Frequency of punishment use (Red) decreases and reward use (Blue) increases over 50 rounds of play in the PN (A), RN (B) and RNP (C) treatments. All data are analyzed at the level of the group to account for interdependence of outcomes for members of a given group. (A) Sign-rank comparing punishment use in rounds 1 and 50: p=0.12; comparing rounds 1–5 and 46–50: p=0.073, decreases; comparing rounds 1–10 and 41–50: p=0.037, decreases. (B) Sign-rank comparing reward use in rounds 1 and 50: p=0.018, increases; comparing rounds 1–5 and 46–50: p=0.033, increases; comparing rounds 1–10 and 41–50: p=0.075, increases. (C) Sign-rank comparing move use in rounds 1 and 50: R, p=0.007, increases; P: p=0.007, decreases; comparing rounds 1–5 and 46–50: R, p=0.006, increases; P, p=0.004, decreases; comparing rounds 1–10 and 41–50: R, p=0.006, increases; P, p=0.009, decreases.

Mean contribution to the public good (A), percentage of maximum possible payoff (B) and mean payoff (C) over 50 rounds of play in the control (Yellow), PN (Red), RN (Blue) and RNP (Green) experiments. All three treatments with targeted reciprocity succeed equally well at increasing contributions and percentage of maximum possible payoff relative to the control, and thus the reward treatments RN and RNP result in significantly higher actual payoffs than the punishment treatment PN. All data are analyzed at the level of the group to account for interdependence of outcomes for members of a given group. (A) Sign-rank test comparing contributions in Round 1 vs Round 50: Control, p=0.028, decrease; PN, p=0.18, no change; RN, p=0.036, increase; RNP, p=0.033, increase. (B) Ranksum comparing percentage of maximum possible payoff in the second half of the game: PN vs control, p=0.013, PN higher; RN vs control, p=0.048, RN higher; RNP vs control, p=0.023, RNP higher; PN vs RN, p=0.67; PN vs RNP, p=0.46; RN vs RNP, p=0.40. (C) Ranksum comparing mean payoff in the second half of the game: PN vs control, p=0.013, PN higher; RN vs control, p<0.001, RN higher; RNP vs control, p=0.001, RNP higher; PN vs RN, p=0.001, RN higher; PN vs RNP, p=0.005, RNP higher; RN vs RNP, p=0.40.

Mean payoff over the 50 rounds of play in the RNP treatment, increases with reward frequency (A) (Tobit, slope=12.7, p<0.001) and decreases with punishment frequency (B) (Tobit, slope=−7.9, p=0.030). Mean contribution to the public good increases with the average probability to reward players who contribute equal to or greater than the group average contribution (C) (Tobit, slope=22.2, p<0.001), and is not significantly related to the probability to punish below average contributors (D) (Tobit, slope=1.1, p=0.69). Mean payoff increases with the probability to cooperate with players who contribute equal to or greater than the group average contribution (E) (Tobit, slope=41.8, p<0.001), and decreases with the probability to punish below average contributors (F) (Tobit, slope=−13.2, p=0.066). Data are analyzed at the level of the group to account for the interdependence of outcomes for members of a given group. To correctly visualize the results of a multiple regression analysis, the y-axis of each panel is adjusted to account for the variation explained by the independent variable shown in the opposing panel (punishment in panels A, C, E and reward in panels B, D, F). See (32) for regression tables, axis adjustment details and further statistical analysis.