{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,12,17]],"date-time":"2025-12-17T18:10:05Z","timestamp":1765995005790,"version":"3.37.3"},"reference-count":38,"publisher":"Springer Science and Business Media LLC","issue":"2","license":[{"start":{"date-parts":[[2022,7,18]],"date-time":"2022-07-18T00:00:00Z","timestamp":1658102400000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"},{"start":{"date-parts":[[2022,7,18]],"date-time":"2022-07-18T00:00:00Z","timestamp":1658102400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"}],"funder":[{"DOI":"10.13039\/100007195","name":"Universit\u00e0 degli Studi di Napoli Federico II","doi-asserted-by":"crossref","id":[{"id":"10.13039\/100007195","id-type":"DOI","asserted-by":"crossref"}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Dyn Games Appl"],"published-print":{"date-parts":[[2023,6]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>We study a class of non-cooperative aggregative games\u2014referred to as <jats:italic>social purpose games<\/jats:italic>\u2014in which the payoffs depend separately on a player\u2019s own strategy (individual benefits) and on a function of the strategy profile which is common to all players (social benefits) weighted by an individual benefit parameter. This structure allows for an asymmetric assessment of a common social benefit across players. We show that these games have a weighted potential, and we investigate its properties. We investigate the payoff structure and the uniqueness of Nash equilibria and social optima. Furthermore, following the literature on partial cooperation, we investigate the leadership of a single coalition of cooperators, while the rest of players act as non-cooperative followers. In particular, we show that social purpose games admit the emergence of a stable coalition of cooperators for the subclass of <jats:italic>strict<\/jats:italic> social purpose games. As a particular application, we study a standard formulation of the <jats:italic>tragedy of the commons<\/jats:italic>. We show that there emerges a single stable coalition of cooperators that curbs the over-exploitation of the common resource.\n<\/jats:p>","DOI":"10.1007\/s13235-022-00457-9","type":"journal-article","created":{"date-parts":[[2022,7,18]],"date-time":"2022-07-18T18:08:37Z","timestamp":1658167717000},"page":"566-588","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":5,"title":["Emergent Collaboration in Social Purpose Games"],"prefix":"10.1007","volume":"13","author":[{"given":"Robert P.","family":"Gilles","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-7326-8735","authenticated-orcid":false,"given":"Lina","family":"Mallozzi","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Roberta","family":"Messalli","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2022,7,18]]},"reference":[{"key":"457_CR1","doi-asserted-by":"publisher","first-page":"27","DOI":"10.1016\/j.geb.2013.03.009","volume":"81","author":"D Acemoglu","year":"2013","unstructured":"Acemoglu D, Jensen MK (2013) Aggregative comparative statics. Games Econ Behav 81:27\u201349","journal-title":"Games Econ Behav"},{"key":"457_CR2","doi-asserted-by":"crossref","unstructured":"Balder E.(1997) Remarks on Nash equilibria for games with additively coupled payoffs. Econ Theor 9:161\u2013167","DOI":"10.1007\/BF01213450"},{"key":"457_CR3","doi-asserted-by":"publisher","first-page":"25","DOI":"10.1016\/0047-2727(86)90024-1","volume":"29","author":"TC Bergstrom","year":"1986","unstructured":"Bergstrom TC, Blume L, Varian HA (1986) On the private provison of public goods. J Public Econ 29:25\u201349","journal-title":"J Public Econ"},{"key":"457_CR4","doi-asserted-by":"publisher","first-page":"175","DOI":"10.1007\/s11238-011-9246-7","volume":"71","author":"S Chakrabarti","year":"2011","unstructured":"Chakrabarti S, Gilles RP, Lazarova EA (2011) Strategic behavior under partial cooperation. Theor Decis 71:175\u2013193","journal-title":"Theor Decis"},{"key":"457_CR5","doi-asserted-by":"publisher","first-page":"455","DOI":"10.1007\/s11238-018-9666-8","volume":"85","author":"S Chakrabarti","year":"2018","unstructured":"Chakrabarti S, Gilles RP, Lazarova EA (2018) Partial cooperation in strategic decision situations. Theor Decis 85:455\u2013478","journal-title":"Theor Decis"},{"key":"457_CR6","doi-asserted-by":"publisher","first-page":"70","DOI":"10.1111\/manc.12349","volume":"89","author":"S Chakrabarti","year":"2021","unstructured":"Chakrabarti S, Gilles RP, Lazarova EA (2021) Stability of cartels in multi-market cournot oligopolies. Manch Sch 89:70\u201385","journal-title":"Manch Sch"},{"key":"457_CR7","doi-asserted-by":"publisher","first-page":"379","DOI":"10.1007\/BF01263279","volume":"26","author":"P Chander","year":"1997","unstructured":"Chander P, Tulkens H (1997) The core of an economy with multilateral environmental externalities. Internat J Game Theory 26:379\u2013401","journal-title":"Internat J Game Theory"},{"key":"457_CR8","doi-asserted-by":"publisher","first-page":"151","DOI":"10.1016\/0165-4896(94)90001-9","volume":"28","author":"LC Corch\u00f3n","year":"1994","unstructured":"Corch\u00f3n LC (1994) Comparative statics for aggregative games the strong concavity case. Math Soc Sci 28:151\u2013165","journal-title":"Math Soc Sci"},{"key":"457_CR9","doi-asserted-by":"publisher","first-page":"923","DOI":"10.1007\/s00199-004-0566-5","volume":"26","author":"R Cornes","year":"2005","unstructured":"Cornes R, Hartley R (2005) Asymmetric contests with general technologies. Econ Theor 26:923\u2013946","journal-title":"Econ Theor"},{"key":"457_CR10","doi-asserted-by":"publisher","first-page":"17","DOI":"10.2307\/134972","volume":"16","author":"C D\u2019Aspremont","year":"1983","unstructured":"D\u2019Aspremont C, Jacquemin A, Gabszewicz JJ, Weymark JA (1983) On the stability of collusive price leadership. Can J Econ 16:17\u201325","journal-title":"Can J Econ"},{"key":"457_CR11","doi-asserted-by":"publisher","first-page":"1220","DOI":"10.1287\/opre.1080.0686","volume":"57","author":"V De Miguel","year":"2009","unstructured":"De Miguel V, Xu H (2009) A Stochastic multiple-leader Stackelberg model: analysis, computation, and application. Oper Res 57:1220\u20131235","journal-title":"Oper Res"},{"key":"457_CR12","doi-asserted-by":"publisher","first-page":"247","DOI":"10.1111\/j.1467-9779.2006.00262.x","volume":"8","author":"E Diamantoudi","year":"2006","unstructured":"Diamantoudi E, Sartzetakis ES (2006) Stable IEA: an analytical approach. J Public Econ Theory 8:247\u2013263","journal-title":"J Public Econ Theory"},{"key":"457_CR13","doi-asserted-by":"publisher","first-page":"77","DOI":"10.1016\/j.geb.2004.10.007","volume":"54","author":"P Dubey","year":"2006","unstructured":"Dubey P, Haimanko O, Zapechelnyuk A (2006) Strategic complements and substitutes, and potential games. Games Econom Behav 54:77\u201394","journal-title":"Games Econom Behav"},{"key":"457_CR14","doi-asserted-by":"publisher","first-page":"211","DOI":"10.1257\/jep.33.4.211","volume":"33","author":"BM Frischmann","year":"2019","unstructured":"Frischmann BM, Marciano A, Ramello GB (2019) Tradegy of the commons after 50 years. J Econ Perspect 33:211\u2013228","journal-title":"J Econ Perspect"},{"key":"457_CR15","doi-asserted-by":"publisher","first-page":"287","DOI":"10.1016\/j.jebo.2020.07.016","volume":"178","author":"RP Gilles","year":"2020","unstructured":"Gilles RP, Pesce M, Diamantaras D (2020) The provision of collective goods through a social division of labour. J Econ Behav Organ 178:287\u2013312","journal-title":"J Econ Behav Organ"},{"key":"457_CR16","doi-asserted-by":"crossref","unstructured":"Greenberg J (1990) The theory of social situations: an alternative game-theoretic approach. Cambridge University Press, Cambridge","DOI":"10.1017\/CBO9781139173759"},{"key":"457_CR17","doi-asserted-by":"publisher","first-page":"1243","DOI":"10.1126\/science.162.3859.1243","volume":"162","author":"G Hardin","year":"1968","unstructured":"Hardin G (1968) The tragedy of the commons. Science 162:1243\u20131248","journal-title":"Science"},{"key":"457_CR18","doi-asserted-by":"publisher","first-page":"1472","DOI":"10.1287\/mnsc.20.11.1472","volume":"20","author":"J Harsanyi","year":"1974","unstructured":"Harsanyi J (1974) An equilibrium-point interpretation of stable sets and a proposed alternative defnition. Manage Sci 20:1472\u20131495","journal-title":"Manage Sci"},{"key":"457_CR19","doi-asserted-by":"publisher","first-page":"45","DOI":"10.1007\/s00199-008-0419-8","volume":"43","author":"MK Jensen","year":"2010","unstructured":"Jensen MK (2010) Aggregative games and best-reply potentials. Econ Theor 43:45\u201366","journal-title":"Econ Theor"},{"key":"457_CR20","doi-asserted-by":"publisher","first-page":"463","DOI":"10.1007\/s10640-005-4994-x","volume":"33","author":"OS Kwon","year":"2006","unstructured":"Kwon OS (2006) Partial international coordination in the great fish war. Environ Resour Econ 33:463\u2013483","journal-title":"Environ Resour Econ"},{"key":"457_CR21","volume-title":"Two lectures on the checks to population: delivered before the University of Oxford, in Michaelmas Term 1832","author":"WF Lloyd","year":"1833","unstructured":"Lloyd WF (1833) Two lectures on the checks to population: delivered before the University of Oxford, in Michaelmas Term 1832. J.H. Parker Publishers, Oxford"},{"key":"457_CR22","doi-asserted-by":"crossref","unstructured":"Karos OS, Robles L (2021) Full farsighted rationality. Games Econom Behav 130:409\u2013424","DOI":"10.1016\/j.geb.2021.09.004"},{"key":"457_CR23","doi-asserted-by":"crossref","unstructured":"Kimya M (2020) Equilibrium coalitional behavior. Theor Econ 15:669\u2013714","DOI":"10.3982\/TE3055"},{"key":"457_CR24","doi-asserted-by":"publisher","first-page":"25","DOI":"10.3390\/g8030025","volume":"8","author":"L Mallozzi","year":"2017","unstructured":"Mallozzi L, Messalli R (2017) Multi-leader multi-follower model with aggregative uncertainty. Games 8:25","journal-title":"Games"},{"key":"457_CR25","doi-asserted-by":"crossref","unstructured":"Mallozzi, L. (2013): \u201cAn application of optimization theory to the study of equilibria for games: a survey. CEJOR Cent. Eur J Oper Res 21:523\u2013539","DOI":"10.1007\/s10100-012-0245-8"},{"key":"457_CR26","doi-asserted-by":"publisher","first-page":"245","DOI":"10.1142\/S0219198908001923","volume":"10","author":"L Mallozzi","year":"2008","unstructured":"Mallozzi L, Tijs S (2008) Conflict and cooperation in symmetric potential games. Int Game Theory Rev 10:245\u2013256","journal-title":"Int Game Theory Rev"},{"key":"457_CR27","first-page":"1","volume":"29","author":"L Mallozzi","year":"2009","unstructured":"Mallozzi L, Tijs S (2009) Coordinating choice in partial cooperative equilibrium. Econ Bull 29:1\u20136","journal-title":"Econ Bull"},{"key":"457_CR28","first-page":"5","volume":"6","author":"L Mallozzi","year":"2012","unstructured":"Mallozzi L, Tijs S (2012) Stackelberg vs Nash assumption in partially cooperative games. Czech Econ Rev 6:5\u201313","journal-title":"Czech Econ Rev"},{"key":"457_CR29","doi-asserted-by":"publisher","first-page":"1159","DOI":"10.1007\/s00355-012-0658-2","volume":"40","author":"M McGuinty","year":"2013","unstructured":"McGuinty M, Milam G (2013) Public good provisions by asymmetric agents: experimental evidence. Soc Choice Welfare 40:1159\u20131170","journal-title":"Soc Choice Welfare"},{"key":"457_CR30","doi-asserted-by":"publisher","first-page":"124","DOI":"10.1006\/game.1996.0044","volume":"14","author":"D Monderer","year":"1996","unstructured":"Monderer D, Shapley LS (1996) Potential games. Games Econ Behav 14:124\u2013143","journal-title":"Games Econ Behav"},{"key":"457_CR31","doi-asserted-by":"publisher","first-page":"500","DOI":"10.1016\/j.eneco.2013.09.005","volume":"46","author":"SM Olmstead","year":"2014","unstructured":"Olmstead SM (2014) Climate change adaptation and water resource management: a review of the literature. Energy Econ 46:500\u2013509","journal-title":"Energy Econ"},{"key":"457_CR32","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9780511807763","volume-title":"Governing the commons: the evolution of institutions for collective action","author":"E Ostrom","year":"1990","unstructured":"Ostrom E (1990) Governing the commons: the evolution of institutions for collective action. Cambridge University Press, Cambridge"},{"key":"457_CR33","doi-asserted-by":"crossref","unstructured":"Selten R (1970) Aggregations theorie des linear-quadratischen modells. In: Selten R (ed) Preispolitik der Mehrproduktenunternehmung in der statischen Theorie. Springer, pp 113\u2013125","DOI":"10.1007\/978-3-642-48888-7_8"},{"key":"457_CR34","doi-asserted-by":"crossref","unstructured":"Ray, D. and R. Vohra (2015) The farsighted stable set. Econometrica 83:977\u20131011","DOI":"10.3982\/ECTA12022"},{"key":"457_CR35","doi-asserted-by":"publisher","first-page":"1763","DOI":"10.3982\/ECTA16047","volume":"87","author":"D Ray","year":"2019","unstructured":"Ray D, Vohra R (2019) Maximality in the farsighted stable set. Econometrica 87:1763\u20131779","journal-title":"Econometrica"},{"key":"457_CR36","doi-asserted-by":"publisher","first-page":"305","DOI":"10.1016\/0304-4068(90)90005-T","volume":"19","author":"X Vives","year":"1990","unstructured":"Vives X (1990) Nash equilibrium with strategic complementaries. J Math Econ 19:305\u2013321","journal-title":"J Math Econ"},{"key":"457_CR37","volume-title":"Theory of games and economic behavior","author":"J von Neumann","year":"1947","unstructured":"von Neumann J, Morgenstern O (1947) Theory of games and economic behavior, 3rd edn. Princeton University Press, Princeton","edition":"3"},{"key":"457_CR38","unstructured":"von Stackelberg H (1934) Marktform und Gleichgewicht, Habilitation, University of Vienna, translated as Market Structure and Equilibrium, Damien Bazin, Lynn Urch, and Rowland Hill (translators), 2011 ed. Springer"}],"container-title":["Dynamic Games and Applications"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s13235-022-00457-9.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s13235-022-00457-9\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s13235-022-00457-9.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,5,24]],"date-time":"2023-05-24T18:24:21Z","timestamp":1684952661000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s13235-022-00457-9"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,7,18]]},"references-count":38,"journal-issue":{"issue":"2","published-print":{"date-parts":[[2023,6]]}},"alternative-id":["457"],"URL":"https:\/\/doi.org\/10.1007\/s13235-022-00457-9","relation":{},"ISSN":["2153-0785","2153-0793"],"issn-type":[{"type":"print","value":"2153-0785"},{"type":"electronic","value":"2153-0793"}],"subject":[],"published":{"date-parts":[[2022,7,18]]},"assertion":[{"value":"30 May 2022","order":1,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"18 July 2022","order":2,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}]}}