Group size effects and critical mass in public goods games

Article


Pereda, M., Capraro, V. and Sánchez, A. 2019. Group size effects and critical mass in public goods games. Scientific Reports. 9 (1). https://doi.org/10.1038/s41598-019-41988-3
TypeArticle
TitleGroup size effects and critical mass in public goods games
AuthorsPereda, M., Capraro, V. and Sánchez, A.
Abstract

Understanding whether the size of the interacting group has an effect on cooperative behavior has been a major topic of debate since the seminal works on cooperation in the 1960s. Half a century later, scholars have yet to reach a consensus, with some arguing that cooperation is harder in larger groups, while others that cooperation is easier in larger groups, and yet others that cooperation attains its maximum in intermediate size groups. Here we add to this field of work by reporting a two-treatment empirical study where subjects play a Public Goods Game with a Critical Mass, such that the return for full cooperation increases linearly for early contributions and then stabilizes after a critical mass is reached (the two treatments differ only on the critical mass). We choose this game for two reasons: it has been argued that it approximates real-life social dilemmas; previous work suggests that, in this case, group size might have an inverted-U effect on cooperation, where the pick of cooperation is reached around the critical mass. Our main innovation with respect to previous experiments is that we implement a within-subject design, such that the same subject plays in groups of different size (from 5 to 40 subjects). Groups are formed at random at every round and there is no feedback. This allows us to explore if and how subjects change their choice as a function of the size of the group. We report three main results, which partially contrast what has been suggested by previous work: in our setting (i) the critical mass has no effect on cooperation; (ii) group size has a positive effect on cooperation; (iii) the most chosen option (played by about 50% of the subjects) is All Defection, followed by All Cooperation (about 10% of the subjects), whereas the rest have a slight trend to switch preferentially from defection to cooperation as the group size increases.

PublisherNature Publishing Group
JournalScientific Reports
ISSN2045-2322
Publication dates
Online02 Apr 2019
Print01 Dec 2019
Publication process dates
Deposited17 Apr 2019
Submitted13 Dec 2018
Accepted14 Mar 2019
Output statusPublished
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Open
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Open
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Copyright Statement

© The Author(s) 2019
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/.

Additional information

Author correction [published 03 September 2019]: Pereda, M., Capraro, V. & Sánchez, A. Author Correction: Group size effects and critical mass in public goods games. Sci Rep 9, 12869 (2019). https://doi.org/10.1038/s41598-019-49306-7
See also Data or Supplementary Material

Digital Object Identifier (DOI)https://doi.org/10.1038/s41598-019-41988-3
LanguageEnglish
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Capraro, V., Rodriguez-Lara, I. and Ruiz-Martos, M. 2020. Preferences for efficiency, rather than preferences for morality, drive cooperation in the one-shot Stag-Hunt game. Journal of Behavioral and Experimental Economics. 86. https://doi.org/10.1016/j.socec.2020.101535
Using social and behavioural science to support COVID-19 pandemic response
Bavel, J., Baicker, K., Boggio, P., Capraro, V., Cichocka, A., Cikara, M., Crockett, M., Crum, A., Douglas, K., Druckman, J., Drury, J., Dube, O., Ellemers, N., Finkel, E., Fowler, J., Gelfand, M., Han, S., Haslam, S., Jetten, J., Kitayama, S., Mobbs, D., Napper, L., Packer, D., Pennycook, G., Peters, E., Petty, R., Rand, D., Reicher, S., Schnall, S., Shariff, A., Skitka, L., Smith, S., Sunstein, C., Tabri, N., Tucker, J., van der Linden, S., van Lange, P., Weeden, K., Wohl, M., Zaki, J., Zion, S. and Willer, R. 2020. Using social and behavioural science to support COVID-19 pandemic response. Nature Human Behaviour. 4 (5), pp. 460-471. https://doi.org/10.1038/s41562-020-0884-z
Lying on networks: the role of structure and topology in promoting honesty
Capraro, V., Perc, M. and Vilone, D. 2020. Lying on networks: the role of structure and topology in promoting honesty. Physical Review E. 101 (3). https://doi.org/10.1103/PhysRevE.101.032305
Social setting, intuition, and experience in lab experiments interact to shape cooperative decision-making
Capraro, V. and Cococcioni, G. 2015. Social setting, intuition, and experience in lab experiments interact to shape cooperative decision-making. Proceedings of the Royal Society B: Biological Sciences. 282 (1811). https://doi.org/10.1098/rspb.2015.0237
Social heuristics and social roles: Intuition favors altruism for women but not for men
Rand, D., Brescoll, V., Everett, J., Capraro, V. and Barcelo, H. 2016. Social heuristics and social roles: Intuition favors altruism for women but not for men. Journal of Experimental Psychology: General. 145 (4), pp. 389-396. https://doi.org/10.1037/xge0000154
Liking but devaluing animals: emotional and deliberative paths to speciesism
Caviola, L. and Capraro, V. 2020. Liking but devaluing animals: emotional and deliberative paths to speciesism. Social Psychological and Personality Science. 11 (8), pp. 1080-1088. https://doi.org/10.1177/1948550619893959
Priming intuition disfavors instrumental harm but not impartial beneficence
Capraro, V., Everett, J. and Earp, B. 2019. Priming intuition disfavors instrumental harm but not impartial beneficence. Journal of Experimental Social Psychology. 83, pp. 142-149. https://doi.org/10.1016/j.jesp.2019.04.006
Time pressure and honesty in a deception game
Capraro, V., Schulz, J. and Rand, D. 2019. Time pressure and honesty in a deception game. Journal of Behavioral and Experimental Economics. 79, pp. 93-99. https://doi.org/10.1016/j.socec.2019.01.007
Gender differences in the trade-off between objective equality and efficiency
Capraro, V. 2020. Gender differences in the trade-off between objective equality and efficiency. Judgment and Decision Making. 15 (4), pp. 534-544.
The effect of norm-based messages on reading and understanding COVID-19 pandemic response governmental rules
Bilancini, E., Boncinelli, L., Capraro, V., Celadin, T. and Di Paolo, R. 2020. The effect of norm-based messages on reading and understanding COVID-19 pandemic response governmental rules . Journal of Behavioral Economics for Policy. 4, pp. 45-55.
"Do the right thing" for whom? An experiment on ingroup favouritism, group assorting and moral suasion
Bilancini, E., Boncinelli, L., Capraro, V., Celadin, T. and Di Paolo, R. 2020. "Do the right thing" for whom? An experiment on ingroup favouritism, group assorting and moral suasion. Judgment and Decision Making. 15 (2), pp. 182-192.
Translucent players: explaining cooperative behavior in social dilemmas
Capraro, V. and Halpern, J. 2019. Translucent players: explaining cooperative behavior in social dilemmas. Rationality and Society. 31 (4), pp. 371-408. https://doi.org/10.1177/1043463119885102
Increasing altruistic and cooperative behaviour with simple moral nudges
Capraro, V., Jagfeld, G., Klein, R., Mul, M. and de Pol, I. 2019. Increasing altruistic and cooperative behaviour with simple moral nudges. Scientific Reports. 9 (1). https://doi.org/10.1038/s41598-019-48094-4
The evolution of lying in well-mixed populations
Capraro, V., Perc, M. and Vilone, D. 2019. The evolution of lying in well-mixed populations. Journal of The Royal Society Interface. 16 (156). https://doi.org/10.1098/rsif.2019.0211
The power of moral words: loaded language generates framing effects in the extreme dictator game
Capraro, V. and Vanzo, A. 2019. The power of moral words: loaded language generates framing effects in the extreme dictator game. Judgment and Decision Making. 14 (3), pp. 309-317.
Author correction: Group size effects and critical mass in public goods games
Pereda, M., Capraro, V. and Sánchez, A. 2019. Author correction: Group size effects and critical mass in public goods games. Springer Nature. https://doi.org/10.1038/s41598-019-49306-7
Grand challenges in social physics: in pursuit of moral behavior
Capraro, V. and Perc, M. 2018. Grand challenges in social physics: in pursuit of moral behavior. Frontiers in Physics. 6. https://doi.org/10.3389/fphy.2018.00107
Doing good vs. avoiding bad in prosocial choice: a refined test and extension of the morality preference hypothesis
Tappin, B. and Capraro, V. 2018. Doing good vs. avoiding bad in prosocial choice: a refined test and extension of the morality preference hypothesis. Journal of Experimental Social Psychology. 79, pp. 64-70. https://doi.org/10.1016/j.jesp.2018.06.005
Does the truth come naturally? Time pressure increases honesty in one-shot deception games
Capraro, V. 2017. Does the truth come naturally? Time pressure increases honesty in one-shot deception games. Economics Letters. 158, pp. 54-57. https://doi.org/10.1016/j.econlet.2017.06.015
Gender differences in moral judgment and the evaluation of gender-specified moral agents
Capraro, V. and Sippel, J. 2017. Gender differences in moral judgment and the evaluation of gender-specified moral agents. Cognitive Processing. 18 (4), pp. 399-405. https://doi.org/10.1007/s10339-017-0822-9
Deliberation favours social efficiency by making people disregard their relative shares: evidence from USA and India
Capraro, V., Corgnet, B., Espín, A. and Hernán-González, R. 2017. Deliberation favours social efficiency by making people disregard their relative shares: evidence from USA and India. Royal Society Open Science. 4 (2). https://doi.org/10.1098/RSOS.160605
To know or not to know? Looking at payoffs signals selfish behavior, but it does not actually mean so
Capraro, V. and Kuilder, J. 2016. To know or not to know? Looking at payoffs signals selfish behavior, but it does not actually mean so. Journal of Behavioral and Experimental Economics. 65, pp. 79-84. https://doi.org/10.1016/j.socec.2016.08.005
People making deontological judgments in the Trapdoor dilemma are perceived to be more prosocial in economic games than they actually are
Capraro, V., Sippel, J., Zhao, B., Hornischer, L., Savary, M., Terzopoulou, Z., Faucher, P. and Griffioen, S. 2018. People making deontological judgments in the Trapdoor dilemma are perceived to be more prosocial in economic games than they actually are. PLoS ONE. 13 (10). https://doi.org/10.1371/journal.pone.0205066
Gender differences in altruism on Mechanical Turk: expectations and actual behaviour
Branas-Garza, P., Capraro, V. and Rascon Ramirez, E. 2018. Gender differences in altruism on Mechanical Turk: expectations and actual behaviour. Economics Letters. 170, pp. 19-23. https://doi.org/10.1016/j.econlet.2018.05.022
Gender differences in lying in sender-receiver games: a meta-analysis
Capraro, V. 2018. Gender differences in lying in sender-receiver games: a meta-analysis. Judgment and Decision Making. 13 (4), pp. 345-355.
Hierarchical invasion of cooperation in complex networks
Vilone, D., Capraro, V. and Ramasco, J. 2018. Hierarchical invasion of cooperation in complex networks. Journal of Physics Communications. 2 (2). https://doi.org/10.1088/2399-6528/aaab2e
Do the right thing: experimental evidence that preferences for moral behavior, rather than equity or efficiency per se, drive human prosociality
Capraro, V. and Rand, D. 2018. Do the right thing: experimental evidence that preferences for moral behavior, rather than equity or efficiency per se, drive human prosociality. Judgment and Decision Making. 13 (1), pp. 99-111.
Push, don't nudge: behavioral spillovers and policy instruments
d'Adda, G., Capraro, V. and Tavoni, M. 2017. Push, don't nudge: behavioral spillovers and policy instruments. Economics Letters. 154, pp. 92-95. https://doi.org/10.1016/j.econlet.2017.02.029
Deliberation favours social efficiency by making people disregard their relative shares: evidence from US and India
Capraro, V., Corgnet, B., Espín, A. and Hernán-González, R. 2017. Deliberation favours social efficiency by making people disregard their relative shares: evidence from US and India. Royal Society Open Science. 4 (2). https://doi.org/10.1098/rsos.160605
Partner selection supported by opaque reputation promotes cooperative behavior
Capraro, V., Giardini, F., Vilone, D. and Paolucci, M. 2016. Partner selection supported by opaque reputation promotes cooperative behavior. Judgment and Decision Making. 11 (6), pp. 589-600.