Similarity of Information in Games

TL;DR

This paper introduces a new measure called CAD for assessing similarity in strategic games, emphasizing agents' conditional beliefs, and demonstrates its effectiveness across various game types.

Contribution

It proposes the CAD stochastic order, a novel similarity measure based on agents' beliefs, addressing limitations of existing measures in game analysis.

Findings

CAD is necessary and sufficient for strategic similarity in binary coordination games.

CAD effectively applies to congestion games, collective action, and auctions.

Homogenization of information influences strategic behavior and market stability.

Abstract

Algorithmic content targeting homogenizes information, with implications for strategic interactions. For example, this increased homogenization was arguably responsible for the run on the Silicon Valley Bank. We argue that existing measures of similarity are inappropriate for studying games -- especially coordination games -- because they do not discipline agents' conditional beliefs. We propose a class of stochastic orders, Concentration Along the Diagonal (CAD), built on agents' conditional beliefs. In canonical binary-action coordination games, greater CAD-similarity is both necessary and sufficient for strategic similarity -- agents adopt the same strategy. We further demonstrate CAD's applicability in congestion games, collective action, and second-price auctions.