DD-012
Incentive to Ignore
Two exact attention theorems and an independently reproduced 175-cell reward census for ex-ante shared-signal access.
Completed finite studyChecked independently
The question
When a shared clue is available through an ex-ante access gate, how many searchers should condition their actions on it, and how does that compare with privately optimal attention under an equal-split discovery prize?
What we found
- DD-C-0059: For every finite N at least 2 and accuracies p and q strictly between zero and one in the frozen access-gated follow/private model, discovery is G_N(0)=1-(1-p)^N and G_N(k)=1-(1-q)(1-p)^(N-k) for k at least 1; its optimum is uniquely one shared-signal reader when q>p, uniquely zero readers when q<p, and exactly zero or one reader when q=p.
- DD-C-0060: In the frozen equal-split attention game, the private gain Delta_k from becoming reader k+1 is strictly decreasing in k and exactly characterizes every weak and strict pure attention-count equilibrium; all-ignore is a weak equilibrium exactly when q<=p, while all-attend is weak exactly when q>=Np/(1+(N-1)p), so all-ignore cannot occur when the unique social optimum is one reader.
- DD-C-0061: In DD-012's 175-cell rational census, equal-split attention has 63 excessive-attention cells, three equilibrium-multiplicity cells with a welfare difference, and 24 cells where all-attend is an equilibrium although one reader is uniquely optimal; sole-rescue, marginal-coverage, universal-pooling, and a binding public-reader license exactly match the social-optimum correspondence in all 175 cells, while off-shared-success yields unique all-ignore in all cells and the assigned-reader subsidy has no socially optimal weak equilibrium in any cell.
What this result covers
Checked independently. The formal evidence wording and registry state remain available below.
Technical details
- Study phase
complete-bounded-study- Registry status
complete-bounded-study- Evidence status
two-verified-theorems-and-independently-reproduced-exact-census
Reproducible evidence
20260721T212943Z_DD-012_9ed0928e_4a3f1ba62b
Files and data
What comes next
preserve the proof, negative mechanism results, immutable run, and regressions; proceed to DD-013 only after merge, CI, Pages, and live-route validation