Nash Equilibria of Rock Paper Scissors Variants

TL;DR

This paper generalizes Rock Paper Scissors to tournament graphs, analyzing Nash equilibria with all strategies having nonzero probabilities, and explores their graph-theoretic properties for small numbers of strategies.

Contribution

It introduces a generalized framework for Rock Paper Scissors using directed graphs and characterizes Nash equilibria in these settings, including new graph-theoretic insights.

Findings

Characterization of Nash equilibria with full support in tournament games

Tabulation of properties for tournaments with up to 7 vertices

Identification of graph-theoretic properties related to equilibria

Abstract

We generalize Rock Paper Scissors to complete directed graphs, or tournaments, on $n$ vertices. Properties of the mixed-strategy Nash equilibria of these tournaments are discussed, particularly those with Nash equilibria where all of the strategies have a nonzero probability. We find graph-theoretic properties of such games and tabulate them for $n \leq 7$.