Cooperation in Multiperson Prisoner's Dilemma Games - Social Loafing

Social loafing is the tendency for individuals to expend less effort when working collectively compared with when working individually. Such reduction of commonly appearing prosocial behavior was observed in the past by psychologists. Generally, the experiments on social loafing confronted individual's efforton task in participation of two persons and several persons. It was observed that decrease of motivation to perform collective tasks changed when number of men had increased,however, not in the linear proportion, but rather exponential. We develop a mathematical model which takes into account various aspects of the phenomena, using multiperson Prisoner's Dilemma (PD) Games. The model - a 2-D system of nonlinear ODE takes into account evolution of the aspiration level in the population and mean frequency of the cooperative behavior. In particular we study limiting properties of the cooperation level in function of the order of the PD game.