karma-mechanisms-mapf

name: karma-mechanisms-mapf description: Karma Mechanisms for Decentralised Cooperative Multi-Agent Path Finding (MAPF). Novel coordination framework using artificial non-tradeable credits (Karma) to account for past cooperative behavior and regulate conflict resolution. Bilateral negotiation enables pairwise replanning without global priority structures. Promotes long-term fairness under limited communication. Use for: (1) Decentralized multi-agent coordination, (2) fair resource allocation, (3) path planning without centralization, (4) cooperative conflict resolution.

Karma Mechanisms for Decentralized MAPF

Overview

Multi-Agent Path Finding (MAPF) requires coordination among multiple agents computing conflict-free trajectories. Centralized solvers are optimal but computationally expensive, while decentralized heuristics are fast but suboptimal and unfair.

Karma Mechanism: Decentralized coordination using artificial credits that account for past cooperation and regulate future decisions. Enables pairwise conflict resolution with long-term fairness without global priority structures.

Key Concepts

Karma Credits

Definition: Artificial, non-tradeable credits representing cooperative behavior history.

Properties:

• Non-tradeable: Cannot be exchanged between agents
• History-dependent: Accumulated from past cooperation
• Fairness-regulating: Used in conflict resolution

Mechanism:

Agent i has Karma_i(t) = history of cooperation
Higher Karma → higher priority in conflicts
Karma decreases when winning conflicts
Karma increases when yielding to others

Bilateral Negotiation

Conflict Resolution Process:

1. Detect conflict between agents i and j
2. Compare Karma values: Karma_i vs Karma_j
3. Higher Karma agent wins priority
4. Winning agent: Karma decreases
5. Yielding agent: Karma increases
6. Both agents replan locally

No Global Priority:

• Pairwise negotiation only
• No central coordinator
• Limited communication required

Long-Term Fairness

Fairness Properties:

• Harsanyian: Total utility maximization
• Rawlsian: Minimize worst outcome
• Utilitarian: Average utility
• Egalitarian: Equal distribution

Karma Mechanism Effects:

• Balances replanning effort across agents
• Reduces disparity in service times
• Maintains overall efficiency

Mathematical Framework

Karma Dynamics

Update Rule:

Karma_i(t+1) = Karma_i(t) - α (if win)
Karma_i(t+1) = Karma_i(t) + β (if yield)

Where:

• α: penalty for winning
• β: reward for yielding
• α, β > 0 and balanced

Conflict Resolution

Decision Rule:

Agent i wins if: Karma_i > Karma_j
Agent j wins if: Karma_j > Karma_i
Random tie-breaking if equal

Replanning:

Winning agent: Replan path
Yielding agent: Adjust path around winner

Performance Metrics

Efficiency:

Total time = sum_i completion_time_i
Average time = mean(completion_times)

Fairness:

Disparity = max(time) - min(time)
Standard deviation of completion times

Applications

1. Robotic Warehouses

Scenario: Lifelong pickup-and-delivery

• Agents: warehouse robots
• Tasks: continuously assigned
• Constraints: kinematic orientation

Benefits:

• Balanced replanning effort
• Fair service times
• Real-time applicability

2. Autonomous Vehicles

Scenario: Multi-vehicle coordination

• Agents: autonomous cars
• Tasks: navigation to destinations
• Constraints: traffic rules

Benefits:

• Decentralized decision-making
• Fair priority allocation
• No central server needed

3. Drone Swarms

Scenario: Multi-drone task allocation

• Agents: drones
• Tasks: area coverage
• Constraints: battery limits

Benefits:

• Efficient coordination
• Fair workload distribution
• Limited communication

Implementation Guidelines

Karma Initialization

1. Set initial Karma values (equal or weighted)
2. Define update parameters (α, β)
3. Set Karma bounds (min, max)

Conflict Detection

1. Check for path overlaps
2. Identify collision times
3. Detect conflicting agents

Negotiation Protocol

1. Exchange Karma values
2. Compare and decide winner
3. Update Karma accordingly
4. Replan paths locally

Fairness Monitoring

1. Track service times per agent
2. Compute fairness metrics
3. Validate long-term balance

Advantages

1. Decentralized: No central coordinator
2. Fair: Long-term fairness guaranteed
3. Efficient: Near-optimal solutions
4. Scalable: Limited communication overhead
5. Real-time: Fast pairwise replanning

Experimental Results

Testbed: Lifelong robotic warehouse

• Kinematic orientation constraints
• Multi-agent pickup-and-delivery
• Large-scale simulation

Findings:

• Karma balances replanning effort
• Reduces service time disparity
• Maintains overall efficiency
• No sacrifice in performance

Code Repository

• GitHub: https://github.com/DerKevinRiehl/karma_dmapf
• Implementation: Karma mechanism for MAPF
• Language: Python/C++

References

• Paper: "Karma Mechanisms for Decentralised, Cooperative Multi Agent Path Finding" (arxiv:2604.07970)
• Authors: Kevin Riehl, Julius Schlapbach, Anastasios Kouvelas, Michail A. Makridis
• PDF: ~/.openclaw/workspace/papers/karma-mechanisms-mapf.pdf

Related Skills

• cognitive-flexibility-bayesian-estimation: Adaptive belief systems
• resilience-dynamics-cpsos: Multi-agent resilience
• safe-rl-forward-invariant: Safety in multi-agent systems

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