Average punishment spent to punish defectors for a group of 4 agents as a function of after an equilibrium time of 5,000,000 simulation periods and for 3200 system realizations.

<p> is fixed to the corresponding value on the x-axis and the initial contribution in period for all agents of a group is randomly drawn form a uniform distribution in . A value of corresponds to an optimal value of the propensity to punish associated to a minimum of the global punishment expenditure.