Truthful Double Auctions under Approximate VCG: Immediate-Penalty Enforcement in P2P Energy Trading

This paper examines truthful double auctions when exact VCG allocation is computationally infeasible and repeated-game punishments are impractical. We analyze an $α$-approximate VCG mechanism and show that truthful reporting becomes a subgame-perfect equilibrium when the immediate penalty exceeds the incentive gap created by approximation, scaled by monitoring accuracy. To validate this result, we construct a PPO-based multi-agent reinforcement learning environment for P2P smart-grid trading, where prosumers incur penalties for bidding far from their true valuations. Across systematic experiments varying approximation accuracy, tolerance, penalty magnitude, and discounting, the learned behavior closely matches theoretical predictions. The findings demonstrate that immediate-penalty approximate VCG mechanisms provide a practical and transparent approach to sustaining truthful behavior in distributed market settings.