Wu et al (2009) Partner selections in public goods games with constant group size

Wu et al (2009) Partner selections in public goods games with constant group size. Physical Review E, 80, 026121.

The model: 

• Scale-free network, initialized half C, half D.
• Each individual picks our a fixed number g of his neighbors to join in public goods games. Two mechanisms for choosing group members: 
• Degree-based: partners are chosen with probability related to number of social ties.
• Reputation-based: based on the number of times the individual has cooperated. 
• After each round where all games are player, each player i chooses a random neighbor j and switches to j’s strategy if j does better with some probability.
• Synchronous updating.

Results: 

• If each individual is picked with equal probabilities, larger group size (up to g = 4) enhanced the evolution of cooperation. 
• With reputation-based groups, the relation is the same, but cooperation is enhanced for g > 1. 
• With degree-based groups, being biased toward high-degree individuals increased cooperation. 

They only studied very small groups, between 2 and 5 players.