Information Value Under Endogenous Feasibility

This paper studies how endogenous feasibility constraints interact with objective misspecification to shape the welfare effects of information. We introduce the Irreversibility Decision Problem, in which an agent navigates a graph of actions under stochastic edge blocking. When agents optimize immediate rewards rather than continuation values, welfare under topology-blind signals is non-monotone in signal precision: better signals can reduce welfare by concentrating choices on locally attractive but globally inferior options. The result extends to general graphs, including trees of arbitrary depth where the probability of correct navigation decays exponentially in $d$. A cognitive threshold $\kappa^*(p, \alpha)$ in the agent's cognitive depth parameter separates the regime where Blackwell's classical ordering holds from the regime where it fails, with $\kappa^*(d) = \Theta(\log d)$ on depth-$d$ trees. On the 2D-lattice IDP, for every below-threshold blocking probability $p \in (0, p_c)$, every $\alpha > \alpha^*$, and every $v_0$ where the embedded-tree threshold is positive, $\sup_{v_0} \kappa^*(v_0, p, \alpha) = +\infty$ in the infinite-volume limit. The welfare decomposition $W = W_{\mathrm{topo}} + W_{\mathrm{info}}$ undergoes a phase transition at the percolation threshold; we characterize this on lattices ($p_c = 1/2$), Erdős–Rényi graphs ($c = 1$), and power-law networks, where the dichotomy is sharpest. For degree exponent $2 < \gamma < 3$, topological loss vanishes at any positive edge-retention rate for the $\theta(1-p)$-fraction of agents lying in the giant component. In the moderate-SNR regime ($|z|<1$) and in a neighborhood of $\beta^*_\kappa$, signal precision $\beta$ and cognitive depth $\kappa$ are supermodular complements, so information-transparency mandates and cognitive-infrastructure investments are jointly determined rather than substitutable. The negative results arise from objective misspecification; a Bayesian agent with structural knowledge is immune.