Mixed Quantal Response Equilibria for Normal Form Games

We introduce the mixed quantal response equilibrium as an alternative statistical approach to normal form games with random utility function and prove its existence. Then we extend the quantal response equilibrium to payoff functions with disturbances outside the family of admissible distributions. Finally, we define the mixed logit quantal response equilibrium, we draw the correspondence between it and the multinomial mixed logit model and prove that any random utility game has a quantal response equilibrium, which additionally is the limit of a parametric mixed logit quantal response equilibrium