Static Nuel Games with Terminal Payoff

TL;DR

This paper analyzes a turn-based multiplayer game called Nuel, establishing the existence of stationary Nash equilibria for any number of players and providing algorithms to compute them.

Contribution

It introduces a variant of the Nuel game with multiple players, proving the existence of stationary Nash equilibria and developing algorithms to find them.

Findings

Existence of stationary Nash equilibria for all N ≥ 2

Algorithms for computing equilibria

Extension of Nuel game theory to multiplayer settings

Abstract

In this paper we study a variant of the Nuel game (a generalization of the duel) which is played in turns by $N$ players. In each turn a single player must fire at one of the other players and has a certain probability of hitting and killing his target. The players shoot in a fixed sequence and when a player is eliminated, the ``move'' passes to the next surviving player. The winner is the last surviving player. We prove that, for every $N\geq2$, the Nuel has a stationary Nash equilibrium and provide algorithms for its computation.