Figure - PMC

Skip to main content

An official website of the United States government

Here's how you know

Here's how you know

Official websites use .gov
A .gov website belongs to an official government organization in the United States.

Secure .gov websites use HTTPS
A lock ( ) or https:// means you've safely connected to the .gov website. Share sensitive information only on official, secure websites.

View full-text article in PMC

. 2018 Jul 27;9:2954. doi: 10.1038/s41467-018-05259-5

Search in PMC
Search in PubMed
View in NLM Catalog
Add to search

© The Author(s) 2018

Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons license, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons license and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this license, visit http://creativecommons.org/licenses/by/4.0/.

PMC Copyright notice

Fig. 5 — Reward improves the likelihood of success for cooperators. a In the control treatment, per-round payoff correlates negatively with cooperation frequency (intercept 0.459, 95% confidence interval [0.369–0.549]; slope −0.452, 95% confidence interval [−0.691 to −0.212]; coefficient of determination R² = 0.197). This negative correlation disappears in the decoy treatment (intercept 0.541, 95% confidence interval [0.431–0.650]; slope 0.128, 95% confidence interval [−0.0511 to 0.306]; coefficient of determination R² = 0.0205). In fact, the angle between the two lines is significantly positive (F-test for the treatment × frequency interaction; F-statistic 13.2; p value 0.0004), indicating that the decoy’s presence improves the likelihood of success for cooperators. b Because frequencies of cooperation and defection in the control treatment sum to unity, regression lines for cooperation and defection in this treatment must exhibit a mirror symmetry (intercept 0.0075, 95% confidence interval [−0.164 to 0.179]; slope 0.452, 95% confidence interval [0.212–0.691]; coefficient of determination R² = 0.197; cf. panel (a)). Although the same symmetry need not hold in the decoy treatment due to reward, regression lines for cooperation and defection are also almost an ideal mirror image of one another (intercept 0.654, 95% confidence interval [0.575–0.733]; slope −0.109, 95% confidence interval [−0.276 to 0.0577]; coefficient of determination R² = 0.0173; cf. panel (a)), indicting that reward worsens the likelihood of success for defectors (F-test for the treatment × frequency interaction; F-statistic 12.9; p value 0.0004). c Per-round payoff shows no correlation with the frequency of reward (intercept 0.614, 95% confidence interval [0.552–0.676]; slope −0.0355, 95% confidence interval [−0.808 to 0.737]; coefficient of determination R² = 0.0083), thus explaining the mirror symmetry of regression lines for cooperation and defection in the decoy treatment. Solid lines represent the ordinary least squares regression, whereas dashed lines are the corresponding 95% prediction confidence intervals