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pvalue_mas_diplomacy_form_fit_draft_2026-02-06.md

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+# pValue Storyworlds for Multi-Agent Diplomacy: Layered Forecasting Toward Form-Fit Scenarios (Draft)
+
+**Author:** Working draft for ongoing AI_Diplomacy program  
+**Date:** 2026-02-06  
+**Status:** Stub for weekend/Monday expansion
+
+## Abstract
+
+We report early results from a pValue/p2Value-augmented multi-agent Diplomacy workflow in which agents use compact storyworlds as reasoning scaffolds for coalition and defection forecasting. Across five focused 1915 runs, we observe stable confidence calibration (`mean confidence = 0.60`) with improving forecast accuracy in later layered scenarios (`best mean Brier = 0.2963` on 2026-02-06). The current evidence suggests that increasingly layered storyworlds can improve action-forecast quality when they are tightly matched to the active strategic dilemma ("form-fit" storyworld selection).
+
+## 1. Problem Statement
+
+Classical Diplomacy agents optimize local utility under adversarial uncertainty, but often under-model recursive social beliefs. We introduce a p-manifold framing where:
+
+- `pValue` terms capture first-order beliefs (A's perceived value of B).
+- `p2Value` terms capture second-order beliefs (A's belief about B's belief regarding A or C).
+
+We test whether adding these dimensions through storyworld prompts improves negotiation forecasting and coalition stability reasoning.
+
+## 2. p-Manifold Formalization (Working)
+
+Let each agent `i` have latent strategic state `x_i` and belief fibers over other agents:
+
+$$
+M_i = x_i \oplus \bigoplus_{j \neq i} p_{ij} \oplus \bigoplus_{j \neq i, k \neq i,j} p^2_{ijk}.
+$$
+
+For a forecast event `e` (e.g., near-term aggression), the current scoring objective is Brier minimization:
+
+$$
+\text{Brier}(\hat p, y) = (\hat p - y)^2, \quad y \in \{0,1\}.
+$$
+
+Storyworld desirability scripts inject pValue and p2Value evidence into choice preference updates, approximating:
+
+$$
+U_i(a) = U^0_i(a) + \lambda_1\,p_{ij} + \lambda_2\,p_{ji} + \lambda_3\,p^2_{ijk}.
+$$
+
+## 3. Experimental Setup
+
+Data source: `C:\projects\AI_Diplomacy\results\focused_1915_pvalue_*`  
+Window: 2026-02-05 to 2026-02-06  
+Runs analyzed: 5
+
+Tracked artifacts per run include:
+
+- `storyworld_forecasts.jsonl`
+- `forecast_scores.jsonl`
+- `storyworld_impact.jsonl`
+- `reasoning_diary.jsonl`
+- `storyworld_play_steps.jsonl`
+- `storyworld_play_reasoning_steps.jsonl`
+
+Aggregate counts over all 5 runs:
+
+- Forecast records: `20`
+- Explicit impact records: `20`
+- Play steps: `70`
+- Reasoning-over-play steps: `67`
+- Negotiation diary signal rows: `24 / 56`
+
+## 4. Layered Storyworld Progression
+
+We observe a succession from simpler forecast framings (coalition/defection) to higher-layer manipulation framing (false concession), followed by a best-performing mixed run.
+
+| Run ID | Date/Time | Forecasts | Mean Confidence | Mean Brier | Storyworld Mix |
+|---|---:|---:|---:|---:|---|
+| focused_1915_pvalue_20260205_233410 | 2026-02-05 23:34:10 | 3 | 0.60 | 0.3600 | coalition+defection |
+| focused_1915_pvalue_20260205_233554 | 2026-02-05 23:35:54 | 3 | 0.60 | 0.3600 | coalition+defection |
+| focused_1915_pvalue_20260206_000333 | 2026-02-06 00:03:33 | 2 | 0.60 | 0.3600 | coalition+backstab |
+| focused_1915_pvalue_20260206_000643 | 2026-02-06 00:06:43 | 6 | 0.60 | 0.3763 | false_concession-heavy |
+| focused_1915_pvalue_20260206_112347 | 2026-02-06 11:23:47 | 6 | 0.60 | **0.2963** | false_concession + coalition + backstab |
+
+Storyworld-level mean Brier across available samples:
+
+- `forecast_coalition_p`: `0.3600` (n=6)
+- `forecast_defection_p`: `0.3600` (n=3)
+- `forecast_backstab_p`: `0.3600` (n=3)
+- `forecast_false_concession_p`: `0.3244` (n=8)
+
+## 5. Form-Fit Storyworld Hypothesis
+
+The current read is that performance gains come less from depth alone and more from **fit** between storyworld rhetorical structure and active board-state incentives.
+
+Working selection rule:
+
+$$
+S^* = \arg\min_{S \in \mathcal{S}} \mathbb{E}[\text{Brier} \mid S, \phi_t],
+$$
+
+where `S` is a candidate storyworld and `\phi_t` encodes current strategic context (threat map, alliance commitments, tempo pressure, and contradiction risk).
+
+## 6. Multi-Agent Reasoning Interpretation
+
+Evidence from `reasoning_diary.jsonl` and `storyworld_impact.jsonl` indicates agents are using forecast rhetoric to:
+
+- stabilize coalition messages with explicit probabilities,
+- justify guarded concessions as trap-setting,
+- communicate contingency plans to multiple recipients.
+
+The next step is to separate narrative compliance from genuine policy shift by testing counterfactual swaps of storyworld assignment at fixed board states.
+
+## 7. Limitations (Current Stub)
+
+- Small run count (`n=5`) and non-randomized assignment.
+- Confidence values are currently concentrated at `0.60`, limiting calibration analysis.
+- Effects may be confounded by prompt drift, recipient set differences, and phase-specific board pressure.
+
+## 8. Next Experiments (Planned)
+
+1. Run ablations over pValue-only vs pValue+p2Value desirability scripts.
+2. Add form-fit selector trained on prior phase features `\phi_t`.
+3. Evaluate coalition durability and betrayal latency as secondary outcomes.
+4. Expand to 4-7 player focused simulation slices with fixed scenario seeds.
+
+## Appendix A: Reproducibility Pointers
+
+Primary run directories:
+
+- `C:\projects\AI_Diplomacy\results\focused_1915_pvalue_20260205_233410`
+- `C:\projects\AI_Diplomacy\results\focused_1915_pvalue_20260205_233554`
+- `C:\projects\AI_Diplomacy\results\focused_1915_pvalue_20260206_000333`
+- `C:\projects\AI_Diplomacy\results\focused_1915_pvalue_20260206_000643`
+- `C:\projects\AI_Diplomacy\results\focused_1915_pvalue_20260206_112347`
+
+Related storyworld bank (current working set):
+
+- `C:\projects\AI_Diplomacy\ai_diplomacy\storyworld_bank_focus_1915`