(DP 2015-13) Helping Cost, Assortative Matching and Production Cycles in the Dynamic Humean Farmer Game

Abstract

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.

JEL Classificatoin: B0, B15, B31, C73