Alliance_Value = Σ(mutual_gains) × trust_coefficient × interaction_frequency

Where:
- mutual_gains = benefits neither player could achieve independently
- trust_coefficient ∈ [0,1] based on historical cooperation reliability
- interaction_frequency = strategic touchpoints per time period

def assess_alliance_potential(external_player, interaction_history):
    """
    Quantitative assessment of alliance formation probability
    """
    resource_complementarity = calculate_capability_overlap(our_skills, their_skills)
    information_transparency = measure_voluntary_disclosure(interaction_history)
    coordination_eagerness = evaluate_synchronization_attempts(their_proposals)
    reputation_entanglement = assess_shared_reputation_stakes(network_analysis)
    
    alliance_score = (
        resource_complementarity * 0.3 +
        information_transparency * 0.25 + 
        coordination_eagerness * 0.25 +
        reputation_entanglement * 0.2
    )
    
    if alliance_score > 0.7:
        return "HIGH_ALLIANCE_POTENTIAL"
    elif alliance_score > 0.4:
        return "MODERATE_ALLIANCE_POTENTIAL" 
    else:
        return "LOW_ALLIANCE_POTENTIAL"

Optimal_Split = argmax[(player1_gain - disagreement1) × (player2_gain - disagreement2)]

Where:
- disagreement_point = outcomes if cooperation fails
- Pareto_efficiency = no alternative split improves both outcomes

class AllianceStability:
    def __init__(self, players, value_function):
        self.players = players
        self.value_function = value_function  # Coalition value
        
    def is_in_core(self, payoff_allocation):
        """
        Check if allocation prevents defection by any sub-coalition
        """
        for coalition in all_possible_coalitions(self.players):
            coalition_value = self.value_function(coalition)
            coalition_allocation = sum(payoff_allocation[p] for p in coalition)
            
            if coalition_value > coalition_allocation:
                return False  # Coalition can improve by defecting
                
        return True  # Allocation is stable

Shapley_Value_i = Σ[(|S|! × (n-|S|-1)! / n!) × (v(S∪{i}) - v(S))]

Where:
- S = all possible coalitions not containing player i
- v(S) = value created by coalition S
- Marginal contribution = v(S∪{i}) - v(S)

class InformationSharingProtocol:
    def __init__(self, classification_levels, trust_ratings):
        self.classifications = {"PUBLIC": 0, "RESTRICTED": 1, "CONFIDENTIAL": 2, "SECRET": 3}
        self.trust_levels = trust_ratings  # Per-ally trust assessment
        
    def authorize_information_sharing(self, information, recipient_ally):
        info_classification = self.classify_information(information)
        ally_clearance = self.trust_levels[recipient_ally]
        
        if ally_clearance >= info_classification:
            return "AUTHORIZED"
        else:
            return "DENIED"

def optimize_resource_allocation(allies, resources, strategic_objectives):
    """
    Maximize collective utility through optimal resource distribution
    """
    # Decision variables: resource allocation to each ally for each objective
    allocation_matrix = create_allocation_variables(allies, resources, strategic_objectives)
    
    # Objective function: maximize total strategic value
    objective = maximize(sum(
        strategic_value(ally, resource, objective) * allocation_matrix[ally][resource][objective]
        for ally in allies
        for resource in resources
        for objective in strategic_objectives
    ))
    
    # Constraints
    constraints = [
        # Resource capacity constraints
        sum(allocation_matrix[ally][resource][objective] 
            for ally in allies for objective in strategic_objectives) <= resource_capacity[resource]
        for resource in resources
    ] + [
        # Fairness constraints (prevent exploitation)
        ally_total_value(ally, allocation_matrix) >= min_acceptable_value[ally]
        for ally in allies
    ]
    
    return solve_optimization(objective, constraints)

Network_Strategic_Power = Σ(ally_individual_power × connection_strength × network_reach)

Where:
- ally_individual_power = their independent strategic capability  
- connection_strength = depth of your relationship
- network_reach = their connections you can access through them

def alliance_portfolio_risk(allies, correlation_matrix, individual_risks):
    """
    Calculate portfolio risk considering ally correlations
    """
    portfolio_variance = 0
    
    for i, ally_i in enumerate(allies):
        for j, ally_j in enumerate(allies):
            weight_i = alliance_weights[ally_i]
            weight_j = alliance_weights[ally_j]
            correlation = correlation_matrix[i][j]
            
            portfolio_variance += (
                weight_i * weight_j * 
                individual_risks[ally_i] * individual_risks[ally_j] * 
                correlation
            )
    
    return math.sqrt(portfolio_variance)

def alliance_health_monitoring(alliance_history, current_performance):
    """
    Predictive analytics for alliance trajectory
    """
    trust_trend = calculate_trust_trend(alliance_history.trust_scores)
    value_trend = calculate_value_trend(alliance_history.mutual_benefits)
    interaction_frequency = current_performance.interaction_rate
    conflict_resolution = current_performance.conflict_success_rate
    
    health_score = (
        trust_trend * 0.3 +
        value_trend * 0.4 + 
        interaction_frequency * 0.15 +
        conflict_resolution * 0.15
    )
    
    if health_score < 0.3:
        return "INTERVENTION_REQUIRED"
    elif health_score < 0.6:
        return "MONITORING_RECOMMENDED"
    else:
        return "ALLIANCE_HEALTHY"

class AllianceAccounting:
    def __init__(self):
        self.value_flows = {"given": [], "received": []}
        self.reciprocity_ratio = 1.0  # Target ratio of given:received
        
    def log_value_exchange(self, value_type, amount, direction):
        timestamp = datetime.now()
        self.value_flows[direction].append({
            "type": value_type,
            "amount": amount, 
            "timestamp": timestamp
        })
        
    def calculate_reciprocity_balance(self, time_window_days=90):
        cutoff_date = datetime.now() - timedelta(days=time_window_days)
        
        recent_given = sum(exchange["amount"] 
                          for exchange in self.value_flows["given"]
                          if exchange["timestamp"] > cutoff_date)
                          
        recent_received = sum(exchange["amount"]
                             for exchange in self.value_flows["received"] 
                             if exchange["timestamp"] > cutoff_date)
        
        if recent_received == 0:
            return float('inf') if recent_given > 0 else 0
            
        return recent_given / recent_received

def analyze_alliance_network_position():
    """
    Calculate your strategic position within the alliance network
    """
    # Build network graph of all allies and their interconnections
    network_graph = build_alliance_network_graph()
    
    # Calculate centrality measures
    degree_centrality = calculate_degree_centrality(network_graph, "you")
    betweenness_centrality = calculate_betweenness_centrality(network_graph, "you") 
    closeness_centrality = calculate_closeness_centrality(network_graph, "you")
    eigenvector_centrality = calculate_eigenvector_centrality(network_graph, "you")
    
    # Strategic implications
    network_power = {
        "direct_influence": degree_centrality,
        "brokerage_power": betweenness_centrality,
        "information_access": closeness_centrality,
        "prestige_association": eigenvector_centrality
    }
    
    return network_power

Strategic_Effectiveness = base_capabilities × (1 + alliance_multiplier)^n

Where:
- base_capabilities = your individual strategic capacity
- alliance_multiplier = average amplification from each alliance
- n = number of active strategic alliances