A unified continuous framework for two-player two-strategy games: Game-theoretic analysis of interactions

Area of Science:

• Game Theory
• Mathematical Biology
• Social Dynamics

Background:

• Traditional 2x2 games use binary choices, limiting real-world applicability.
• Existing models lack mathematical descriptions for continuous strategic interactions.
• Current 2x2 games are often studied in isolation, hindering broader theoretical connections.

Purpose of the Study:

• To propose a unified, continuous mathematical framework for 2x2 games.
• To introduce Linear Dualism Games (LDG) for modeling strategic interactions.
• To establish mathematical descriptions for competition, mutualism, and exploitation within a unified model.

Main Methods:

• Developed a continuous strategy space for 2x2 games, termed Linear Dualism Games (LDG).
• Defined cooperation and defection domains within the LDG strategy space.
• Applied LDG to mathematically describe and connect various interaction types and game models.

Main Results:

• LDG provides a unified framework connecting diverse 2x2 games.
• Demonstrated how interaction types (competition, mutualism) vary across LDG domains.
• Identified new 2x2 game variants, including the battle of the allies and converted gang game.

Conclusions:

• Linear Dualism Games offer a more realistic and unified approach to studying strategic interactions.
• The LDG framework reveals underlying connections between seemingly disparate game theory models.
• This work expands the landscape of known 2x2 games and their mathematical underpinnings.