DD-022
Coordination-Free Positive Sharing
Exact private and posterior-only shared symmetric equilibria yield a certified strict positive-sharing interval at p=3/5, with a preserved every-equilibrium negative result.
Completed finite studyChecked independently
The question
Can sharing a realized pair of correlated private signals strictly increase both group discovery and each anonymous agent's expected equal-split payoff by allowing posterior-contingent congestion response without role assignment, correlated randomization, or action authority?
What we found
- DD-C-0104: In DD-022's two-agent hidden-dependence game, let t=2p-1 and A=t^2+rho(1-t^2). Within anonymous label-equivariant strategies that follow a private signal with probability r, the symmetric Bayes-Nash equilibrium is r=1 when A<=3t and r=1/2+3t/(2A) when A>3t, with the separately stated uninformative boundary.
- DD-C-0105: In DD-022, public agreement has posterior u=1/2+t/(1+A) on the agreed label and positive-probability disagreement has posterior 1/2. In the selected provenance-blind posterior-only identical-mixing game, the favored target is chosen with probability one when u>=2/3 and with probability 3u-1 otherwise; disagreement selects probability 1/2.
- DD-C-0106: At p=3/5, discovery under DD-022's selected shared posterior-only symmetric equilibrium exceeds discovery under its private anonymous symmetric Bayes-Nash equilibrium exactly when rho lies in ((5sqrt(73)-17)/48,1), with equality at the algebraic root and at rho=1.
- DD-C-0107: On the exact interval in DD-C-0106, sharing also strictly raises each agent's ex-ante expected payoff; total realized and expected payoff equals the discovery indicator and probability, and player symmetry gives each agent exactly one half.
- DD-C-0108: DD-022's complete 42-cell rational grid contains six positive, 18 negative, and 18 neutral selected shared-minus-private discovery comparisons.
- DD-C-0109: DD-022's positive-sharing comparison does not survive every equilibrium. At p=3/5, opposite constant-target private pure equilibria exist for every rho and attain discovery one; signal-ownership-aware symmetric shared rules can also split targets on disagreement, so the posterior-only mixed result is selection-dependent.
- DD-C-0110: At p=3/5, the gap from DD-021's centralized binary top-two value V_2=1 to DD-022's selected shared discovery is (7+3rho)/25 for rho<=1/6 and (4+3rho)/(13+12rho) for rho>1/6, and is strictly positive throughout rho in [0,1].
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
six-verified-results-one-independently-reproduced-bounded-classification-with-selection-negative-result
Reproducible evidence
20260722T210334Z_DD-022_2376d5b7_ad67765ca8
Files and data
- Frozen source law, coordination-free protocol, equilibrium selections, and comparison baselines
- Bounded execution and validation gates
- Exact private, shared, threshold, payoff, and implementation-gap proofs
- Independent equilibrium, algebra, boundary, and selection audit
- Audited results, bounded classification, baselines, and limitations
- Complete 42-cell exact selected-equilibrium and pure-correspondence registry
- Algebraic root and exact isolating-interval certificate
- Ten rejected registered corruptions
What comes next
preserve the immutable run, posterior-only selection scope, claims DD-C-0104 through DD-C-0110, and output-connected Lab