### ?

## Quantum Mean-Field Games with the Observations of Counting Type

Quantum games and mean-field games (MFG) represent two important new branches of

game theory. In a recent paper the author developed quantum MFGs merging these two branches.

These quantum MFGs were based on the theory of continuous quantum observations and filtering

of diffusive type. In the present paper we develop the analogous quantum MFG theory based on

continuous quantum observations and filtering of counting type. However, proving existence and

uniqueness of the solutions for resulting limiting forward-backward system based on jump-type

processes on manifolds seems to be more complicated than for diffusions. In this paper we only

prove that if a solution exists, then it gives an e-Nash equilibrium for the corresponding N-player

quantum game. The existence of solutions is suggested as an interesting open problem.