ETD

• graph neural networks
• graph representation learning
• noncooperative game theory

Graph Neural Networks (GNNs) have emerged as a powerful framework for learning over relational data, supporting applications from molecular modeling to social networks. Despite their success, standard GNNs suffer from fundamental limitations: as depth increases, message passing tends to homogenize node representations (oversmoothing) or compress long-range dependencies through topological bottlenecks (oversquashing). These issues hinder scalability and reduce the discriminative power of embeddings. This thesis proposes a novel extension of the message passing framework that defines aggregation within certain layers as a competitive, game-theoretic interaction among nodes. Each node is modeled as a rational player that strategically allocates aggregation weights to maximize a payoff defined in terms of Dirichlet energy, a metric that measures the diversity of embeddings across graph edges. By framing this interaction as a potential game, we obtain a well-structured layer design where equilibria correspond to stable and energy-preserving aggregation strategies. In this way, competitive layers directly mitigate oversmoothing by maintaining diversity in node embeddings as depth increases, allowing deeper networks to preserve discriminative information and achieve higher accuracy on homophilic benchmarks where standard architectures collapse.