论文标题
纳什（Nash
Nash Equilibria for Exchangeable Team against Team Games, their Mean Field Limit, and Role of Common Randomness
论文作者
论文摘要
我们研究有限数量的有限和无限决策者的团队中的随机平均比赛。对于静态和动态设置中的这类游戏，我们建立了NASH平衡的存在，并表明NASH平衡在有限决策者制造商制度和对称性中表现出了无限范围的交换性。为了达到这些存在和结构定理，我们在各种分散信息结构下以合适的拓扑结构赋予了一组随机策略，这导致了一组随机策略的所需凸度和紧凑性。然后，我们建立了一个随机的NASH平衡的存在，该均衡是在每个团队中的决策者中可以交换（不一定是对称的），用于一般可交换的随机游戏。随着每个团队中的决策者数量进入无穷大（那是在团队之间的平均场地比赛），使用de Finetti代表定理，我们表明了每个团队中的决策者之间的随机NASH平衡存在，并且在每个团队中的决策者中都存在，也存在独立随机。最后，我们确定在团队中（对称）中的一类平均场比赛的NASH平衡构成了相应的限制前（可交换）比赛的NASH均衡，这些球队中有大量但有限的决策者数量。因此，我们表明，与小型团队不同的是，大型团队合作的团队游戏并不是必需的。
We study stochastic mean-field games among finite number of teams with large finite as well as infinite number of decision makers. For this class of games within static and dynamic settings, we establish the existence of a Nash equilibrium, and show that a Nash equilibrium exhibits exchangeability in the finite decision maker regime and symmetry in the infinite one. To arrive at these existence and structural theorems, we endow the set of randomized policies with a suitable topology under various decentralized information structures, which leads to the desired convexity and compactness of the set of randomized policies. Then, we establish the existence of a randomized Nash equilibrium that is exchangeable (not necessarily symmetric) among decision makers within each team for a general class of exchangeable stochastic games. As the number of decision makers within each team goes to infinity (that is for the mean-field game among teams), using a de Finetti representation theorem, we show existence of a randomized Nash equilibrium that is symmetric (i.e., identical) among decision makers within each team and also independently randomized. Finally, we establish that a Nash equilibrium for a class of mean-field games among teams (which is symmetric) constitutes an approximate Nash equilibrium for the corresponding pre-limit (exchangeable) game among teams with large but finite number of decision makers. We thus show that common randomness is not necessary for large team-against-team games, unlike the case with small sized teams.
