Strategic information asymmetry in tail-risk markets

Abstract

This paper develops a novel information-theoretic measure of strategic asymmetry, asymmetric information entropy, that quantifies disparities in agents’ knowledge states through differential Shannon entropy. I integrate $k$-level cognitive hierarchies with Bayesian games to analyze how strategic depth attenuates information gaps, proving almost sure convergence and Pareto-optimal limit equilibria. Using generalized extreme value distributions, I show strategic restructuring alters financial market outcomes through parameter shifts in tail risk and location that converge geometrically under Lipschitz belief updating. Empirical analysis of U.S. tender offers reveals legal defenses (Level-2 strategies) increase bid premiums versus the baseline, while combined strategies exhibit subadditive effects. The proposed entropy measure formalizes Akerlof-style market failures, providing a quantitative basis for securities regulation and mechanism design.