Managing multiple agents by automatically adjusting incentives (2409.02960v1)

Abstract: In the coming years, AI agents will be used for making more complex decisions, including in situations involving many different groups of people. One big challenge is that AI agent tends to act in its own interest, unlike humans who often think about what will be the best for everyone in the long run. In this paper, we explore a method to get self-interested agents to work towards goals that benefit society as a whole. We propose a method to add a manager agent to mediate agent interactions by assigning incentives to certain actions. We tested our method with a supply-chain management problem and showed that this framework (1) increases the raw reward by 22.2%, (2) increases the agents' reward by 23.8%, and (3) increases the manager's reward by 20.1%.

• The paper presents a manager-agent framework that automatically adjusts incentives to align self-interested agents with global objectives.
• It employs a MARL approach with state and reward augmentation, achieving improvements of 22.2% in raw rewards and 23.8% overall for agents.
• The study demonstrates practical utility in supply chain optimization by diversifying supplier choices to improve order fulfillment ratios.

Incentive-Based Management of Multi-Agent Systems via Automated Manager Agents

Introduction

The paper addresses the challenge of aligning the objectives of self-interested agents in general-sum multi-agent environments with broader system-level or societal goals. While prior work in multi-agent reinforcement learning (MARL) has demonstrated success in zero-sum and cooperative games, scalable solutions for general-sum settings—where agent interests are not perfectly aligned—remain limited. The authors propose a novel framework in which a manager agent dynamically assigns incentives and auxiliary state information to other agents, with the explicit goal of maximizing aggregate system performance while minimizing incentive costs. This approach is motivated by practical scenarios such as supply chain management, where decentralized actors must be coordinated for optimal global outcomes.

Methodology

Multi-Agent Reinforcement Learning with a Manager

The core contribution is the introduction of a manager agent into a Markov Game environment. The manager observes the global state and selects actions that consist of both auxiliary state signals and incentive payments for each agent. The agents' observations and rewards are thus augmented:

• State augmentation: Each agent's state is concatenated with a manager-provided auxiliary state vector.
• Reward augmentation: Each agent's reward is incremented by a manager-provided incentive, which is a function of the agent's previous action and the auxiliary state.

The manager's objective is to maximize the sum of the agents' raw rewards minus the total incentives paid, formalized as:

$$J^M = \sum_t \gamma^t \left\{ \sum_i (r^i_t - \hat{r}^i_t) \right\}$$

where $r^i_t$ is the environment reward for agent $i$ and $\hat{r}^i_t$ is the incentive.

Application to Supply Chain Optimization

The framework is instantiated in a supply chain environment with three factory agents and two suppliers. Each factory agent decides how many parts to order from each supplier, balancing profit maximization and timely order fulfillment (Order Fulfillment Ratio, OFR). The environment is designed such that supplier 0 is cheaper but capacity-constrained, while supplier 1 is more expensive but has higher capacity. Without coordination, agents tend to overload the cheaper supplier, leading to delays and suboptimal global performance.

The manager agent observes the full system state and the agents' previous actions, and outputs auxiliary state vectors for each agent. Incentives are computed as the inner product of the auxiliary state and the agent's previous action, effectively rewarding agents for actions that align with system-level objectives (e.g., ordering from the more expensive supplier when necessary to meet OFR targets).

Training Regime

Both the agents and the manager are trained using DDPG with two-layer fully connected networks. The agents' actions are discretized, and the manager's action space is continuous. Training is conducted over 500 episodes with 10 random seeds, and performance is evaluated on the final 25 episodes.

Experimental Results

The introduction of the manager agent yields significant improvements across multiple metrics:

• Raw reward (excluding incentives): Increased by 22.2%
• Agents' total reward (including incentives): Increased by 23.8%
• Manager's reward (system reward minus incentives): Increased by 20.1%

The results demonstrate that the manager successfully induces agents to diversify their supplier choices, reducing over-reliance on the cheaper supplier and improving the OFR. Notably, the profit component of the agents' reward decreases slightly, but this is offset by a larger increase in the OFR component, leading to a net gain in total reward. The manager learns to minimize incentive payments over time, indicating efficient use of resources.

Implications and Limitations

The proposed manager-agent framework provides a scalable and flexible approach to automated mechanism design in MARL settings. By dynamically adjusting incentives and auxiliary information, the manager can steer self-interested agents toward globally desirable equilibria without requiring centralized control or explicit coordination protocols.

However, the approach assumes that agents are naive RL learners and do not attempt to strategically exploit the manager. In real-world deployments, agents may be more sophisticated or adversarial, necessitating robust manager policies that anticipate and counteract potential gaming of the incentive scheme. Additionally, the method's reliance on high-dimensional observations and continuous action spaces may present computational challenges in larger-scale environments.

Future Directions

Potential avenues for future research include:

• Extending the framework to settings with heterogeneous agent learning algorithms, including non-RL or human agents.
• Investigating robustness to strategic manipulation by agents.
• Exploring alternative manager objectives, such as fairness or risk sensitivity.
• Scaling to more complex, partially observable, or non-stationary environments.
• Integrating with other mechanism design techniques, such as auction-based or contract-theoretic approaches.

Conclusion

The paper presents a principled and empirically validated approach for managing self-interested agents in general-sum MARL environments via a manager agent that dynamically assigns incentives and auxiliary state information. The method achieves substantial improvements in system-level performance in a supply chain optimization task, demonstrating the practical utility of automated incentive design in multi-agent systems. The framework opens new directions for research at the intersection of MARL, mechanism design, and organizational AI.