Distributed Algorithms for Aggregative Games on Graphs
研究了在网络上进行的聚合博弈，玩家通过局部信息交换估计全局聚合量，提出了同步和异步分布式算法，并证明其几乎必然收敛到纳什均衡。
We consider a class of Nash games, termed as aggregative games, being played over a networked system. In an aggregative game, a player’s objective is a function of the aggregate of all the players’ decisions. Every player maintains an estimate of this aggregate, and the players exchange this information with their local neighbors over a connected network. We study distributed synchronous and asynchronous algorithms for information exchange and equilibrium computation over such a network. Under standard conditions, we establish the almost-sure convergence of the obtained sequences to the equilibrium point. We also consider extensions of our schemes to aggregative games where the players’ objectives are coupled through a more general form of aggregate function. Finally, we present numerical results that demonstrate the performance of the proposed schemes.