DD-017
Threshold Equilibrium Selection
Verified pure and tied-mode equilibrium boundaries with independently reproduced welfare and small-coalition censuses.
Completed finite studyChecked independently
The question
Which decentralized threshold-search occupancies are Nash equilibria, which survive small strict-improvement coalitions, and how far can their discovery value lie below the deterministic minimum-team planner?
What we found
- DD-C-0075: An occupancy n is a weak pure Nash equilibrium of the frozen equal-split threshold game if and only if every agent on every occupied candidate j weakly prefers pi_j/n_j when n_j>=tau, or zero otherwise, to pi_k/(n_k+1) when n_k+1>=tau, or zero otherwise, for every alternative candidate k.
- DD-C-0076: Independent uniform mixing over the highest-posterior candidates is a symmetric mixed Nash equilibrium for every finite strictly positive posterior when tau>=2; at tau=1 it is an equilibrium exactly when the common support payoff pi_max*[1-(1-1/m)^N]/(N/m) weakly exceeds every unsupported posterior mass, and this condition can fail.
- DD-C-0077: In DD-017's 160 registered rational games, 52 have a weak pure Nash equilibrium with zero discovery and therefore infinite pure price of anarchy under the declared positive-planner-over-zero convention.
- DD-C-0078: Among DD-017's 160 registered games, eight have no pairwise-strict-stable weak pure Nash equilibrium and 35 have no exact-size-tau-strict-stable weak pure Nash equilibrium.
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-two-independently-reproduced-bounded-censuses
Reproducible evidence
20260722T024032Z_DD-017_033452f6_3d2c74fdfb
Files and data
- Frozen equilibrium and deviation concepts
- Living bounded execution plan
- Focused adjacent-literature and terminology boundary
- Pure-Nash and tied-mode symmetric-mixture proofs
- Exact bounded equilibrium and coalition-stability report
- Public-safe bounded equilibrium summary
- Public-safe exact 160-game registry
- Independent labeled and aggregate verification record
- Four registered corruption rejections
What comes next
preserve PR 104, the immutable run, and distinct equilibrium concepts; continue the authorized Program V4 queue at DD-015