Separating conditional and unconditional cooperation in a sequential Prisoner’s Dilemma game

<div><p>Most theories of social exchange distinguish between two different types of cooperation, depending on whether or not cooperation occurs conditional upon the partner’s previous behaviors. Here, we used a multinomial processing tree model to distinguish between positive and negative reciprocity and cooperation bias in a sequential Prisoner’s Dilemma game. In Experiments 1 and 2, the facial expressions of the partners were varied to manipulate cooperation bias. In Experiment 3, an extinction instruction was used to manipulate reciprocity. The results confirm that people show a stronger cooperation bias when interacting with smiling compared to angry-looking partners, supporting the notion that a smiling facial expression in comparison to an angry facial expression helps to construe a situation as cooperative rather than competitive. Reciprocity was enhanced for appearance-incongruent behaviors, but only when participants were encouraged to form expectations about the partners’ future behaviors. Negative reciprocity was not stronger than positive reciprocity, regardless of whether expectations were manipulated or not. Experiment 3 suggests that people are able to ignore previous episodes of cheating as well as previous episodes of cooperation if these turn out to be irrelevant for predicting a partner’s future behavior. The results provide important insights into the mechanisms of social cooperation.</p></div

Example morph.

<p>On the left side, the participant's face (eye brows, eyes, nose mouth) is shown that has been pasted into the shape of the stimulus person's face. On the right side, an example for a stimulus face is shown. In the center, the face morph is shown (morph ratio = 40:60). Both faces are used for illustration purposes only (i.e., because of copyright restrictions, the faces do not correspond to faces actually used in the present study). Written consent (as outlined in the PLoS consent form) was obtained from both individuals before publishing these photos.</p

Mean cooperation-game investments for self- and other-resembling interactants in each of the 20 trials of the cooperation game.

<p>Mean cooperation-game investments for self- and other-resembling interactants in each of the 20 trials of the cooperation game.</p

The reciprocity model used in the present experiments.

<p>Rounded rectangles on the left side represent the types of partners presented in the test (cooperators, cheaters, and new faces). Rectangles on the right represent the participants’ decisions (“I cooperate”, or “I do not cooperate”). The letters along the links represent the probabilities of different strategies (<i>R</i>₊: positive reciprocity; <i>R</i>_–: negative reciprocity; <i>A</i>: cooperation bias).</p

The source monitoring model of Bayen, Murnane, and Erdfelder (1996).

<p>Rounded rectangles represent the type of faces presented in the test (cooperators, cheaters, and new faces). Rectangles on the right represent the participant’s decisions in the memory test (“Cooperator”, “Cheater”, “New”). The letters along the links represent the probability of different cognitive processes (<i>D</i>₊: recognizing the face of a cooperator as old; <i>d</i>₊: remembering that the face was associated with cooperation; <i>D</i>_–: recognizing the face of a cheater as old; <i>d</i>_–: remembering that the face was associated with defection; <i>D</i>_New: recognizing a new face as new, <i>b</i>: guessing that an unrecognized face was old; <i>a</i>: bias towards guessing that a face was associated with cooperation rather than defection).</p

Schematic illustration of a trial of the sequential Prisoner’s Dilemma game.

<p>The example face was taken from the Center of Vital Longevity database [<a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0187952#pone.0187952.ref067" target="_blank">67</a>].</p

Player 1’s payoff in a typical Prisoner’s Dilemma (PD).

<p>Player 1’s payoff in a typical Prisoner’s Dilemma (PD).</p

Estimates of the parameters for cooperation bias (<i>A</i>) and positive (<i>R</i>_<i>+</i>) and negative reciprocity (<i>R</i>_<i>–</i>) as a function of the facial expressions of the partners (smiling vs. angry) with bootstrapped standard errors in Experiment 2.

<p>Estimates of the parameters for cooperation bias (<i>A</i>) and positive (<i>R</i>_<i>+</i>) and negative reciprocity (<i>R</i>_<i>–</i>) as a function of the facial expressions of the partners (smiling vs. angry) with bootstrapped standard errors in Experiment 2.</p

Results of the norming study.

<p>Mean ratings for mismatching and matching parent-child face pairs (taken from the KinFace database) and participant-morph face pairs. Upper panel: Mean facial resemblance ratings on a scale ranging from 1 (“very dissimilar”) to 6 (“very similar”). Lower panel: Mean ratings of the perceived degree of kinship on a scale ranging from 1 (“not related”) to 6 (“closely related”). The error bars represent the standard errors of the means.</p

Estimates of the parameters for cooperation bias (<i>A</i>) and positive (<i>R</i>_<i>+</i>) and negative reciprocity (<i>R</i>_<i>–</i>) as a function of group (control vs. extinction) with bootstrapped standard errors in Experiment 3.

<p>Estimates of the parameters for cooperation bias (<i>A</i>) and positive (<i>R</i>_<i>+</i>) and negative reciprocity (<i>R</i>_<i>–</i>) as a function of group (control vs. extinction) with bootstrapped standard errors in Experiment 3.</p