The instability of the voluntary contribution mechanism

I consider systems with voluntary contribution mechanisms (VCM) in a quasilinear environment, showing that they are not asymptotically stable under simultaneous difference equations, and are structurally unstable under simultaneous differential equations. However, a VCM system is stable in a Cobb–Douglas (CD) environment under simultaneous differential equations; it is also stable under simultaneous difference equations given conditions on the slope of best response functions and the number of players. Most of the parameters investigated in nonlinear experiments on the VCM so far have been on the boundaries between stability and instability, and there has been hardly any work on instability. Therefore, research on the private provision of public goods faces a new challenge in addition to free riding.