A Versatile Stochastic Duel Game

TL;DR

This paper introduces a novel stochastic duel game model combining game theory and fluctuation processes, providing analytical tools for strategic decision making in duel-type scenarios with practical applications.

Contribution

It proposes a new hybrid stochastic game model for duel-type scenarios, offering analytical solutions and demonstrating its application in practical and business contexts.

Findings

Derived optimal decision parameters including crossing moments and iteration counts.

Developed a compact closed joint functional for strategic analysis.

Applied the model to conventional and business duel scenarios.

Abstract

This paper deals with a standard stochastic game model with a continuum of states under the duel-type setup. It newly proposes a hybrid model of game theory and the fluctuation process, which could be applied for various practical decision making situations. The unique theoretical stochastic game model is targeted to analyze a two-person duel-type game in the time domain. The parameters for strategic decisions including the moments of crossings, prior crossings, and the optimal number of iterations to get the highest winning chance are obtained by the compact closed joint functional. This paper also demonstrates the usage of a new time based stochastic game model by analyzing a conventional duel game model in the distance domain and briefly explains how to build strategies for an atypical business case to show how this theoretical model works.