In this paper, we investigate game theoretical multi-agent formation control problem. The main challenge of this problem is how to enable local execution of game strategies, e.g., Nash equilibrium, which generally requires global information in the presence of communication topology among agents. Toward this, we first derive open-loop Nash equilibrium for agents minimizing formation error based performance indices and proceed to introduce a distributed estimation scheme to facilitate local implementation of the derived Nash strategies. In addition, a shrinking horizon control technique is integrated into the proposed scheme to handle unexpected state changes. The proposed scheme is fully distributed and ensures an E Nash equilibrium. An illustrative example is presented to verify the effectiveness. (C) 2019 Elsevier Ltd. All rights reserved.