Synchronization and extinction in cyclic games with mixed strategies

Area of Science:

• Evolutionary Game Theory
• Mathematical Biology
• Complex Systems

Background:

• Cyclic Lotka-Volterra models are fundamental in understanding strategy dynamics.
• Agents typically use fixed strategies or simple probabilistic rules.
• Time-dependent probability distributions introduce adaptive learning mechanisms.

Purpose of the Study:

• To investigate cyclic Lotka-Volterra models with agents employing time-dependent probability distributions.
• To analyze the impact of a novel learning rule based on loss and strategy replacement.
• To characterize system properties using mean-field rate equations and numerical simulations.

Main Methods:

• Agent-based modeling with an 'urn' analogy for strategy probabilities (β balls).
• Implementation of a learning rule where losses lead to replacing losing strategy balls with winning ones.
• Analysis using mean-field rate equations and spatial numerical simulations.

Main Results:

• The three-strategy model exhibits a transition from neutral stability to stability with increased probability distribution discretization.
• Spatially synchronized temporal oscillations emerge in the three-strategy model for large β (continuous distribution approximation).
• The four-strategy model remains neutrally stable, with distinct emergent regimes influenced by system size and discretization.

Conclusions:

• The discretization level of probability distributions significantly impacts the stability of cyclic Lotka-Volterra models.
• Adaptive learning rules, modeled via urn dynamics, introduce complex behaviors like synchronized oscillations.
• System size and discretization are key factors in determining emergent dynamics in multi-strategy cyclic games.