Noisy fighter-bomber duel

TL;DR

This paper analyzes a duel game where one player uses resources continuously and the other in discrete portions, providing an explicit solution for the game's strategies and value.

Contribution

It introduces a new model of a noisy duel with explicit solutions, combining continuous and discrete resource usage strategies.

Findings

Explicit solution for the game strategy and value.

Characterization of optimal resource consumption.

Insights into the dynamics of noisy duels.

Abstract

We discuss a duel-type game in which Player I uses his resource continuously and Player II distributes it by discrete portions. Each player knows how much resources he and his opponent have at every moment of time. The solution of the game is given in an explicit form. Keywords: noisy duel, payoff, strategy, the value of a game, consumption of resource.