Evolutionary matching-pennies game on bipartite regular networks

Area of Science:

• Complex Systems
• Game Theory
• Statistical Physics

Background:

• Evolutionary game theory models strategic interactions and evolution on networks.
• Previous studies often simplify network structures or update rules.

Purpose of the Study:

• To investigate evolutionary games on chessboard and random regular graphs.
• To analyze the impact of myopic strategy updates and network topology on game dynamics.
• To explore the emergence of correlations and phase transitions in these systems.

Main Methods:

• Simulations of evolutionary games on specified network structures.
• Application of a myopic strategy update rule, analogous to Glauber dynamics.
• Analysis of stationary states, neighbor correlations, and entropy production.
• Extension to games with mixed interaction types (anticoordination and matching-pennies).

Main Results:

• A stationary state is reached with equal probabilities for both strategies.
• Nearest neighbor correlations vanish, but weak correlations appear between second and third neighbors.
• Entropy production quantifies deviation from detailed balance in stationary states.
• Ising-type order-disorder transitions are observed in extended evolutionary games.

Conclusions:

• The myopic update rule on these networks leads to a unique stationary state.
• Network structure and game rules influence correlation patterns and emergent phase transitions.
• This work provides insights into the dynamics of cooperation and competition in structured populations.