It is known that Eisert–Wilkens–Lewenstein scheme and Marinatto–Weber scheme are widely used to quantize simultaneous games. Further, distributed quantum game can be implemented in quantum networks using the schemes based on client–server model and peer-to-peer model. While most of the research works focus on simultaneous games, in this work, we propose the quantum circuit implementation of sequential game, namely cop and robber game using peer-to-peer model. Thus we have made a modest attempt to show the possibility of implementing sequential games in quantum circuits. Further, quantum version of cop and robber game is analyzed. Implications of the results are discussed from the game-theoretic point of view and quantum circuit point of view. © 2020, Springer Science+Business Media, LLC, part of Springer Nature.