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.
翻译:以快速时间规模运行的市场为动力,我们为在线联合游戏提供了一个框架,配有时间变化的联盟值,并提出实时支付分配机制。具体地说,我们设计了两种在线分配算法,以跟踪Shapley值和核心值,这是在联合游戏理论中研究最广泛的两种支付分配标准。我们显示,我们提议的算法所产生的支付分配轨迹与时间变化解决方案的相近之处相近。我们采用了操作者理论视角,以显示我们的算法趋同。实时当地电力市场和协作能源预测市场的数值模拟显示了我们的算法表现:{在线支付与参与者的静态支付(分享和核心)之间的差别很小;在线算法大大改善了机制在市场参与者人数方面的可扩展性。