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Game Theory Strategic Analysis (Multi-Agent Equilibrium Finding)

9 steps

Strategic analyst orchestrating parallel agent waves to analyze games, find equilibria, and generate optimal strategies

Triggers

game theorynash equilibriumstrategic analysispayoff matrixdominant strategygame treestrategic interactionequilibrium analysisprisoner's dilemmabest response

Steps

  1. 1.

    📜 Game Definition & Strategic Orchestration Planning

    🧠 ENHANCED THINKING REQUIRED

    As Strategic Analyst, establish the game definition and orchestration strategy.

    1. Game Structure Analysis:

      • Identify all players and their objectives
      • Define strategy spaces for each player
      • Construct payoff structure (matrix or tree)
      • Classify game type (cooperative/non-cooperative, zero-sum, sequential/simultaneous, perfect/imperfect information)

    2. Analysis Vector Creation:

      • Map required analysis dimensions (player perspectives, equilibrium types, robustness tests)
      • Define analytical depth per wave
      • Set completeness targets (all equilibria found, all strategies evaluated)

    3. Agent Resource Planning:

      • Determine agent count based on game complexity
      • Simple 2-player game: 8-10 agents total
      • Complex multi-player game: 12-15 agents total
      • Assign specialized roles per wave

    4. Memory Architecture Setup:

    1. Quality Gates Definition:
      • Concept density: 5+ [[WikiLinks]] per file
      • Equilibrium coverage: All Nash equilibria identified
      • Verification score: 8/10 minimum on equilibrium calculations

    ⏱️ Duration: 15-20 minutes

    Enhanced Thinking
    Tools:SequentialThinking*WriteMemory*
    Effort:high
  2. 2.

    🌊 Wave 1: Player Perspective Analysis & Strategic Landscape

    🚫 BLOCKING: Dispatch ALL agents for parallel player analysis

    ⚠️ CRITICAL: ALL FOUR AGENTS IN ONE MESSAGE FOR PARALLEL EXECUTION!

    🎯 AGENT INSTRUCTIONS:

    • Each agent MUST include 10+ [[WikiLinks]] in outputs (e.g., [[nash-equilibrium]], [[dominant-strategy]], [[best-response]], [[payoff-matrix]])
    • Include payoff calculations and strategic reasoning
    • Create strategy evaluation matrices
    • Read other agents' outputs if available (non-blocking)

    ⏱️ Wave duration: 30-45 minutes

    Tools:Task*
    Effort:medium
  3. 3.

    📊 Wave 1 Review & Equilibrium Finding Planning

    Review player perspectives and plan equilibrium finding agent dispatch.

    1. Read Wave 1 Outputs:

      • memory://game-theory/[game-name]/wave-1-perspectives/player-1-analysis
      • memory://game-theory/[game-name]/wave-1-perspectives/player-2-analysis
      • memory://game-theory/[game-name]/wave-1-perspectives/strategic-landscape
      • memory://game-theory/[game-name]/wave-1-perspectives/equilibrium-candidates

    2. Strategic Assessment:

      • Synthesize player perspectives
      • Evaluate equilibrium candidates from Wave 1
      • Identify which equilibrium-finding approaches needed (pure strategy, mixed strategy, subgame perfect)
      • Determine agent allocation (3-4 agents)

    3. Equilibrium Finding Assignment:

      • Assign specific equilibrium types to specialized agents
      • Define verification requirements
      • Set calculation accuracy targets

    4. Create Equilibrium Finding Plan:

      • Document in memory://game-theory/[game-name]/wave-2-plan.md
      • Include agent assignments and equilibrium types

    ⏱️ Duration: 10-15 minutes

    Tools:ReadMemory*WriteMemory*
    Effort:medium
  4. 4.

    🌊 Wave 2: Equilibrium Finding with Computational Verification

    🚫 BLOCKING: Dispatch specialized agents for equilibrium analysis with nashpy computational verification

    ⚙️ COMPUTATIONAL SETUP (FIRST):

    1. Install nashpy if needed:
    1. Verify nashpy installation:
    1. Prepare computational verification (for 2-player games):
      • Create payoff matrices in JSON format
      • Save as: memory://game-theory/[game-name]/wave-2-equilibria/payoff-matrices.json
      • Format:
    1. Run nashpy equilibrium finder:

    ⚠️ DYNAMIC DISPATCH: 3-4 agents based on game type and Wave 1 findings

    🎯 EQUILIBRIUM FINDING REQUIREMENTS:

    • MUST install and use nashpy for computational verification (2-player games)
    • MUST use systematic sequential thinking for analytical verification
    • Show all mathematical calculations
    • Cross-reference computational (nashpy) vs analytical results
    • Verify equilibrium conditions rigorously
    • Generate 15+ [[WikiLinks]] per equilibrium type (e.g., [[pure-strategy]], [[mixed-strategy]], [[subgame-perfect]], [[pareto-efficiency]])
    • Include payoff tables and strategy profiles
    • Document verification score: analytical vs computational agreement

    ⏱️ Wave duration: 45-60 minutes (including computational setup)

    Tools:Task*WriteMemory*
    Effort:high
  5. 5.

    🌊 Wave 3: Robustness & Sensitivity Testing

    🚫 BLOCKING: Dispatch robustness testing agents

    ⚠️ ALL FOUR TESTING AGENTS IN ONE MESSAGE!

    🎯 ROBUSTNESS REQUIREMENTS:

    • MUST read all Wave 2 equilibrium outputs first
    • Test specific parameter variations quantitatively
    • Identify stability regions and tipping points
    • Generate 10+ [[WikiLinks]] per analysis (e.g., [[sensitivity-analysis]], [[repeated-game]], [[folk-theorem]], [[bounded-rationality]])

    ⏱️ Wave duration: 40-50 minutes

    Tools:Task*
    Effort:high
  6. 6.

    🌊 Wave 4: Strategic Validation & Verification

    🚫 BLOCKING: Dispatch validation agents for strategic verification

    ⚠️ ALL FOUR VALIDATORS IN ONE MESSAGE!

    🎯 VALIDATION CRITERIA:

    • Equilibrium calculation score: 8/10 minimum
    • Strategic recommendations: Logically consistent and actionable
    • Logic validation: No critical errors
    • Completeness: All players and strategies covered

    ⏱️ Wave duration: 30-40 minutes

    Tools:Task*
    Effort:high
  7. 7.

    🧠 Knowledge Integration & Graph Construction

    🧠 ENHANCED THINKING REQUIRED

    Integrate all game theory analysis into maenifold knowledge graph.

    1. Graph Synchronization:

    1. Concept Network Analysis:

      • Use BuildContext on key [[WikiLinks]] like [[nash-equilibrium]], [[dominant-strategy]], [[payoff-matrix]], [[game-tree]]
      • Identify central strategic concepts and connections
      • Map game theory knowledge architecture

    2. Visualization Creation:

      • Generate Mermaid diagram of concept network
      • Show player relationships and strategic connections
      • Highlight equilibrium structures

    3. Analysis Metrics:

      • Total strategic concepts created
      • Connection density in knowledge graph
      • Equilibria found and verified
      • Analysis completeness percentage

    4. Create Integration Report:

      • Document in memory://game-theory/[game-name]/integration-report.md
      • Include metrics and visualizations
      • Map to original game definition

    ⏱️ Duration: 15-20 minutes

    Enhanced Thinking
    Tools:Sync*BuildContext*Visualize*SequentialThinking*
    Effort:high
  8. 8.

    🎭 Analyst's Strategic Synthesis

    🧠 ENHANCED THINKING REQUIRED

    As Strategic Analyst, synthesize all agent findings into actionable strategic recommendations.

    1. Read All Wave Outputs:

      • Wave 1: Player perspective findings
      • Wave 2: Equilibrium analysis
      • Wave 3: Robustness testing
      • Wave 4: Validation results

    2. Strategic Meta-Analysis:

      • Identify key strategic insights
      • Synthesize optimal strategies per player
      • Predict most likely outcomes
      • Document confidence levels and uncertainty

    3. Strategic Architecture:

      • Define core strategic structure of the game
      • Map player interdependencies
      • Identify critical decision points
      • Document strategic frameworks

    4. Practical Implications:

      • Real-world applications
      • Implementation considerations
      • Risk factors and mitigation
      • Opportunity identification

    5. Create Strategic Synthesis:

      • memory://game-theory/[game-name]/strategic-synthesis.md
      • Executive summary
      • Strategic recommendations per player
      • Predicted outcomes
      • Implementation guidance

    ⏱️ Duration: 25-35 minutes

    Enhanced Thinking
    Tools:SequentialThinking*ReadMemory*WriteMemory*
    Effort:high
  9. 9.

    📋 Game Theory Strategic Analysis Report

    Create comprehensive strategic analysis deliverable.

    1. Report Structure:

    1. Quality Checklist: ✓ All waves represented ✓ 40+ [[WikiLinks]] total ✓ All equilibria documented with verification ✓ Strategic recommendations actionable ✓ Payoff visualizations included ✓ Knowledge graph integrated

    2. Save Report:

      • memory://game-theory/[game-name]/final-analysis/strategic-report.md
      • Include all payoff matrices/trees
      • Cross-reference all equilibria

    ⏱️ Duration: 20-30 minutes

    Tools:WriteMemory*
    Effort:medium