Automated Market Making for Energy Sharing

TL;DR

This paper introduces an axiomatic framework for automated market makers in local energy sharing markets, analyzing their equilibrium and efficiency through a mean-field game approach with practical numerical results.

Contribution

It develops a novel axiomatic theory for AMMs in energy markets, incorporating mechanisms with linear, Lipschitz payment functions and demonstrating their efficiency and equilibrium properties.

Findings

AMMs can achieve up to 40% gains from trade.

The proposed mechanisms are budget-balanced and ex-ante efficient.

Implementation of batch execution and concentrated liquidity is effective.

Abstract

We develop an axiomatic theory for Automated Market Makers (AMMs) in local energy sharing markets and analyze the Markov Perfect Equilibrium of the resulting economy with a Mean-Field Game. In this game, heterogeneous prosumers solve a Bellman equation to optimize energy consumption, storage, and exchanges. Our axioms identify a class of mechanisms with linear, Lipschitz continuous payment functions, where prices decrease with the aggregate supply-to-demand ratio of energy. We prove that implementing batch execution and concentrated liquidity allows standard design conditions from decentralized finance-quasi-concavity, monotonicity, and homotheticity-to construct AMMs that satisfy our axioms. The resulting AMMs are budget-balanced and achieve ex-ante efficiency, contrasting with the strategy-proof, expost optimal VCG mechanism. Since the AMM implements a Potential Game, we solve its equilibrium by first computing the social planner's optimum and then decentralizing the allocation. Numerical experiments using data from the Paris administrative region suggest that the prosumer community can achieve gains from trade up to 40% relative to the grid-only benchmark.