Helping cost, assortative matching and production cycles in the dynamic humean farmer game

We reformulate the Humean farmer game on the basis of random assignment of advantage and the cost e of helping in another's harvest. The result is a game that is a coordination game if e < ½ or a dominant strategy Prisoner's Dilemma Game if e > ½ which allows a joint treatment of the two interpretations of the Humean farmer game. We employ two behavioral types initially: the conditionally cooperative (H-type) and the free riding (NH-type). We employ replication dynamics with assortative matching and multiple production cycles to investigate which evolutionarily stable (EE) monomorphic population it engenders. We show that the ceiling for effort cost e to support an EE monomorphic H-type population in the Stag-Hunt game rises to (1 + b)/2 from 1/2 in pure random matching case. As the assortative index b rises, the basin of attraction of the EE H-type solution rises. When the assortative matching is perfect (b = 1), in the Stag-Hunt game version (0 < e < ½), the monomorphic NH-type population (s* = 0) is no longer EE while the monomorphic H-type solution (s** = 1) is EE; in the Dominant Strategy game version (e > ½), s* = 0 is EE iff e > (3/4) while s** = 1 is EE.