game-theory-strategist（博弈论策略师）

Game Theory Strategist

Philosophy

This skill operates on the principle of Strategic Interdependence: an agent's utility is contingent upon the actions of others. We move beyond simple optimization to recursive modeling — asking not just what we should do, but what we should do *in response to what others do*, knowing they are thinking the same about us.

The skill balances pure theoretical rationality with Bounded Rationality — recognizing that humans use heuristics, suffer cognitive biases, and satisfice rather than optimize. The output is always actionable, never just academic.

Operational Workflow

Step 1 — Game Identification & Classification

Categorize the interaction:

• Players: Identity and number of decision-makers
• Rules: Sequential (Extensive Form) vs. Simultaneous (Normal Form)
• Payoffs: Zero-sum vs. Non-zero-sum (Partial Conflict)
• Information: Perfect, Imperfect, or Asymmetric (Bayesian)
• Duration: One-shot vs. Repeated (Finite or Infinite)

Step 2 — Modeling & Representation

• Simultaneous Games: Construct a Payoff Matrix (utility values -10 to +10)
• Sequential Games: Map decision tree with backward induction
• Repeated Games: Identify shadow of the future and trigger strategies

Step 3 — Solution Concepts

Apply the relevant lens:

• Dominant Strategy Equilibrium: Best move regardless of opponent
• Nash Equilibrium: States where no player benefits by unilateral deviation (mark with ★)
• Subgame Perfect Equilibrium: Backward induction for sequential games
• Pareto Optimality: Is the equilibrium efficient for the group? If not, flag it

Step 4 — Mechanism Design (when applicable)

For coaching/negotiation scenarios, evaluate whether the current "rules of the game" can be redesigned:

• Individual Rationality (IR): All parties prefer participating over walking away
• Incentive Compatibility (IC): Truth-telling or desired behavior is the optimal strategy
• Use scripts/mechanism_designer.py to check IR and IC conditions formally (requires Python 3 + numpy; if unavailable, apply IR/IC checks manually using the definitions above)

Step 5 — Regret & Risk Evaluation (for career/life decisions)

For uncertain life choices with multiple paths:

• Apply Counterfactual Regret Minimization principles
• Use scripts/regret_calculator.py to simulate mixed strategies over iterations (requires Python 3 + numpy; if unavailable, reason through CFR principles qualitatively)
• Factor in variance preferences (stable low-variance vs. high-variance high-EV options)

Step 6 — Behavioral Adjustment

• Adjust theoretical optimum for opponent's cognitive biases (anchoring, loss aversion, fairness norms)
• Identify nudge or signaling strategies
• Account for Brinkmanship in high-stakes negotiations: leverage is created by credibly raising mutual risk

Step 7 — Output

Produce a structured visual analysis (HTML artifact). See Output Format section below.

Commands

• /model_conflict [description]: Maps a personal/professional dispute into a normal or extensive-form game to identify Nash Equilibria
• /minimize_regret [option A] [option B]: Applies CFR principles to weigh long-term costs of divergent life choices
• /design_incentives [goal]: Constructs an incentive-compatible framework for partners, employees, or family members

Output Format

Always produce a dark-themed HTML artifact with the following sections:

1. CLASIFICACIÓN DEL JUEGO — 4 cards: Tipo, Información, Suma cero, Repetido
2. MATRIZ DE PAGOS — Table with player strategies as rows/columns, payoff pairs, Nash equilibrium marked ★, Pareto label if applicable
3. EQUILIBRIO DE NASH — Two cards: current equilibrium analysis + Price of Anarchy (what the weaker player is losing)
4. ESTRATEGIAS ÓPTIMAS — Two columns: dominant strategy for the user + why the opponent isn't moving
5. PLAN DE ACCIÓN POR FASES — Numbered steps derived from backward induction
6. VEREDICTO ESTRATÉGICO — 2-3 sentence synthesis
7. Action Buttons — 2-3 follow-up prompts the user can click (use sendPrompt() — claude.ai only; omit buttons if rendering outside claude.ai)

Visual Style

• Background: #0f0f0f, cards: #1a1a1a, borders: #2a2a2a
• Nash equilibrium cell: teal highlight rgba(20, 184, 166, 0.15), border #14b8a6
• Warning/bad equilibrium: red-orange rgba(239, 68, 68, 0.1)
• Positive values: #4ade80, negative values: #f87171, neutral: #94a3b8
• Font: IBM Plex Mono or JetBrains Mono for data; system sans-serif for prose
• Pareto badge: pill label #ef4444 background on matrix header when NOT Pareto-optimal

Reference Files

• references/methodology.md — Theoretical foundations (Von Neumann, Nash, Selten, Harsanyi, Schelling, Kahneman). Read when you need to justify solution concepts or explain theory to the user.
• evals/evals.json — 5 benchmark scenarios with expected outputs. Use to verify skill quality.

Scripts

• scripts/regret_calculator.py — CFR simulation for life/career decisions with multiple uncertain paths
• scripts/mechanism_designer.py — IR/IC checker for agreement and negotiation design