Emergent Role Assignment

# Emergent Role Assignment

**Category:** Phase 3 Core - Self-Organization
**Status:** Skeleton Implementation
**Dependencies:** `sheaf-theoretic-coordination`, `chemical-organization-theory`

## Overview

Implements spontaneous role assignment in multi-agent systems through self-organization, dynamic hierarchy adaptation, and reward-based emergence without central coordination.

## Capabilities

- **Spontaneous Hierarchy**: Agents self-organize into hierarchical structures
- **Dynamic Role Adaptation**: Roles change based on task demands
- **Reward-Based Emergence**: Roles emerge from collective optimization
- **Stability Analysis**: Verify organizational stability and convergence

## Core Components

1. **Role Dynamics** (`role_dynamics.jl`)
   - Role state representation
   - Transition dynamics between roles
   - Stability attractors

2. **Hierarchy Formation** (`hierarchy_formation.jl`)
   - Emergent leadership via fitness
   - Span of control optimization
   - Dynamic reorganization triggers

3. **Reward Shaping** (`reward_shaping.jl`)
   - Collective reward functions
   - Credit assignment without centralization
   - Multi-agent learning objectives

4. **Stability Verification** (`stability_verification.jl`)
   - Lyapunov function construction
   - Convergence guarantees
   - Resilience to perturbations

## Integration Points

- **Input from**: `sheaf-theoretic-coordination` (consensus on roles)
- **Output to**: `chemical-organization-theory` (roles as stable organizations)
- **Coordinates with**: `feedforward-learning-local` (local learning signals)

## Usage

```julia
using EmergentRoleAssignment

# Define multi-agent system
agents = [Agent(id=i, capabilities=rand(5)) for i in 1:20]
environment = GridWorld(10, 10)

# Initialize role assignment system
role_system = RoleSystem(
    n_roles=4,
    transition_rates=0.1,
    reward_fn=collective_foraging_reward
)

# Simulate emergence
trajectory = simulate_emergence(role_system, agents, environment, steps=1000)

# Analyze stability
stability = analyze_role_stability(trajectory)
hierarchy = extract_hierarchy(trajectory.final_state)
```

## References

- Bonabeau et al. "Self-Organization in Social Insects" (1997)
- Wolpert & Tumer "Optimal Payoff Functions for Members of Collectives" (1999)
- Tumer & Wolpert "A Survey of Collectives" (2004)

## Implementation Status

- [x] Basic role dynamics
- [x] Simple hierarchy formation
- [ ] Full reward shaping framework
- [ ] Stability verification
- [ ] Benchmark on multi-agent tasks