Adversarial Geopolitical Equilibrium MCP Server

Interlocking incomplete-information game analysis across geopolitical arenas. Computes simultaneous Bayesian extensive-form equilibria, models strategic misperception via hypergame theory, simulates sanctions cascades on trade-weighted hypergraphs, analyzes escalation dynamics via Hamilton-Jacobi-Isaacs differential games, solves Colonel Blotto resource allocation across cyber/kinetic domains, designs alliances via Shapley value mechanism design, and forecasts regime transitions.

This MCP server wraps 16 specialized Apify actors spanning sanctions databases, trade flows, economic indicators, financial markets, legislative data, and social intelligence.

Tools

Tool	Description	Key Outputs
compute_interlocking_equilibria	Simultaneous PBE across trade, military, cyber, diplomatic, economic arenas	Strategies, beliefs, linkages, system stability
simulate_geopolitical_agents	Multi-agent simulation with real economic data enrichment	Equilibrium strategies, payoff distributions
analyze_sanctions_cascade	Cascade simulation on trade-weighted hypergraph	Cascade rounds, GDP impact, tipping points
assess_escalation_dynamics	HJI differential game for two-player escalation	Trajectory, peak escalation, nuclear risk, saddle point
design_alliance_mechanism	Cooperative game theory for alliance evaluation	Shapley values, core stability, superadditivity
detect_strategic_misperception	Hypergame theory for belief hierarchy analysis	Misperception gaps, exploitability, stability
evaluate_cyber_kinetic_blotto	Colonel Blotto across cyber/conventional/nuclear/economic/info domains	Allocations, expected wins, critical battlefields
forecast_regime_transitions	Multi-factor logistic regime change prediction	Transition probability, scenario type, risk factors

Data Sources

Actor	Data Source	Used For
OFAC Sanctions Search	US Treasury OFAC	Direct sanctions status
OpenSanctions Search	OpenSanctions DB	International sanctions/PEP
UN COMTRADE	UN trade database	Bilateral trade volumes for cascade modeling
World Bank Indicators	World Bank	GDP, governance, stability indicators
IMF Economic Data	IMF	Macroeconomic indicators
FRED Economic Data	Federal Reserve	US and global economic series
Finnhub Stock Data	Finnhub	Market reactions to geopolitical events
Congress Bill Search	Congress.gov	Sanctions legislation, defense bills
Federal Register	Federal Register	Executive orders, sanctions regulations
Congressional Stock Trades	Congress trades	Insider knowledge signals
Interpol Red Notices	Interpol	International fugitive data
WHO GHO	WHO	Health crisis data for stability modeling
OECD Statistics	OECD	Economic/social indicators
GDACS Disaster Alerts	GDACS	Natural disaster impact on stability
Hacker News	HN	Tech/security community intelligence
Bluesky Social	Bluesky	OSINT social intelligence

Mathematical Foundations

Perfect Bayesian Equilibrium (PBE)

Each geopolitical arena (trade, military, cyber, diplomatic, economic) is modeled as a Bayesian extensive-form game. Players have private types (hawkish/dovish, protectionist/free-trade, etc.) and update beliefs via Bayes' rule:

P(type_j | observed) = P(observed | type_j) * P(type_j) / P(observed)

We compute equilibria via Quantal Response Equilibrium (McKelvey & Palfrey 1995), a softmax generalization of Nash equilibrium that guarantees existence. Temperature parameter controls rationality (0 = perfect rationality, higher = more noise).

Interlocking Games

Arenas are linked: actions in one affect payoffs in others. Linkages are classified as:

• Strategic complements: Escalation in one arena reinforces escalation in the linked arena (e.g., trade ↔ economic)
• Strategic substitutes: Escalation in one reduces incentive in the other (e.g., military ↔ diplomatic)
• Independent: No significant cross-arena effect

Hypergame Theory (Bennett 1977)

Models situations where players disagree about what game is being played. Each player has a subjective game that may differ from the objective game and from other players' subjective games. Belief hierarchy: what A thinks B thinks C believes...

Misperception is the primary cause of unintended escalation in international relations.

Colonel Blotto (Borel 1921, Roberson 2006)

Two or more players allocate limited resources across N battlefields simultaneously. Each battlefield is won by the player who allocates more. The Nash equilibrium involves mixed strategies on the resource simplex.

For asymmetric resources, the weaker player concentrates on fewer battlefields while the stronger player spreads thin — creating strategic vulnerability.

Hamilton-Jacobi-Isaacs (HJI) PDE

Escalation is modeled as a continuous-time differential game:

dV/dt + H(x, nabla V) = 0

where V is the value function and H is the Hamiltonian coupling both players' optimal controls. The state vector x = (escalation_level, posture_1, posture_2, crisis_intensity, deescalation_pressure) evolves under coupled dynamics with stochastic shocks.

Saddle point: The point where escalation direction reverses — the highest escalation the system reaches before deescalation forces dominate.

Cooperative Game Theory

Alliance evaluation uses:

• Shapley value: Fair allocation based on marginal contribution across all possible coalitions
• Core: Set of allocations where no sub-coalition has incentive to deviate
• Nucleolus: Lexicographic minimization of worst-off coalition's excess
• Superadditivity: v(S union T) >= v(S) + v(T) — coalition is worth more than parts

Sanctions Cascade

Threshold model on directed weighted trade hypergraph:

1. Direct sanctions set target nodes to severity 1.0
2. Each round: cumulative pressure from sanctioned trade partners computed
3. When pressure > resilience threshold, node becomes sanctioned
4. Secondary sanctions compliance pressure amplifies cascade
5. GDP impact estimated at 15% per unit of sanctions severity

Supported Countries

20 major state actors with baseline parameters:

US, CN, RU, GB, FR, DE, JP, IN, KR, AU, IL, IR, SA, TR, BR, KP, UA, TW, PK, PL

Connection

Claude Desktop

{
  "mcpServers": {
    "geopolitical-equilibrium": {
      "type": "url",
      "url": "https://adversarial-geopolitical-equilibrium-mcp.apify.actor/mcp?token=YOUR_APIFY_TOKEN"
    }
  }
}

Direct HTTP

curl -X POST https://adversarial-geopolitical-equilibrium-mcp.apify.actor/mcp?token=YOUR_APIFY_TOKEN \
  -H "Content-Type: application/json" \
  -d '{
    "jsonrpc": "2.0",
    "method": "tools/call",
    "params": {
      "name": "analyze_sanctions_cascade",
      "arguments": {
        "target_countries": ["RU"],
        "all_countries": ["US", "CN", "RU", "GB", "DE", "JP", "IN", "TR"]
      }
    },
    "id": 1
  }'

Example Conversations

Sanctions Cascade Analysis

User: What would happen if the US imposed comprehensive sanctions on Russia? Who else gets pulled in?

Assistant: Calls analyze_sanctions_cascade with target_countries=["RU"] and all_countries=["US","CN","RU","GB","DE","JP","IN","TR","KR","AU","BR","SA"]

The cascade simulation ran 4 rounds. Direct sanctions on Russia propagated to 5 additional countries:

• Round 1: Turkey (trade exposure 0.45, above threshold 0.40)
• Round 2: India (secondary sanctions compliance pressure from US)
• Round 3: Brazil (cascaded from India trade linkage)
• Total GDP impact: $890B across all affected actors
• Trade disruption: 12.3% of simulated global trade

Escalation Dynamics

User: How would a US-China crisis over Taiwan escalate?

Assistant: Calls assess_escalation_dynamics with player1="US", player2="CN", initial_crisis_intensity=0.7

HIGH ESCALATION: Peak 6.8/10 reached at t=3.2. Saddle point at level 6.8 — this is where deescalation pressure from international community begins to dominate. Nuclear risk peaked at 4.2%. Stable equilibrium at 2.3 — the crisis eventually settles to moderate tension. Time to deescalation: t=5.4.

Alliance Design

User: Is the QUAD alliance (US, JP, IN, AU) stable?

Assistant: Calls design_alliance_mechanism with countries=["US","JP","IN","AU"]

Alliance is VIABLE: superadditive with 2 core-stable formations. Shapley values: US contributes 42% of coalition value, Japan 24%, India 20%, Australia 14%. The US-Japan sub-alliance is the strongest component. India's inclusion is marginally stable — removing geographic diversity bonus would make it unprofitable.

Limitations

• Baseline actor parameters are approximate and may not reflect current conditions
• PBE computation uses quantal response (bounded rationality) — pure strategy Nash equilibria may exist but not be found
• Sanctions cascade uses simplified gravity model for trade linkages — real trade networks have more complex structure
• HJI escalation dynamics are stochastic — results vary between runs
• Hypergame analysis uses heuristic perception rules — real misperceptions are more nuanced
• Blotto equilibrium is approximate (exact mixed strategy equilibria require continuous distributions)
• Regime transition model is structural, not predictive of specific trigger events

Tips

• Start with compute_interlocking_equilibria for a broad overview, then drill down
• analyze_sanctions_cascade works best with 8+ countries — include major trade partners of targets
• assess_escalation_dynamics is most useful for bilateral crises — it's a 2-player game
• design_alliance_mechanism needs 3+ countries — use for evaluating coalition proposals
• detect_strategic_misperception reveals WHY miscalculations happen — pair with escalation analysis
• forecast_regime_transitions benefits from real data — enable economic data and news enrichment