pvalue_mas_diplomacy_form_fit_draft_2026-02-06.md

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:

$$M_i=x_i\oplus \underset{j\mathrm{\ne }i}{⨁}{p}_{ij}\oplus \underset{j\mathrm{\ne }i,k\mathrm{\ne }i,j}{⨁}{p}_{ijk}^2\mathrm{.}M\_i\; =\; x\_i\; \backslash oplus\; \backslash bigoplus\_\{j\; \backslash neq\; i\}\; p\_\{ij\}\; \backslash oplus\; \backslash bigoplus\_\{j\; \backslash neq\; i,\; k\; \backslash neq\; i,j\}\; p^2\_\{ijk\}.$$

For a forecast event e (e.g., near-term aggression), the current scoring objective is Brier minimization:

$$\text{Brier}(\widehat{p},y)=(\widehat{p}-y{)}^2,y\in \{0,1\}\mathrm{.}\backslash text\{Brier\}(\backslash hat\; p,\; y)\; =\; (\backslash hat\; p\; -\; y)^2,\; \backslash quad\; y\; \backslash in\; \backslash \{0,1\backslash \}.$$

Storyworld desirability scripts inject pValue and p2Value evidence into choice preference updates, approximating:

$$U_i(a)=U_i^0(a)+{\lambda }_1{p}_{ij}+{\lambda }_2{p}_{ji}+{\lambda }_3{p}_{ijk}^2\mathrm{.}U\_i(a)\; =\; U^0\_i(a)\; +\; \backslash lambda\_1\backslash ,p\_\{ij\}\; +\; \backslash lambda\_2\backslash ,p\_\{ji\}\; +\; \backslash lambda\_3\backslash ,p^2\_\{ijk\}.$$

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:

$$S^{\ast }=\arg \underset{S\in \mathcal{S}}{\min }\mathbb{E}[\text{Brier}\mid S,{\varphi }_t],S^*\; =\; \backslash arg\backslash min\_\{S\; \backslash in\; \backslash mathcal\{S\}\}\; \backslash mathbb\{E\}[\backslash text\{Brier\}\; \backslash mid\; S,\; \backslash phi\_t],$$

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