Different Forms of Imbalance in Strongly Playable Discrete Games I: Two-Player RPS Games

TL;DR

This paper introduces formal definitions of imbalance and playability in two-player discrete games, particularly RPS variants, linking strategic dominance to inequality measures and exploring their extremal cases.

Contribution

It formalizes imbalance and playability in discrete games, relates them to dominated strategies, and constructs maximally imbalanced yet playable RPS games.

Findings

Maximally balanced and playable games have no dominated strategies.

Constructed a (2n+1)-RPS game that maximizes imbalance measures.

Imbalance aligns with economic inequality concepts.

Abstract

We construct several definitions of imbalance and playability, both of which are related to the existence of dominated strategies. Specifically, a maximally balanced game and a playable game cannot have dominated strategies for any player. In this context, imbalance acts as a measure of inequality in strategy, similar to measures of inequality in wealth or population dynamics. Conversely, playability is a slight strengthening of the condition that a game has no dominated strategies. It is more accurately aligned with the intuition that all strategies should see play. We show that these balance definitions are natural by exhibiting a (2n+1)-RPS that maximizes all proposed imbalance definitions among playable RPS games. We demonstrate here that this form of imbalance aligns with the prevailing notion that different definitions of inequality for economic and game-theoretic distributions must agree on both the maximal and minimal cases. In the sequel paper, we utilize these definitions for multiplayer games to demonstrate that a generalization of this imbalanced RPS is at least nearly maximally imbalanced while remaining playable for under 50 players.