Nonantagonistic noisy duels of discrete type with an arbitrary number of actions

TL;DR

This paper analyzes a generalized nonzero-sum noisy duel game with multiple actions, establishing the existence of epsilon-equilibria, their maxmin properties, and conditions for Pareto optimality.

Contribution

It extends the noisy duel model to multiple actions, proving epsilon-equilibrium existence and Pareto optimality conditions in a nonzero-sum setting.

Findings

Existence of epsilon-equilibrium strategies.

Equilibrium strategies are epsilon-maxmin.

Conditions for Pareto optimality of equilibrium plays.

Abstract

We study a nonzero-sum game of two players which is a generalization of the antagonistic noisy duel of discrete type. The game is considered from the point of view of various criterions of optimality. We prove existence of epsilon-equilibrium situations and show that the epsilon-equilibrium strategies that we have found are epsilon-maxmin. Conditions under which the equilibrium plays are Pareto-optimal are given. Keywords: noisy duel, payoff function, strategy, equilibrium situation, Pareto optimality, the value of a game.