From coin-tossing to rock-paper-scissors and beyond: A log-exp gap theorem for selecting a leader

TL;DR

This paper investigates a class of leader selection games, including coin-tossing and rock-paper-scissors, revealing their stochastic complexity behaviors and providing a unifying theoretical framework.

Contribution

It introduces a log-exp gap theorem that characterizes the complexity of leader selection games, encompassing various well-known game-based algorithms.

Findings

Complexity exhibits either logarithmic or exponential behavior.

Theoretical framework unifies different leader selection game analyses.

Applications span multiple domains with similar stochastic properties.

Abstract

A class of games for finding a leader among a group of candidates is studied in detail. This class covers games based on coin-tossing and rock-paper-scissors as special cases and its complexity exhibits similar stochastic behaviors: either of logarithmic mean and bounded variance or of exponential mean and exponential variance. Many applications are also discussed.