A complete classification of evolutionary games with environmental feedback

Area of Science:

• Game Theory
• Environmental Science
• Behavioral Economics

Background:

• The tragedy of the commons highlights how individual rational choices can deplete shared resources.
• Feedback-evolving games model interactions where individual actions impact environmental resources, which in turn affect payoffs.
• Previous research primarily focused on the Prisoner's Dilemma (PD) in abundant resource scenarios.

Purpose of the Study:

• To extend the feedback-evolving game framework beyond the PD game.
• To classify social dilemma dynamics across four game structures (PD, Chicken, Stag-Hunt, Trivial) in replete environments.
• To investigate emergent phenomena like initial condition dependence and persistent oscillations.

Main Methods:

• Theoretical extension of the feedback-evolving game model.
• Inclusion of Chicken, Stag-Hunt (SH), and Trivial games alongside the Prisoner's Dilemma (PD).
• Utilizing a dilemma phase plane to visualize transient dynamics of game structure changes.

Main Results:

• Initial condition dependence (bistability) is prevalent across the analyzed game structures.
• Persistent oscillation dynamics were observed even in replete environments for Chicken and SH games.
• The study provides a more complete classification of social dilemmas within feedback-evolving game systems.

Conclusions:

• The generalized feedback-evolving game framework accommodates a wider range of social dilemma scenarios.
• Environmental feedback can lead to complex dynamics, including bistability and oscillations, across different game structures.
• This research advances the theoretical understanding of environmental resource management and game theory.