Periodic attractor in the discrete time best-response dynamics of the Rock-Paper-Scissors game

TL;DR

This paper demonstrates that the discrete time best-response dynamics in the Rock-Paper-Scissors game lead to finite, periodic attractors, with detailed analysis of their bifurcations, number, period, and strategies.

Contribution

It provides a rigorous analysis of the periodic attractors in discrete best-response dynamics for RPS, including bifurcation behavior and exact characterization.

Findings

Attractor of discrete best-response dynamics is finite and periodic

Bifurcation analysis of the attractor behavior

Exact number, period, and location of periodic strategies identified

Abstract

The Rock-Paper-Scissors (RPS) game is a classic non-cooperative game widely studied in terms of its theoretical analysis as well as in its applications, ranging from sociology and biology to economics. Many experimental results of the RPS game indicate that this game is better modelled by the discretized best-response dynamics rather than continuous time dynamics. In this work we show that the attractor of the discrete time best-response dynamics of the RPS game is finite and periodic. Moreover we also describe the bifurcations of the attractor and determine the exact number, period and location of the periodic strategies.