Pattern Formation in Agent-Based and PDE Models for Evolutionary Games with Payoff-Driven Motion.

Area of Science:

• Evolutionary Game Theory
• Mathematical Biology
• Spatial Dynamics

Background:

• Spatial structure significantly impacts cooperative behavior and population success.
• Understanding movement dynamics is crucial for evolutionary game models.

Purpose of the Study:

• To investigate how random and directed motion affect spatial patterns and payoffs in hawk-dove games.
• To compare stochastic and deterministic (PDE) models for spatial evolutionary games.

Main Methods:

• Utilized both stochastic spatial models and partial differential equation (PDE) models.
• Analyzed the hawk-dove game dynamics under different movement strategies (diffusive vs. payoff-driven).

Main Results:

• Turing patterns emerge in diffusive motion when hawks move faster than doves, increasing population size and payoff.
• Payoff-driven motion yields decreased population size and payoff in stochastic models.
• PDE models show complex behavior with payoff-driven motion, including potential instabilities.

Conclusions:

• Hawk mobility positively influences population size and payoff in diffusive spatial games.
• Payoff-driven motion requires careful consideration in PDE models due to potential instabilities.
• Nonlocal PDE models may be better suited for spatial patterns in directed motion evolutionary games.