Stochastic Duel with Three or More Players

Abstract

Consider a stochastic duel with many players. Each player chooses an opponent to shoot at, makes a hit after a random amount of time that follows an exponential distribution, and is killed as soon as being hit for the first time. The duel continues until all but one player is killed, and the lone survivor is declared the winner. The goal of each player is to decide which opponent to target at any given time in order to maximize their winning probability. We develop an algorithm to compute each players optimal strategy and winning probability. In particular, the strongest player the one having the largest kill rate need not be the most likely to win, and it is not necessarily optimal for each player to shoot at their strongest opponent. We also consider a variation of the game in which players arrive sequentially to select their own kill rates, knowing the selections made by players who arrived earlier. In this sequential-move game with three players, the first player wants to be mediocre and the third player has the best chance to win. Our findings enable further understanding of military conflicts that involve three or more adversaries in the same area of operations.

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Document Details

Document Type
Technical Report
Publication Date
Jun 01, 2023
Accession Number
AD1213218

Entities

People

  • Robert M. Donovan

Organizations

  • Naval Postgraduate School

Tags

DTIC Thesaurus Topics

  • Applied Mathematics
  • Cyber Warfare
  • Differential Equations
  • Equations
  • Information Operations
  • Lanchester Equations
  • Literature Surveys
  • Mathematics
  • Military Operations
  • Operations Research
  • Probability
  • Random Variables
  • Schools
  • Sequential Games
  • United States
  • United States Naval Academy
  • Warfare

Readers

  • Educational Psychology
  • Game Theory.
  • Military History of the United States in the 20th Century.