{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,7]],"date-time":"2026-04-07T11:56:22Z","timestamp":1775562982360,"version":"3.50.1"},"reference-count":28,"publisher":"MDPI AG","issue":"11","license":[{"start":{"date-parts":[[2020,11,20]],"date-time":"2020-11-20T00:00:00Z","timestamp":1605830400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>This paper proposes a further development of the mathematical theory of swarms to behavioral dynamics of social and economic systems, with an application to the modeling of price series in a market. The complexity features of the system are properly described by modeling the asymmetric interactions between buyers and sellers, specifically considering the so-called cherry picking phenomenon, by which not only prices but also qualities are considered when buying a good. Finally, numerical simulations are performed to depict the predictive ability of the model and to show interesting emerging behaviors, as the coordination of buyers and their division in endogenous clusters.<\/jats:p>","DOI":"10.3390\/sym12111912","type":"journal-article","created":{"date-parts":[[2020,11,20]],"date-time":"2020-11-20T09:46:18Z","timestamp":1605865578000},"page":"1912","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":15,"title":["Cherry Picking: Consumer Choices in Swarm Dynamics, Considering Price and Quality of Goods"],"prefix":"10.3390","volume":"12","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-4477-5639","authenticated-orcid":false,"given":"Damian","family":"Knopoff","sequence":"first","affiliation":[{"name":"CIEM CONICET and FaMAF, National University of Cordoba, 5000 C\u00f3rdoba, Argentina"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Valeria","family":"Secchini","sequence":"additional","affiliation":[{"name":"School of Science of Nature, University of Torino, 10100 Torino, Italy"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-7416-0870","authenticated-orcid":false,"given":"Pietro","family":"Terna","sequence":"additional","affiliation":[{"name":"School of Economics, University of Torino, 10100 Torino, Italy"},{"name":"Fondazione Collegio Carlo Alberto, 10100 Torino, Italy"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2020,11,20]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"853","DOI":"10.1109\/TAC.2007.895842","article-title":"Emergent behavior in flocks","volume":"52","author":"Cucker","year":"2007","journal-title":"IEEE T. Automat. Contr."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"353","DOI":"10.3934\/nhm.2020022","article-title":"Swarms dynamics approach to behavioral economy: Theoretical tools and price sequences","volume":"15","author":"Bellomo","year":"2020","journal-title":"Netw. Heterog. Media"},{"key":"ref_3","doi-asserted-by":"crossref","unstructured":"Bellomo, N., Bellouquid, A., Gibelli, L., and Outada, N. (2017). A Quest Towards a Mathematical Theory of Living Systems, Birkh\u00e4user.","DOI":"10.1007\/978-3-319-57436-3"},{"key":"ref_4","unstructured":"Pareschi, L., and Toscani, G. (2013). Interacting Multiagent Systems: Kinetic Equations and Monte Carlo Methods, Oxford University Press."},{"key":"ref_5","doi-asserted-by":"crossref","unstructured":"Bellomo, N., Ha, S.-Y., and Outada, N. (2020). Towards a mathematical theory of behavioral swarms. ESAIM Contr. Op. Ca. Va., in press.","DOI":"10.1051\/cocv\/2020071"},{"key":"ref_6","doi-asserted-by":"crossref","unstructured":"Dolfin, M., Leonida, L., and Muzzupappa, E. (2019). Forecasting Efficient Risk\/Return Frontier for Equity Risk with a KTAP Approach\u2014A Case Study in Milan Stock Exchange. Symmetry, 11.","DOI":"10.3390\/sym11081055"},{"key":"ref_7","doi-asserted-by":"crossref","unstructured":"Dolfin, M., Knopoff, D., Limosani, M., and Xibilia, M.G. (2019). Credit risk contagion and systemic risk on networks. Mathematics, 7.","DOI":"10.3390\/math7080713"},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"14041","DOI":"10.1142\/S021820252050027X","article-title":"From particles to firms: On the kinetic theory of climbing up evolutionary landscapes","volume":"30","author":"Bellomo","year":"2020","journal-title":"Math. Model. Methods Appl. Sci."},{"key":"ref_9","doi-asserted-by":"crossref","unstructured":"Lachowicz, M., Leszczy\u0144ski, H., and Pu\u017aniakowska\u2013Ga\u0142uch, E. (2019). Diffusive and Anti-Diffusive Behavior for Kinetic Models of Opinion Dynamics. Symmetry, 11.","DOI":"10.3390\/sym11081024"},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"405","DOI":"10.1142\/S0218202513400137","article-title":"On a mathematical theory of complex systems on networks with application to opinion formation","volume":"24","author":"Knopoff","year":"2014","journal-title":"Math. Model. Methods Appl. Sci."},{"key":"ref_11","doi-asserted-by":"crossref","unstructured":"Buffa, B., Knopoff, D., and Torres, G. (2020). Parameter estimation and measurement of social inequality in a kinetic model for wealth distribution. Mathematics, 8.","DOI":"10.3390\/math8050786"},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"1051","DOI":"10.1142\/S0218202516500251","article-title":"Stochastic evolutionary differential games toward a systems theory of behavioral social dynamics","volume":"26","author":"Bellomo","year":"2016","journal-title":"Math. Mod. Meth. Appl. Sci."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"362","DOI":"10.1016\/j.physa.2018.02.070","article-title":"Kinetic models for goods exchange in a multi-agent market","volume":"499","author":"Brugna","year":"2018","journal-title":"Phys. A Stat. Mech. Appl."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"57","DOI":"10.1007\/BF02512229","article-title":"How to build and use agent-based models in social science","volume":"1","author":"Gilbert","year":"2000","journal-title":"Mind Soc."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"262","DOI":"10.1016\/S0020-0255(02)00280-3","article-title":"Agent-based computational economics: Modeling economies as complex adaptive systems","volume":"149","author":"Tesfatsion","year":"2003","journal-title":"Inform. Sci."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"7","DOI":"10.18564\/jasss.4259","article-title":"The odd protocol for describing agent-based and other simulation models: A second update to improve clarity, replication, and structural realism","volume":"23","author":"Grimm","year":"2020","journal-title":"J. Artif. Soc. S."},{"key":"ref_17","first-page":"49","article-title":"Recent advances in opinion modeling: Control and social influence","volume":"Volume 1","author":"Albi","year":"2017","journal-title":"Active Particles, Advances in Theory, Models, and Applications Modeling and Simulation in Science, Engineering"},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"681","DOI":"10.1142\/S0218202519400037","article-title":"Social dynamics models with time-varying influence","volume":"29","author":"McQuade","year":"2019","journal-title":"Math. Models Methods Appl. Sci."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"2628","DOI":"10.1137\/18M1168911","article-title":"Sparse control of Hegselmann-Krause models: Black hole and declustering","volume":"57","author":"Piccoli","year":"2019","journal-title":"SIAM J. Control Optim."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"1232","DOI":"10.1073\/pnas.0711437105","article-title":"Interaction ruling animal collective behavior depends on topological rather than metric distance: Evidence from a field study","volume":"105","author":"Ballerini","year":"2008","journal-title":"Proc. Natl. Acad. Sci. USA"},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"745","DOI":"10.1142\/S0218202517500154","article-title":"A quest toward a mathematical theory of the dynamics of swarms","volume":"27","author":"Bellomo","year":"2017","journal-title":"Math. Mod. Meth. Appl. Sci."},{"key":"ref_22","doi-asserted-by":"crossref","unstructured":"Lachowicz, M., and Leszczy\u0144ski, H. (2020). Modeling Asymmetric Interactions in Economy. Mathematics, 8.","DOI":"10.3390\/math8040523"},{"key":"ref_23","doi-asserted-by":"crossref","unstructured":"Hsu, J., Morgenstern, J., Rogers, R., Roth, A., and Vohra, R. (2016, January 19\u201321). Do prices coordinate markets?. Proceedings of the Forty-eighth Annual ACM symposium on Theory of Computing, Cambridge, MA, USA.","DOI":"10.1145\/2897518.2897559"},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"3275","DOI":"10.1257\/aer.20130564","article-title":"Intertemporal price discrimination: Dynamic arrivals and changing values","volume":"106","author":"Garrett","year":"2016","journal-title":"Am. Econ. Rev."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"245","DOI":"10.2307\/2118517","article-title":"Sticky prices: New evidence from retail catalogs","volume":"110","author":"Kashyap","year":"1995","journal-title":"Quarter. J. Econ."},{"key":"ref_26","doi-asserted-by":"crossref","unstructured":"Mazzoli, M., Morini, M., and Terna, P. (2019). Rethinking Macroeconomics with Endogenous Market Structurel, Cambridge University Press.","DOI":"10.1017\/9781108697019"},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"1861","DOI":"10.1142\/S021820251350053X","article-title":"On the difficult interplay between life \u201ccomplexity\u201d and mathematical sciences","volume":"23","author":"Bellomo","year":"2013","journal-title":"Math. Mod. Meth. Appl. Sci."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"1901","DOI":"10.1142\/S0218202519500374","article-title":"Traffic, crowds, and swarms. From kinetic theory and multiscale methods to applications and research perspectives","volume":"29","author":"Albi","year":"2019","journal-title":"Math. Mod. Meth. Appl. Sci."}],"container-title":["Symmetry"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2073-8994\/12\/11\/1912\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T10:35:01Z","timestamp":1760178901000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2073-8994\/12\/11\/1912"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2020,11,20]]},"references-count":28,"journal-issue":{"issue":"11","published-online":{"date-parts":[[2020,11]]}},"alternative-id":["sym12111912"],"URL":"https:\/\/doi.org\/10.3390\/sym12111912","relation":{},"ISSN":["2073-8994"],"issn-type":[{"value":"2073-8994","type":"electronic"}],"subject":[],"published":{"date-parts":[[2020,11,20]]}}}