Distribution of winners in truel games

TL;DR

This paper analyzes the distribution of winners in truel games using Markov chain theory, providing both known and new expressions for winning probabilities and equilibrium points.

Contribution

It introduces detailed expressions for the distribution of winners in truels, extending previous work on winning probabilities and equilibrium analysis.

Findings

Derived expressions for winner distributions in truels

Reproduced known winning probabilities and equilibrium points

Provided new insights into the distribution of outcomes

Abstract

In this work we present a detailed analysis using the Markov chain theory of some versions of the truel game in which three players try to eliminate each other in a series of one-to-one competitions, using the rules of the game. Besides reproducing some known expressions for the winning probability of each player, including the equilibrium points, we give expressions for the actual distribution of winners in a truel competition.