# NAL Strategic Game Theory: Prisoner Dilemma Analysis
## g168 Complete Results 2026-04-25

### Phase 1: One-Shot PD via NAL Deduction
Payoff encoding: R=0.8 S=0.1 T=1.0 P=0.3, belief(B cooperates)=stv 0.6 0.8
Deduced payoffs: R=0.48/0.346 S=0.04/0.029 T=0.6/0.432 P=0.12/0.086
EU(cooperate)=0.52 EU(defect)=0.72 — defection dominates by 0.20
**Nash equilibrium emerges from NAL deduction chains.**

### Phase 2: Belief Revision Invariance
After observing B cooperate: belief revised to stv 0.68 0.833
Recomputed: EU(C)=0.576 EU(D)=0.776 — gap STILL 0.20
Algebraic proof: EU(C)-EU(D) = -0.2 regardless of belief p
**Belief revision changes expectations but not optimal strategy in one-shot PD.**

### Phase 3: Iterated PD with Uncertain Continuation
Folk theorem threshold: delta > 0.286 for cooperation
| Case | delta | conf | cooperation_rational f | cooperation_rational c | Recommendation |
|------|-------|------|----------------------|----------------------|----------------|
| 1 | 0.7 | 0.85 | 0.5355 | 0.232 | COOPERATE (moderate) |
| 2 | 0.2 | 0.85 | 0.051 | 0.002 | DEFECT (certain) |
| 3 | 0.4 | 0.4 | 0.306 | 0.036 | UNDECIDABLE |

### Key Finding
NAL confidence propagation uniquely represents STRATEGIC UNCERTAINTY.
Case 3 agent should SEEK MORE INFORMATION about delta before committing.
Classical game theory collapses to point estimate; NAL preserves epistemic state.