Online coalitional games for real-time payoff distribution with applications to energy markets

TL;DR

This paper introduces online algorithms for real-time payoff distribution in coalitional games, specifically targeting energy markets, demonstrating convergence and scalability through simulations.

Contribution

It proposes two novel online distributed algorithms for tracking the Shapley value and the core in dynamic coalitional games, with proven convergence properties.

Findings

Algorithms effectively track time-varying solutions.

Online methods improve scalability in energy markets.

Payoff differences between online and static solutions are minimal.

Abstract

Motivated by the markets operating on fast time scales, we present a framework for online coalitional games with time-varying coalitional values and propose real-time payoff distribution mechanisms. Specifically, we design two online distributed algorithms to track the Shapley value and the core, the two most widely studied payoff distribution criteria in coalitional game theory. We show that the payoff distribution trajectory resulting from our proposed algorithms converges to a neighborhood of the time-varying solutions. We adopt an operator-theoretic perspective to show the convergence of our algorithms. Numerical simulations of a real-time local electricity market and cooperative energy forecasting market illustrate the performance of our algorithms: {the difference between online payoffs and static payoffs (Shapley and the core) to the participants is little; online algorithms considerably improve the scalability of the mechanism with respect to the number of market participants.