The performance of Dynamic Adaptive Streaming (DAS) in multi-client scenarios can be improved by taking advantage of the aggregation capability of Named Data Networking (NDN). In this paper, we propose a client-side game theory based (GB) ABR algorithm for NDN that can achieve proactive aggregation of requests among clients as much as possible without requiring coordinating with other clients or scheduling by a central controller. We model the interaction between a DAS client and network as an incomplete information non-cooperative game. Then, this game is transformed into a complete but imperfect information game by Harsanyi transformation, and each client can issue an appropriate bitrate request by solving the Bayesian Nash Equilibrium (BNE) problem respectively. By designing the payoff function pair elaborately, the equilibrium point of the game can correspond to the situation that multiple clients issuing the same video bitrate request, that is, requests aggregation, which will reduce the repeated traffic and also achieve fairness. Compared with the existing solutions, through simulation and real-world experiments in multi-client video distribution scenarios, the GB algorithm outperforms the comparison algorithms in terms of overall Quality of Experience (QoE), fairness, and network bandwidth utilization, etc.