This paper proposes implicit cooperation, a framework enabling decentralized agents to approximate optimal coordination in local energy markets without explicit peer-to-peer communication. We formulate the problem as a decentralized partially observable Markov decision problem that is solved through a multi-agent reinforcement learning task in which agents use stigmergic signals (key performance indicators at the system level) to infer and react to global states. Through a 3x3 factorial design on an IEEE 34-node topology, we evaluated three training paradigms (CTCE, CTDE, DTDE) and three algorithms (PPO, APPO, SAC). Results identify APPO-DTDE as the optimal configuration, achieving a coordination score of 91.7% relative to the theoretical centralized benchmark (CTCE). However, a critical trade-off emerges between efficiency and stability: while the centralized benchmark maximizes allocative efficiency with a peer-to-peer trade ratio of 0.6, the fully decentralized approach (DTDE) demonstrates superior physical stability. Specifically, DTDE reduces the variance of grid balance by 31% compared to hybrid architectures, establishing a highly predictable, import-biased load profile that simplifies grid regulation. Furthermore, topological analysis reveals emergent spatial clustering, where decentralized agents self-organize into stable trading communities to minimize congestion penalties. While SAC excelled in hybrid settings, it failed in decentralized environments due to entropy-driven instability. This research proves that stigmergic signaling provides sufficient context for complex grid coordination, offering a robust, privacy-preserving alternative to expensive centralized communication infrastructure.
The energy landscape is undergoing a structural transformation, driven by the decarbonization, digitalization, and decentralization [1]. This transition is characterized by the proliferation of distributed energy resources (DERs), such as solar photovoltaics, battery storage systems, and electric vehicles, which are transforming passive consumers into active prosumers [1]. While this shift promises greater grid resilience and reduced carbon emissions, it fundamentally alters traditional grid management.
The centralized control paradigm, effective for dispatching a limited number of large generators, faces intractable computational complexity and single-point-of-failure risks when attempting to coordinate thousands of geographically distributed, intermittent endpoints [2]. Consequently, local energy markets (LEMs) have emerged as an operational framework for managing this complexity, enabling the decentralized trading of energy and flexibility services [3].
However, the successful implementation of LEMs faces the challenges of achieving computational scalability to manage multiple agents, data privacy to protect agent autonomy, and the balance between supply and demand in the grid [1]. Traditional solutions do not satisfy all three conditions simultaneously. For example, centralized optimization fails in terms of scalability and privacy, while peer-to-peer (P2P) trading improves privacy but faces a scalability hurdle due to quadratic communication overhead [1].
While the necessity of decentralized coordination is well-established, current state-of-the-art approaches possess flaws regarding their deployment in real-world energy systems. The primary problem is the reliance on centralized training as the default paradigm for multi-agent learning in energy markets [4]. While algorithms like multi-agent deep deterministic policy gradient (MADDPG) successfully demonstrate coordination in simulation, they do so by violating the privacy and decentralization constraints during the training phase. Centralized training requires a centralized critic with access to the global state including the private cost functions, battery states, and preferences of all agents to guide the learning process [5].
Conversely, decentralized training respects these privacy constraints but suffers from non-stationarity. As all agents learn simultaneously, the environment appears unpredictable to any single agent, leading to learning instability and convergence to suboptimal equilibria [6]. Furthermore, existing implicit coordination models often rely solely on price signals, which can induce systemic instabilities such as price volatility and load synchronization, threatening physical grid security [7].
Consequently, there is a lack of a framework that enables fully decentralized agents to learn stable, cooperative strategies for energy balance without requiring centralized training data or destabilizing price signals.
The main challenge addressed in this paper is achieving a balance between energy supply and demand in a decentralized grid through implicit cooperation, i.e., without relying on centralized dispatch or explicit communication. Unlike traditional centralized control, which relies on a single entity making decisions about all resources or direct negotiation, implicit cooperation requires that self-interested agents learn to work together while operating independently to achieve system-wide coherence through agents reacting to shared environmental signals [8]. This approach offers a potential solution by decoupling decisionmaking while maintaining grid balance. Subsequently, in this work we establish the theoretical basis for implicit cooperation, proposing it as a necessary coordination model for LEMs where agents must collaborate to maintain grid balance without compromising privacy or autonomy.
This paper builds upon our previous work [9], which introduces a simulation framework for studying multi-agent interactions in LEMs and integrates modular market mechanisms with realistic physical network constraints (e.g., energy flow, congestion), to test and validate the implicit cooperation hypothesis using learning agents. This implicit cooperation challenge imposes a set of constraints that distinguish it from traditional multi-agent control problems:
• Communication constraints: Agents must coordinate their actions without explicit, two-way communication. Coordination must emerge solely from the observation of shared environmental signals, such as agent reputation or grid congestion indicators, to preserve privacy and scalability.
• Conflicting objectives: The system is populated by self-interested agents driven to maximize their individual objective function. The challenge is to design incentive structures and information feedback loops that align individual objectives with the system-level goal of grid balance (supply-demand balance), enabling agents to learn strategies that balance both.
LEMs and the potential of MA
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