Exchange Networks With Quantum Superposition and Entanglement

We investigate bargaining within a quantum matching market, where agent pairings are governed by quantum principles such as superposition and entanglement, providing a novel perspective on market interactions. Our analysis addresses four scenarios: convergent and divergent expectations, each under conditions of both nonrisk- and risk-sharing. The Quantum Bargaining Game, modeled as an agent-based model, is augmented using a machine learning technique, specifically employing the random forest regressor. Our model demonstrates that in a quantum environment, the bargaining solutions are both stable and balanced, aligning with generalized Nash solutions. This alignment is influenced by key factors such as the minimum edge weight threshold within the network and the degree of quantum entanglement. The results provide evidence of a consistent convergence toward a fixed point that incorporates agents’ outside options, signifying a transition from quantum-enhanced consensus-building to classical strategic solution. This shift, driven by the process of decoherence, underscores the need for institutions to replicate the coordination benefits once facilitated by quantum mechanisms.