Equilibrium and Pareto-optimality in noisy non-zero sum discrete duel

We study a non-zero sum game which is a generalization of the antagonistic noisy one-versus-one duel. Equilibrium and $\varepsilon$-equilibrium points are presented in explicit form. It is shown that the $\varepsilon$-equilibrium strategies of both players coincide with their $\varepsilon$-maxmin strategies. We give the conditions under which the equilibrium strategy is a maxmin strategy. Pareto optimal games are investigated.