Fig 1.
High level of cooperation in iPD.
(A) Dual operant box diagram and the matrix with positive(blue) and negative(red) reinforcement is shown. The iPD game had four possible states: R(reward) mutual cooperation, P(punishment) mutual defection, T(temptation) in which subject defected and opponent cooperated and S(sucker) subject cooperated and opponent defected. The opponent´s light was driven in order to perform a Tit for tat strategy. (B,C) Time-course of cooperation and timeout rate along the last 23 games sessions. In the last 5 sessions, the mean ± sem of cooperation was 0.86 ± 0.05 and timeout was 0.23 ± 0.08. (D) Total reward versus timeout for all animals (color bar means cooperation mean). Each animal was compared with the regression line fit to a population with cooperation level set to 60% (black continuous line). The higher the cooperation levels, the larger the total reward and the lower the total timeout. (E) Markov Chain diagram shows the probabilities of transition between states (p(c|T−1) = 0.76, p(c|R−1) = 0.85, p(c|S−1) = 0.93, p(c|P−1) = 0.87). The arrow represents transitions: driven by cooperation in blue, and driven by defection in red (the arrow thickness is proportional to transition probability). Below, bars show occupancy ratio when cooperation reaches stability. Probabilities were: p(R) = 0.76, p(T) = 0.1, p(P) = 0.04, p(S) = 0.1. Asterisks denote significant differences from multiple comparisons using one-way ANOVA and Bonferroni correction. (F) Evolution cooperation rate before and after reversal. Graphs show a moving average with samples of 3 sessions (the mean and sem from reversal on the last five sessions was 0.87 ± 0.04).
Table 1.
Treatment 1: testing of high cooperation and reversion. Treatment 2 and 3: effect in cooperation by change of pay-off matrix. The matrix changed over the group with same word (A or B).
Fig 2.
Effect of changes in the amount of positive reinforcement of R and T.
(A) The rats were pre-trained by pay-off matrix [PR = 1, PT = 3, PP = 4, PS = 8 and contrast ] (filled dots) and the cooperation was strongly affected by change of temptation payoff, decreasing when T payoff increased and matrix with changed to [R = 1, T = 5, P = 4, S = 8 and contrast
] (open circles). There was a significant difference (red circle) in two animals with p < 9.8e−06 (wilcoxon rank-sum test) and the other did not modify her behavior in spite of matrix change. (B) The cooperation enhanced when the matrix changed to [R = 2, T = 3, P = 4, S = 8 and
] (open circles) and the difference was statistically different (p < 0.0062) in two of three subjects, because one had no significant difference after matrix change, p > 0.05(cooperation: 0.7063). (C) The 3D plots related cooperation, reward and timeout. In the group of cooperative animals (filled dots), the change in T (3 pellets to 5 pellets) increased both timeout and reward in order to decrease cooperation (open circles). The comparison between cooperation mean of both groups was significantly different, p < 0.05. (D) In the group of non-cooperative animals (filled dots), they learned to cooperate (open circles) by receiving more reward without significant changes in total timeout. The cooperation was significantly different, p > 0.05. (E,F) The mean of occupancy state rate graph (last five sessions) from cooperative (left) and non-cooperative (right) groups (Mean ± sem). Asterisks denote significant difference, after matrix changed, among T, R, P or S state occupancy and dash line indicates the level of equal rate in each state (that corresponds to a strategy with strongly random component). Before changes (filled dots) and after changes (open circles).
Fig 3.
Markov chain diagrams and contrast index.
Markov chain diagrams are shown (the size of circle means of occupancy state rate and the arrow’s width are proportional to the probability of cooperate given (A) occupancy state and transition probabilities for an animal that disrupted its cooperative behavior when contrast index was changed to
and pay-off matrix was changed [PT, PR, PP, PS] = [3p, 1p, 4s, 8s] to [5p, 1p, 4s, 8s] (p = pellet and s = seconds). The thickness of blue arrows (conditional probabilities of cooperation) become thinner after change (for values see Table 1). (B) The opposite situation can be seen, non-cooperative animal becomes more cooperative when
was decreased to
in a matrix that favors cooperation. The blue arrows become thicker after change (for values see Table 1). (C, D) shows cooperation and timeout levels as a function of CI. Here, it can be seen that both variables follow an inverted U profile in correlation with the contrast index increase and if the payoff matrix favors or not the cooperation behavior.