive the same feedback about others' strategies.