game-theory - SKILL.md Agent Skill

name: game-theory description: > Backward induction and game tree analysis for research strategy selection. Provides dimension extraction templates, strategy card formats, sensitivity analysis framework, and expected value calculations. Use when evaluating which research approach combination has the highest probability of exceeding SOTA, or when building a strategy matrix.

Game-Theoretic Research Strategy Analysis

Dimension Extraction Template

From the literature knowledge base, extract independent axes of variation:

dimensions:
  D1_representation:
    name: "Feature Representation"
    options:
      - id: d1a
        name: "Raw time-domain"
        known_in: ["Paper1", "Paper2"]     # who already used this
      - id: d1b
        name: "Frequency-domain (FFT/STFT)"
        known_in: ["Paper3"]
    # ... more options

  D2_architecture:
    name: "Core Architecture"
    options: [...]

  # Typically 4-7 dimensions, 3-5 options each

Independence rule: Changing one dimension must NOT force changes in another. Mutual exclusivity: Options within a dimension are mutually exclusive.

Strategy Card Template

For each viable combination:

strategy_id: S-{number}
combination: { D1: d1c, D2: d2d, D3: d3b, D4: d4b, D5: d5b }

scores:
  feasibility: X/10          # Can we actually build this?
  novelty: X/10              # Is this new enough for the target venue?
  sota_potential: X/10        # Probability of beating SOTA?
  theoretical_soundness: X/10 # Is the math clean?

backward_induction:
  target_outcome: "Metric > threshold on Dataset"
  required_properties:
    - property: "Must capture multi-scale features"
      provided_by: "D1=d1c (CWT)"
    - property: "Must be robust to noise"
      provided_by: "D3=d3b (Lipschitz)"
  critical_success_factors:
    - "Parameter X must be tuned correctly"

expected_value:
  improvement_over_sota: "+X.X%"
  confidence: "LOW | MEDIUM | HIGH"

Backward Induction Procedure

Define terminal payoffs: For each strategy, estimate P(beat SOTA) and E[improvement]
Identify chance nodes: Training stability, data quality, hyperparameter sensitivity
Assign probabilities: Based on literature evidence and domain knowledge
Propagate backwards: E[value] = Σ p(chance) × payoff(decision)
Select: Strategy with highest risk-adjusted E[value]

Risk adjustment: risk_adjusted = E[value] × (1 - variance_penalty)

Sensitivity Analysis Template

For top 3 strategies, evaluate each critical parameter:

Parameter         Base    Range        Impact    Notes
────────────────────────────────────────────────────
[param_name]      [val]   [low, high]  HIGH/MED  [why it matters]

Robustness verdict:

All critical params right → X% chance of beating SOTA
2/3 right → Y% chance
1/3 right → Z% chance

Probability Calibration Rules

NEVER assign P > 0.90 to any single strategy (overconfidence kills research)
NEVER assign P < 0.05 unless the approach is fundamentally flawed
Use literature reproduction rates as anchors (~60-70% of ML papers reproduce)
Downweight novel combinations (less evidence) vs well-tested ones