On a discrete arbitration procedure with quadratic payoff function

We consider a two-person bargaining model with arbitrator's participation. The players make their offers and the arbitrator's decision is simulated by a random variable with uniform distribution on the set $\{-n,-(n-1),\dots,-1,0,1,\dots,n-1,n\}$. We use a new arbitration procedure. The Nash equilibrium in this game in mixed strategies is found.