Maintaining a consistent persona is essential for building a human-like conversational model. However, the lack of attention to the partner makes the model more egocentric: they tend to show their persona by all means such as twisting the topic stiffly, pulling the conversation to their own interests regardless, and rambling their persona with little curiosity to the partner. In this work, we propose COSPLAY(COncept Set guided PersonaLized dialogue generation Across both partY personas) that considers both parties as a "team": expressing self-persona while keeping curiosity toward the partner, leading responses around mutual personas, and finding the common ground. Specifically, we first represent self-persona, partner persona and mutual dialogue all in the concept sets. Then, we propose the Concept Set framework with a suite of knowledge-enhanced operations to process them such as set algebras, set expansion, and set distance. Based on these operations as medium, we train the model by utilizing 1) concepts of both party personas, 2) concept relationship between them, and 3) their relationship to the future dialogue. Extensive experiments on a large public dataset, Persona-Chat, demonstrate that our model outperforms state-of-the-art baselines for generating less egocentric, more human-like, and higher quality responses in both automatic and human evaluations.