Figure 2

Simulations of Prisoner's Dilemma (PD) matrices with added normally distributed random error of variance 1.0 in all cases. Bars represent the number of matrices in which all inequalities for PD remained in tact, given as the mean +/- 2 standard deviations (from 5 simulations) of valid PD matrices out of 1000. To determine whether inequalities conformed to PD, each of the payoff ratios T/R, P/S and R/P were calculated, from which deviations from the requisite < 1 were used to detect violations of each part of the PD ranking sequence. Diamonds represent the consequent number of valid PD games +/- 2 standard deviations, between any two randomly drawn players, expected under the same parameters. Payoffs of 0 or 1 (as in the simulation of the "typical" payoff matrix 0, 1, 3, 5) sometimes became negative after the addition of random error, in which case we checked for inequalities with absolute values rather than ratios.