Cyclic dominance in a two-person Rock-Scissors-Paper game

TL;DR

This paper investigates the cyclic dominance behavior in a parametrized two-player Rock-Scissors-Paper game, revealing stable heteroclinic cycles influenced by tie payoffs.

Contribution

It introduces a parametrized model demonstrating stable heteroclinic cycles in a two-player RSP game, highlighting the role of tie payoffs in cyclic dominance.

Findings

Cyclic behavior occurs near heteroclinic cycles in the game.

The heteroclinic cycle stability is maximized across various parameters.

Tie payoffs significantly influence the stability of cyclic dominance.

Abstract

The Rock-Scissors-Paper game has been studied to account for cyclic behaviour under various game dynamics. We use a two-person parametrised version of this game. The cyclic behaviour is observed near a heteroclinic cycle, in a heteroclinic network, with two nodes such that, at each node, players alternate in winning and losing. This cycle is shown to be as stable as possible for a wide range of parameter values. The parameters are related to the players' payoff when a tie occurs.