Irreversible Failure Reverses the Value of Information

TL;DR

This paper analyzes how irreversible failure in dynamic games with hidden states causes increased informational opacity to be strategically necessary for equilibrium survival, reversing the usual value of information.

Contribution

It introduces a limit-viability framework showing that greater information can decrease survival prospects due to irreversible failure risks, highlighting opacity as a strategic choice.

Findings

Greater informational precision increases collapse probability.

Opacity can restore equilibrium viability in failure-prone environments.

Positive opacity is necessary for equilibrium survival in extended games.

Abstract

We study dynamic games with hidden states and absorbing failure, where belief-driven actions can trigger irreversible collapse. In such environments, equilibria that sustain activity generically operate at the boundary of viability. We show that this geometry endogenously reverses the value of information: greater informational precision increases the probability of collapse on every finite horizon. We formalize this mechanism through a limit-viability criterion, and model opacity as a strategic choice of the information structure via Blackwell garbling. When failure is absorbing, survival values become locally concave in beliefs, implying that transparency destroys equilibrium viability while sufficient opacity restores it. In an extended game where agents choose the information structure ex ante, strictly positive opacity is necessary for equilibrium survival. The results identify irreversible failure--not coordination, misspecification, or ambiguity--as a primitive force generating an endogenous demand for opacity in dynamic games.