Are there any research papers focused on implementing a game/puzzle or game theory in Quantum Computing.
To start, I would read "The next stage: quantum game theory" by E.W.Piotrowski, J. Sladkowski. While the paper is from 2003, the authors discuss how developments in quantum computation allow the extension of the scope of game theory. It includes some basic history as well as some basic ideas and recent developments in quantum game theory.
These same authors also wrote a paper entitled "Quantum Bargaining Games" in 2001 which I would think will also be useful in your research. It's part of a larger analysis they did of "quantum-like" descriptions of market economics with roots in the then recently developed quantum game theory".
I think these two papers would be great starting points.
I would also check out James Wootton's "Using a simple puzzle game to benchmark quantum computers" in which he created a puzzle game called "Quantum Awesomeness". I recommend this primarily because it's slightly related but completely awesome.