Equilibrium and Pareto-optimality in noisy discrete duels with an arbitrary number of actions

We study a nonzero-sum game of two players that is a generalization of the antagonistic noisy duel of discrete type. The game is considered from the point of view of various criteria of optimality. We prove the existence of $\varepsilon$-equilibrium situations and show that the $\varepsilon$-equilibrium strategies that we found are $\varepsilon$-maxmin. Conditions under which the equilibrium plays are Pareto-optimal are given.