Figure 1

Inequalities in simulated Prisoner's Dilemma (PD) matrices. Values greater than 1 indicate that the ratio conforms to that part of a valid PD matrix. All of three ratios must be > 1 for the entire matrix to conform to PD. These are representative graphs for a single simulation on 1000 initial payoff matrices of (3, 4, 5, 6) after adding normally distributed errors of zero mean and a variance of 1.0. Note that ratios can be quite large in cases where small payoffs (< 3.0) became even smaller after adding negative errors (P may be divided by an S approaching 0, in which case the value P/S becomes large). To avoid very high ratio values we increased all initial mean payoff values in our simulations so that the minimum was three. The frequency of valid PD cases is not affected by increasing absolute values of the payoffs.