{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,11,18]],"date-time":"2025-11-18T21:01:02Z","timestamp":1763499662796,"version":"build-2065373602"},"reference-count":49,"publisher":"MDPI AG","issue":"8","license":[{"start":{"date-parts":[[2021,8,1]],"date-time":"2021-08-01T00:00:00Z","timestamp":1627776000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100014422","name":"Szko\u0142a G\u0142\u00f3wna Handlowa w Warszawie","doi-asserted-by":"publisher","award":["Badania statutowe"],"award-info":[{"award-number":["Badania statutowe"]}],"id":[{"id":"10.13039\/501100014422","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>The present paper reports simulation results for a simple model of reference group influence on market choices, e.g., brand selection. The model was simulated on three types of random graphs, Erdos\u2013Renyi, Barabasi\u2013Albert, and Watts\u2013Strogatz. The estimates of equilibria based on the simulation results were compared to the equilibria of the theoretical model. It was verified that the simulations exhibited the same qualitative behavior as the theoretical model, and for graphs with high connectivity and low clustering, the quantitative predictions offered a viable approximation. These results allowed extending the results from the simple theoretical model to networks. Thus, by increasing the positive response towards the reference group, the third party may create a bistable situation with two equilibria at which respective brands dominate the market. This task is easier for large reference groups.<\/jats:p>","DOI":"10.3390\/e23081007","type":"journal-article","created":{"date-parts":[[2021,8,1]],"date-time":"2021-08-01T21:51:07Z","timestamp":1627854667000},"page":"1007","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Market Choices Driven by Reference Groups: A Comparison of Analytical and Simulation Results on Random Networks"],"prefix":"10.3390","volume":"23","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-0728-5315","authenticated-orcid":false,"given":"Micha\u0142","family":"Ramsza","sequence":"first","affiliation":[{"name":"Department of Mathematics and Mathematical Economics, SGH Warsaw School of Economics, Al. Niepodleg\u0142o\u015bci 162, 02-554 Warsaw, Poland"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2021,8,1]]},"reference":[{"key":"ref_1","unstructured":"Merton, R.K., and Rossi, A.K. (1949). Contributions to the theory of reference groups and social structure. Social Theory and Social Structure, Free Press."},{"key":"ref_2","unstructured":"Merton, R.K. (1949). Social Theory and Social Structure, Free Press."},{"key":"ref_3","doi-asserted-by":"crossref","unstructured":"Asch, S. (1952). Social Psychology, Prentice Hall.","DOI":"10.1037\/10025-000"},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"102","DOI":"10.1086\/208685","article-title":"Students and Housewives: Differences in Susceptibility to Reference Group Influence","volume":"4","author":"Park","year":"1977","journal-title":"J. Consum. Res."},{"key":"ref_5","unstructured":"Wright, J.D. (2015). Social Influence, Sociology of. International Encyclopedia of the Social & Behavioral Sciences, Elsevier. [2nd ed.]."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"167","DOI":"10.1137\/S003614450342480","article-title":"The structure and function of complex networks","volume":"45","author":"Newman","year":"2003","journal-title":"SIAM Rev."},{"key":"ref_7","doi-asserted-by":"crossref","unstructured":"Doreian, P., Batagelj, V., and Ferligoj, A. (2005). Generalized Blockmodeling, Cambridge University Press. Number 25.","DOI":"10.1017\/CBO9780511584176"},{"key":"ref_8","first-page":"455","article-title":"Generalized blockmodeling with Pajek","volume":"1","author":"Batagelj","year":"2004","journal-title":"Metod. Zv."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"730","DOI":"10.1086\/226141","article-title":"Social structure from multiple networks. I. Blockmodels of roles and positions","volume":"81","author":"White","year":"1976","journal-title":"Am. J. Sociol."},{"key":"ref_10","doi-asserted-by":"crossref","unstructured":"Mu\u00f1oz, H., Vicente, E., Gonz\u00e1lez, I., Mateos, A., and Jim\u00e9nez-Mart\u00edn, A. (2021). ConvGraph: Community Detection of Homogeneous Relationships in Weighted Graphs. Mathematics, 9.","DOI":"10.3390\/math9040367"},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"221","DOI":"10.1080\/0022250X.1994.9990145","article-title":"The nature of the social agent","volume":"19","author":"Carley","year":"1994","journal-title":"J. Math. Sociol."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"129","DOI":"10.1080\/00222500902718239","article-title":"Structural Balance: A Dynamic Perspective","volume":"33","author":"Abell","year":"2009","journal-title":"J. Math. Sociol."},{"key":"ref_13","first-page":"43","article-title":"Networks, crowds, and markets: Reasoning about a highly connected world","volume":"9","author":"Easley","year":"2012","journal-title":"Significance"},{"key":"ref_14","doi-asserted-by":"crossref","unstructured":"Jackson, M.O. (2010). Social and Economic Networks, Princeton University Press.","DOI":"10.2307\/j.ctvcm4gh1"},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"1771","DOI":"10.1073\/pnas.1013213108","article-title":"Continuous-time model of structural balance","volume":"108","author":"Marvel","year":"2011","journal-title":"Proc. Natl. Acad. Sci. USA"},{"key":"ref_16","doi-asserted-by":"crossref","unstructured":"K\u0142opotek, R.A. (2020). Modeling Bimodal Social Networks Subject to the Recommendation with the Cold Start User-Item Model. Computers, 9.","DOI":"10.3390\/computers9010011"},{"key":"ref_17","doi-asserted-by":"crossref","unstructured":"Kinateder, M., and Merlino, L.P. (2021). The Evolution of Networks and Local Public Good Provision: A Potential Approach. Games, 12.","DOI":"10.3390\/g12030055"},{"key":"ref_18","unstructured":"Goyal, S. (2012). Connections: An Introduction to the Economics of Networks, Princeton University Press."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"112","DOI":"10.1257\/mic.2.1.112","article-title":"Na\u00efve Learning in Social Networks and the Wisdom of Crowds","volume":"2","author":"Golub","year":"2010","journal-title":"Am. Econ. J. Microecon."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"3","DOI":"10.1007\/s13235-010-0004-1","article-title":"Opinion dynamics and learning in social networks","volume":"1","author":"Acemoglu","year":"2011","journal-title":"Dyn. Games Appl."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"7280","DOI":"10.1073\/pnas.082080899","article-title":"Agent-based modeling: Methods and techniques for simulating human systems","volume":"99","author":"Bonabeau","year":"2002","journal-title":"Proc. Natl. Acad. Sci. USA"},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"118","DOI":"10.1080\/01621459.1974.10480137","article-title":"Reaching a consensus","volume":"69","author":"DeGroot","year":"1974","journal-title":"J. Am. Stat. Assoc."},{"key":"ref_23","doi-asserted-by":"crossref","unstructured":"Friedkin, N.E., and Johnsen, E.C. (2011). Social Influence Network Theory: A Sociological Examination of Small Group Dynamics, Cambridge University Press.","DOI":"10.1017\/CBO9780511976735"},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"1201","DOI":"10.1093\/restud\/rdr004","article-title":"Bayesian learning in social notworks","volume":"78","author":"Acemoglu","year":"2011","journal-title":"Rev. Econ. Stud."},{"key":"ref_25","doi-asserted-by":"crossref","unstructured":"Helbing, D. (1995). Quantitative Sociodynamics. Stochastic Methods and Models of Social Interaction Procesess, Kluwer Academic Publishers.","DOI":"10.1007\/978-94-015-8516-3"},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1109\/TNET.2008.925623","article-title":"Virus Spread in Networks","volume":"17","author":"Omic","year":"2009","journal-title":"IEEE\/ACM Trans. Netw."},{"key":"ref_27","doi-asserted-by":"crossref","unstructured":"Shioda, S., Nakajima, K., and Minamikawa, M. (2020). Information spread across social network services with non-responsiveness of individual users. Computers, 9.","DOI":"10.3390\/computers9030065"},{"key":"ref_28","doi-asserted-by":"crossref","unstructured":"Alsaif, S.A., Hidri, A., and Hidri, M.S. (2021). Towards Inferring Influential Facebook Users. Computers, 10.","DOI":"10.3390\/computers10050062"},{"key":"ref_29","first-page":"44","article-title":"Group stability: A socio-cognitive approach","volume":"7","author":"Carley","year":"1990","journal-title":"Adv. Group Process."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"183","DOI":"10.1086\/208911","article-title":"Reference group influence on product and brand purchase decisions","volume":"9","author":"Bearden","year":"1982","journal-title":"J. Consum. Res."},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"198","DOI":"10.1086\/209296","article-title":"The influence of familial and peer-based reference groups on consumer decisions","volume":"19","author":"Childers","year":"1992","journal-title":"J. Consum. Res."},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"339","DOI":"10.1207\/S15327663JCP1303_14","article-title":"You are what they eat: The influence of reference groups on consumers\u2019 connections to brands","volume":"13","author":"Escalas","year":"2003","journal-title":"J. Consum. Psychol."},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"404","DOI":"10.1207\/s15327663jcp1604_11","article-title":"To be or not be? The influence of dissociative reference groups on consumer preferences","volume":"16","author":"White","year":"2006","journal-title":"J. Consum. Psychol."},{"key":"ref_34","first-page":"157","article-title":"Reference group Influence on Consumer Decision Making Process: A study in the Brazilian sports utilitarian vehicles segment","volume":"10","author":"Serralvo","year":"2010","journal-title":"J. Acad. Bus. Econ."},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"611","DOI":"10.1007\/s00191-015-0402-z","article-title":"Market choices driven by reference groups. An evolutionary approach","volume":"25","author":"Ramsza","year":"2015","journal-title":"J. Evol. Econ."},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"8788","DOI":"10.1073\/pnas.1320040111","article-title":"Experimental evidence of massive-scale emotional contagion through social networks","volume":"111","author":"Kramer","year":"2014","journal-title":"Proc. Natl. Acad. Sci. USA"},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"873","DOI":"10.1111\/1468-0262.00429","article-title":"Deterministic approximation of stochastic evolution in games","volume":"71","author":"Benaim","year":"2003","journal-title":"Econometrica"},{"key":"ref_38","unstructured":"Wiggins, S. (2003). Introduction to Applied Nonlinear Dynamical Systems and Chaos, Springer."},{"key":"ref_39","first-page":"290","article-title":"On random graphs","volume":"6","author":"Erdos","year":"1959","journal-title":"Publ. Math."},{"key":"ref_40","first-page":"17","article-title":"On the evolution of random graphs","volume":"5","author":"Erdos","year":"1960","journal-title":"Publ. Math. Inst. Hung. Acad. Sci."},{"key":"ref_41","doi-asserted-by":"crossref","first-page":"261","DOI":"10.1007\/BF02066689","article-title":"On the strength of connectedness of a random graph","volume":"12","author":"Erdos","year":"1961","journal-title":"Acta Math. Acad. Sci. Hung."},{"key":"ref_42","doi-asserted-by":"crossref","first-page":"509","DOI":"10.1126\/science.286.5439.509","article-title":"Emergence of scaling in random networks","volume":"286","author":"Albert","year":"1999","journal-title":"Science"},{"key":"ref_43","doi-asserted-by":"crossref","first-page":"440","DOI":"10.1038\/30918","article-title":"Collective dynamics of \u2018small-world\u2019networks","volume":"393","author":"Watts","year":"1998","journal-title":"Nature"},{"key":"ref_44","doi-asserted-by":"crossref","unstructured":"Watts, D.J. (1999). Small Worlds: The Dynamics of Networks between Order and Randomness, Princeton University Press.","DOI":"10.1515\/9780691188331"},{"key":"ref_45","doi-asserted-by":"crossref","first-page":"5766","DOI":"10.1073\/pnas.082090499","article-title":"A simple model of global cascades on random networks","volume":"99","author":"Watts","year":"2002","journal-title":"Proc. Natl. Acad. Sci. USA"},{"key":"ref_46","unstructured":"Bollobas, B. (1985). Random Graphs, Academic Press."},{"key":"ref_47","doi-asserted-by":"crossref","first-page":"113","DOI":"10.1016\/0166-218X(88)90008-X","article-title":"Threshold phenomena in random structures","volume":"19","author":"Cohen","year":"1988","journal-title":"Discret. Appl. Math."},{"key":"ref_48","doi-asserted-by":"crossref","first-page":"47","DOI":"10.1103\/RevModPhys.74.47","article-title":"Statistical mechanics of complex networks","volume":"74","author":"Albert","year":"2002","journal-title":"Rev. Mod. Phys."},{"key":"ref_49","doi-asserted-by":"crossref","first-page":"350","DOI":"10.1016\/j.ins.2016.12.027","article-title":"Clustering coefficients of large networks","volume":"382","author":"Li","year":"2017","journal-title":"Inf. Sci."}],"container-title":["Entropy"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1099-4300\/23\/8\/1007\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T06:38:44Z","timestamp":1760164724000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1099-4300\/23\/8\/1007"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021,8,1]]},"references-count":49,"journal-issue":{"issue":"8","published-online":{"date-parts":[[2021,8]]}},"alternative-id":["e23081007"],"URL":"https:\/\/doi.org\/10.3390\/e23081007","relation":{},"ISSN":["1099-4300"],"issn-type":[{"type":"electronic","value":"1099-4300"}],"subject":[],"published":{"date-parts":[[2021,8,1]]}}}