eprintid: 47730 rev_number: 15 eprint_status: archive userid: 1482 importid: 105 dir: disk0/00/04/77/30 datestamp: 2023-04-12 13:48:23 lastmod: 2024-01-11 14:25:40 status_changed: 2024-01-11 14:25:40 type: monograph metadata_visibility: show creators_name: Peña, Jorge creators_name: Heifetz, Aviad creators_name: Nöldeke, Georg creators_idrefppn: 260087777 creators_idrefppn: 164589422 creators_idrefppn: 12629819X creators_halaffid: 506116 title: The shirker’s dilemma and the prospect of cooperation in large groups ispublished: pub subjects: subjects_ECO abstract: Cooperation usually becomes harder to sustain as groups become larger because incentives to shirk increase with the number of potential contributors to collective action. But is this always the case?Here we study a binary-action cooperative dilemma where a public good is provided as long as not more than a given number of players shirk from a costly cooperative task. We find that at the stable polymorphic equilibrium, which exists when the cost of cooperation is low enough, the probability of cooperating increases with group size and reaches a limit of one when the group size tends to infinity. Nevertheless, increasing the group size may increase or decrease the probability that the public good is provided at such an equilibrium, depending on the cost value. We also prove that the expected payoff to individuals at the stable equilibrium (i.e., their fitness) decreases with group size. For low enough costs of cooperation, both the probability of provision of the public good and the expected payoff converge to positive values in the limit of large group sizes. However, we also find that the basin of attraction of the stable polymorphic equilibrium is a decreasing function of group size and shrinks to zero in the limit of very large groups. Overall, we demonstrate non-trivial comparative statics with respect to group size in an otherwise simple collective action problem. date: 2023-04 date_type: published publisher: IAST Working Paper official_url: http://iast.fr/pub/128025 faculty: tse divisions: tse keywords: replicator dynamics keywords: evolutionary game theory keywords: collective action keywords: cooperation keywords: group size language: en has_fulltext: TRUE view_date_year: 2023 full_text_status: public monograph_type: working_paper series: IAST Working Paper volume: 23-152 place_of_pub: Toulouse pages: 31 institution: Université Toulouse Capitole department: Toulouse School of Economics book_title: IAST Working Paper oai_identifier: oai:tse-fr.eu:128025 harvester_local_overwrite: creators_idrefppn harvester_local_overwrite: creators_halaffid harvester_local_overwrite: pending harvester_local_overwrite: department harvester_local_overwrite: institution harvester_local_overwrite: place_of_pub harvester_local_overwrite: pages oai_lastmod: 2024-01-09T08:53:58Z oai_set: tse site: ut1 citation: Peña, Jorge , Heifetz, Aviad and Nöldeke, Georg (2023) The shirker’s dilemma and the prospect of cooperation in large groups. IAST Working Paper, n. 23-152, Toulouse document_url: https://publications.ut-capitole.fr/id/eprint/47730/1/wp_iast_152.pdf