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A network model of immigration: Enclave formation vs. cultural integration
1.  Dept. of Biomathematics, UCLA, Los Angeles, CA 900951766, USA 
2.  Dept. of Mathematics, CSUN, Los Angeles, CA 913308313, USA 
3.  Dept. of Mathematics, UCLA, Los Angeles, CA 900951555, USA 
Successfully integrating newcomers into native communities has become a key issue for policy makers, as the growing number of migrants has brought cultural diversity, new skills, but also, societal tensions to receiving countries. We develop an agentbased network model to study interacting "hosts" and "guests" and to identify the conditions under which cooperative/integrated or uncooperative/segregated societies arise. Players are assumed to seek socioeconomic prosperity through game theoretic rules that shift network links, and cultural acceptance through opinion dynamics. We find that the main predictor of integration under given initial conditions is the timescale associated with cultural adjustment relative to social link remodeling, for both guests and hosts. Fast cultural adjustment results in cooperation and the establishment of hostguest connections that are sustained over long times. Conversely, fast social link remodeling leads to the irreversible formation of isolated enclaves, as migrants and natives optimize their socioeconomic gains through ingroup connections. We discuss how migrant population sizes and increasing socioeconomic rewards for hostguest interactions, through governmental incentives or by admitting migrants with highly desirable skills, may affect the overall immigrant experience.
References:
[1] 
R. Axelrod, The dissemination of culture: A model with local convergence and global polarization, The Journal of Conflict Resolution, 41 (1997), 203226. doi: 10.1177/0022002797041002001. 
[2] 
P. Barron, K. Kaiser and M. Pradhan, Local Conflict in Indonesia: Measuring Incidence and Identifying Patterns, World Bank Policy Research Paper 3384, 2004. 
[3] 
J. W. Berry, Acculturation and adaptation in a new society, International Migration Quarterly Review, 30 (1992), 6985. doi: 10.1111/j.14682435.1992.tb00776.x. 
[4] 
J. W. Berry, Living successfully in two cultures, International Journal of Intercultural Relations, 29 (2005), 697712. 
[5] 
J. W. Berry, U. Kim, T. Minde and D. Mok, Comparative studies of acculturative stress, The International Migration Review, 21 (1987), 491511. 
[6] 
P. Boyle, K. Halfacree and V. Robinson, Exploring contemporary migration, 2nd edition, Pearson Education Limited, London and New York, 2013. 
[7]  S. Castles and M. J. Miller, The Age of Migration: International Population Movements in the Modern World, The Guilford Press, New York, 2003. 
[8] 
E. M. Chaney, Foreword: The world economy and contemporary migration, The International Migration Review, 13 (1979), 204212. doi: 10.2307/2545027. 
[9] 
Y.S. Chiang, Cooperation could evolve in complex networks when activated conditionally on network characteristics, Journal of Artificial Societies and Social Simulation, 16 (2013), 6. doi: 10.18564/jasss.2148. 
[10] 
Y.L. Chuang, M. R. D'Orsogna and T. Chou, A bistable belief dynamics model for radicalization within sectarian conflict, Quarterly of Applied Mathematics, 75 (2017), 1937. doi: 10.1090/qam/1446. 
[11] 
M. D. Cohen, R. L. Riolo and R. Axelrod, The role of social structure in the maintenance of cooperative regimes, Rationality and Society, 13 (2001), 532. doi: 10.1177/104346301013001001. 
[12] 
M. H. Crawford and B. C. Campbell (eds.), Causes and Consequences of Human Migration, Cambridge University Press, Cambridge, UK, 2012. doi: 10.1017/CBO9781139003308. 
[13] 
A. P. Damm, Determinants of recent immigrants'location choices: Quasiexperimental evidence, Journal of Population Economics, 22 (2009), 145174. 
[14] 
G. Deffuant, D. Neau, F. Amblard and G. Weisbuch, Mixing beliefs among interacting agents, Advances in Complex Systems, 3 (2000), 8798. doi: 10.1142/S0219525900000078. 
[15] 
M. H. DeGroot, Reaching a consensus, Journal of the American Statistical Association, 69 (1974), 118121. 
[16] 
K. Fehl, D. J. van der Post and D. Semmann, Coevolution of behaviour and social network structure promotes human cooperation, Ecology Letters, 14 (2011), 546551. doi: 10.1111/j.14610248.2011.01615.x. 
[17] 
K. Felijakowski and R. Kosinski, Bounded confidence model in complex networks, International Journal of Modern Physics C, 24 (2013), 1350049, 12pp. doi: 10.1142/S0129183113500496. 
[18] 
K. Felijakowski and R. Kosinski, Opinion formation and selforganization in a social network in an intelligent agent system, ACTA Physica Polonica B, 45 (2014), 21232134. doi: 10.5506/APhysPolB.45.2123. 
[19] 
M. Fossett, Ethnic preferences, social distance dynamics, and residential segregation: Theoretical explorations using simulation analysis, The Journal of Mathematical Sociology, 30 (2006), 185273. doi: 10.1080/00222500500544052. 
[20] 
N. E. Friedkin, Choice shift and group polarization, American Sociological Review, 64 (1999), 856875. 
[21] 
A. Gabel, P. L. Krapivsky and S. Redner, Highly dispersed networks by enhanced redirection, Physical Review E, 88 (2013), 050802(R). doi: 10.1103/PhysRevE.88.050802. 
[22] 
S. Galam, Heterogeneous beliefs, segregation, and extremism in the making of public opinions, Physical Review E, 71 (2005), 046123. doi: 10.1103/PhysRevE.71.046123. 
[23] 
S. Galam, Stubbornness as an unfortunate key to win a public debate: An illustration from sociophysics, Society, 15 (2016), 117130. doi: 10.1007/s112990150175y. 
[24] 
S. Galam and M. A. Javarone, Modeling radicalization phenomena in heterogeneous populations, PLOS One, 11 (2016), e0155407. doi: 10.1371/journal.pone.0155407. 
[25] 
B. Golub and M. O. Jackson, Naíve learning in social networks and the wisdom of crowds, American Economic Journal: Microeconomics, 2 (2010), 112149. doi: 10.1257/mic.2.1.112. 
[26] 
D. Hales, Cooperation without memory or space: Tags, groups and the Prisoner's Dilemma, in MultiAgentBased Simulation. (eds. S. Moss and P. Davidsson), Springer, Berlin/Heidelberg, 2000, 157–166. doi: 10.1007/3540445617_12. 
[27] 
R. A. Hammond and R. Axelrod, The evolution of ethnocentrism, Journal of Conflict Resolution, 50 (2006), 926936. doi: 10.1177/0022002706293470. 
[28] 
D. J. Haw and J. Hogan, A dynamical systems model of unorganized segregation, The Journal of Mathematical Sociology, 42 (2018), 113127. doi: 10.1080/0022250X.2018.1427091. 
[29] 
A. D. Henry, P. Pralat and C.Q. Zhang, Emergence of segregation in evolving social networks, PNAS, 108 (2011), 86058610. doi: 10.1073/pnas.1014486108. 
[30]  P. Ireland, Becoming Europe: Immigration Integration And The Welfare State, University of Pittsburgh Press, Pittsburgh, PA, 2004. 
[31] 
M. A. Javarone, A. E. Atzeni and S. Galam, Emergence of cooperation in the Prisoner's Dilemma driven by conformity, in Applications of Evolutionary Computation. EvoApplications 2015. Lecture Notes in Computer Science (eds. A. Mora and G. Squillero), vol. 9028, Springer, Cham, 2015, 155–163. doi: 10.1007/9783319165493_13. 
[32] 
W. Kandel and J. Cromartie, New patterns of Hispanic settlement in rural America, Technical Report 99, United States Department of Agriculture, 2004. 
[33] 
T. B. Klos, Decentralized interaction and coadaptation in the repeated prisoners dilemma, Computational and Mathematical Organization Theory, 5 (1999), 147165. 
[34] 
R. Koopmans, Tradeoffs between equality and difference: Immigrant integration, multiculturalism and the welfare state in crossnational perspective, Journal of Ethnic and Migration Studies, 36 (2010), 126. doi: 10.1080/13691830903250881. 
[35] 
U. Krause, A discrete nonlinear and nonautonomous model of consensus formation, in Communications in Difference Equations (eds. S. Elaydi, G. Ladas, J. Popenda and J. Rakowski), Amsterdam: Gordon and Breach, 2000, 227–236. 
[36] 
D. T. Lichter, D. Parisi and M. C. Taquino, Emerging patterns of Hispanic residential segregation: Lessons from rural and small–town America, Rural Sociology, 81 (2016), 483518. doi: 10.1111/ruso.12108. 
[37] 
D. T. Lichter, D. Parisi, M. C. Taquino and S. M. Grice, Residential segregation in new Hispanic destinations: Cities, suburbs, and rural communities compared, Social Science Research, 39 (2010), 215230. doi: 10.1016/j.ssresearch.2009.08.006. 
[38] 
A. Németh and K. Takács, The evolution of altruism in spatially structured populations, Journal of Artificial Societies and Social Simulations, 10 (2007), 113. 
[39] 
A. Nowak, J. Szamrej and B. Latané, From private attitude to public opinion: A dynamic theory of social impact, Psychological Review, 97 (1990), 362376. doi: 10.1037/0033295X.97.3.362. 
[40] 
N. Priest, Y. Paradies, A. Ferdinand, L. Rouhani and M. Kelaher, Patterns of intergroup contact in public spaces: Microecology of segregation in Australian communities, Societies, 4 (2014), 3044. doi: 10.3390/soc4010030. 
[41] 
R. Riolo, The Effects of TagMediated Selection of Partners in Evolving Populations Playing the Iterated Prisoner's Dilemma, Technical report, Santa Fe Institute, Santa Fe, NM, 1997. 
[42] 
R. L. Riolo, M. D. Cohen and R. Axelrod, Evolution of cooperation without reciprocity, Nature, 414 (2001), 441443. doi: 10.1038/35106555. 
[43] 
F. C. Santos, J. M. Pacheco and T. Lenaerts, Cooperation prevails when individuals adjust their social ties, PLoS Computational Biology, 2 (2006), e140. doi: 10.1371/journal.pcbi.0020140. 
[44] 
M. Semyonov and A. Tyree, Community segregation and the costs of ethnic subordination, Social Forces, 59 (1981), 649666. 
[45] 
E. S. Stewart, UK dispersal policy and onward migration: Mapping the current state of knowledge, Journal of Refugee Studies, 25 (2012), 2549. doi: 10.1093/jrs/fer039. 
[46] 
A. Szolnoki and M. Perc, Competition of tolerant strategies in the spatial public goods game, New Journal of Physics, 18 (2016), 083021. doi: 10.1088/13672630/18/8/083021. 
[47] 
UNHCR, Global trends: Forced displacement in 2017, Technical report, The UN Refugee Agency, The United Nations, 2018, http://www.unhcr.org/5b27be547.pdf. 
[48] 
Q. Wang, H. Wang, Z. Zhang, Y. Li, Y. Liu and M. Perc, Heterogeneous investments promote cooperation in evolutionary public goods games, Physica A, 502 (2018), 570575. 
[49] 
D. J. Watts and S. H. Strogatz, Collective dynamics of 'smallworld' networks, Nature, 393 (1998), 440442. 
[50] 
G. Weisbuch, G. Deffuant, F. Amblard and J.P. Nadal, Meet, discuss, and segregate, Complexity, 7 (2002), 5563. doi: 10.1002/cplx.10031. 
[51] 
J. S. White, R. Hamad, X. Li, S. Basu, H. Ohlsson, J. Sundquist and K. Sundquist, Longterm effects of neighbourhood deprivation on diabetes risk: Quasiexperimental evidence from a refugee dispersal policy in Sweden, The Lancet Diabetes and Endocrinology, 4 (2016), 517524. doi: 10.1016/S22138587(16)300092. 
show all references
References:
[1] 
R. Axelrod, The dissemination of culture: A model with local convergence and global polarization, The Journal of Conflict Resolution, 41 (1997), 203226. doi: 10.1177/0022002797041002001. 
[2] 
P. Barron, K. Kaiser and M. Pradhan, Local Conflict in Indonesia: Measuring Incidence and Identifying Patterns, World Bank Policy Research Paper 3384, 2004. 
[3] 
J. W. Berry, Acculturation and adaptation in a new society, International Migration Quarterly Review, 30 (1992), 6985. doi: 10.1111/j.14682435.1992.tb00776.x. 
[4] 
J. W. Berry, Living successfully in two cultures, International Journal of Intercultural Relations, 29 (2005), 697712. 
[5] 
J. W. Berry, U. Kim, T. Minde and D. Mok, Comparative studies of acculturative stress, The International Migration Review, 21 (1987), 491511. 
[6] 
P. Boyle, K. Halfacree and V. Robinson, Exploring contemporary migration, 2nd edition, Pearson Education Limited, London and New York, 2013. 
[7]  S. Castles and M. J. Miller, The Age of Migration: International Population Movements in the Modern World, The Guilford Press, New York, 2003. 
[8] 
E. M. Chaney, Foreword: The world economy and contemporary migration, The International Migration Review, 13 (1979), 204212. doi: 10.2307/2545027. 
[9] 
Y.S. Chiang, Cooperation could evolve in complex networks when activated conditionally on network characteristics, Journal of Artificial Societies and Social Simulation, 16 (2013), 6. doi: 10.18564/jasss.2148. 
[10] 
Y.L. Chuang, M. R. D'Orsogna and T. Chou, A bistable belief dynamics model for radicalization within sectarian conflict, Quarterly of Applied Mathematics, 75 (2017), 1937. doi: 10.1090/qam/1446. 
[11] 
M. D. Cohen, R. L. Riolo and R. Axelrod, The role of social structure in the maintenance of cooperative regimes, Rationality and Society, 13 (2001), 532. doi: 10.1177/104346301013001001. 
[12] 
M. H. Crawford and B. C. Campbell (eds.), Causes and Consequences of Human Migration, Cambridge University Press, Cambridge, UK, 2012. doi: 10.1017/CBO9781139003308. 
[13] 
A. P. Damm, Determinants of recent immigrants'location choices: Quasiexperimental evidence, Journal of Population Economics, 22 (2009), 145174. 
[14] 
G. Deffuant, D. Neau, F. Amblard and G. Weisbuch, Mixing beliefs among interacting agents, Advances in Complex Systems, 3 (2000), 8798. doi: 10.1142/S0219525900000078. 
[15] 
M. H. DeGroot, Reaching a consensus, Journal of the American Statistical Association, 69 (1974), 118121. 
[16] 
K. Fehl, D. J. van der Post and D. Semmann, Coevolution of behaviour and social network structure promotes human cooperation, Ecology Letters, 14 (2011), 546551. doi: 10.1111/j.14610248.2011.01615.x. 
[17] 
K. Felijakowski and R. Kosinski, Bounded confidence model in complex networks, International Journal of Modern Physics C, 24 (2013), 1350049, 12pp. doi: 10.1142/S0129183113500496. 
[18] 
K. Felijakowski and R. Kosinski, Opinion formation and selforganization in a social network in an intelligent agent system, ACTA Physica Polonica B, 45 (2014), 21232134. doi: 10.5506/APhysPolB.45.2123. 
[19] 
M. Fossett, Ethnic preferences, social distance dynamics, and residential segregation: Theoretical explorations using simulation analysis, The Journal of Mathematical Sociology, 30 (2006), 185273. doi: 10.1080/00222500500544052. 
[20] 
N. E. Friedkin, Choice shift and group polarization, American Sociological Review, 64 (1999), 856875. 
[21] 
A. Gabel, P. L. Krapivsky and S. Redner, Highly dispersed networks by enhanced redirection, Physical Review E, 88 (2013), 050802(R). doi: 10.1103/PhysRevE.88.050802. 
[22] 
S. Galam, Heterogeneous beliefs, segregation, and extremism in the making of public opinions, Physical Review E, 71 (2005), 046123. doi: 10.1103/PhysRevE.71.046123. 
[23] 
S. Galam, Stubbornness as an unfortunate key to win a public debate: An illustration from sociophysics, Society, 15 (2016), 117130. doi: 10.1007/s112990150175y. 
[24] 
S. Galam and M. A. Javarone, Modeling radicalization phenomena in heterogeneous populations, PLOS One, 11 (2016), e0155407. doi: 10.1371/journal.pone.0155407. 
[25] 
B. Golub and M. O. Jackson, Naíve learning in social networks and the wisdom of crowds, American Economic Journal: Microeconomics, 2 (2010), 112149. doi: 10.1257/mic.2.1.112. 
[26] 
D. Hales, Cooperation without memory or space: Tags, groups and the Prisoner's Dilemma, in MultiAgentBased Simulation. (eds. S. Moss and P. Davidsson), Springer, Berlin/Heidelberg, 2000, 157–166. doi: 10.1007/3540445617_12. 
[27] 
R. A. Hammond and R. Axelrod, The evolution of ethnocentrism, Journal of Conflict Resolution, 50 (2006), 926936. doi: 10.1177/0022002706293470. 
[28] 
D. J. Haw and J. Hogan, A dynamical systems model of unorganized segregation, The Journal of Mathematical Sociology, 42 (2018), 113127. doi: 10.1080/0022250X.2018.1427091. 
[29] 
A. D. Henry, P. Pralat and C.Q. Zhang, Emergence of segregation in evolving social networks, PNAS, 108 (2011), 86058610. doi: 10.1073/pnas.1014486108. 
[30]  P. Ireland, Becoming Europe: Immigration Integration And The Welfare State, University of Pittsburgh Press, Pittsburgh, PA, 2004. 
[31] 
M. A. Javarone, A. E. Atzeni and S. Galam, Emergence of cooperation in the Prisoner's Dilemma driven by conformity, in Applications of Evolutionary Computation. EvoApplications 2015. Lecture Notes in Computer Science (eds. A. Mora and G. Squillero), vol. 9028, Springer, Cham, 2015, 155–163. doi: 10.1007/9783319165493_13. 
[32] 
W. Kandel and J. Cromartie, New patterns of Hispanic settlement in rural America, Technical Report 99, United States Department of Agriculture, 2004. 
[33] 
T. B. Klos, Decentralized interaction and coadaptation in the repeated prisoners dilemma, Computational and Mathematical Organization Theory, 5 (1999), 147165. 
[34] 
R. Koopmans, Tradeoffs between equality and difference: Immigrant integration, multiculturalism and the welfare state in crossnational perspective, Journal of Ethnic and Migration Studies, 36 (2010), 126. doi: 10.1080/13691830903250881. 
[35] 
U. Krause, A discrete nonlinear and nonautonomous model of consensus formation, in Communications in Difference Equations (eds. S. Elaydi, G. Ladas, J. Popenda and J. Rakowski), Amsterdam: Gordon and Breach, 2000, 227–236. 
[36] 
D. T. Lichter, D. Parisi and M. C. Taquino, Emerging patterns of Hispanic residential segregation: Lessons from rural and small–town America, Rural Sociology, 81 (2016), 483518. doi: 10.1111/ruso.12108. 
[37] 
D. T. Lichter, D. Parisi, M. C. Taquino and S. M. Grice, Residential segregation in new Hispanic destinations: Cities, suburbs, and rural communities compared, Social Science Research, 39 (2010), 215230. doi: 10.1016/j.ssresearch.2009.08.006. 
[38] 
A. Németh and K. Takács, The evolution of altruism in spatially structured populations, Journal of Artificial Societies and Social Simulations, 10 (2007), 113. 
[39] 
A. Nowak, J. Szamrej and B. Latané, From private attitude to public opinion: A dynamic theory of social impact, Psychological Review, 97 (1990), 362376. doi: 10.1037/0033295X.97.3.362. 
[40] 
N. Priest, Y. Paradies, A. Ferdinand, L. Rouhani and M. Kelaher, Patterns of intergroup contact in public spaces: Microecology of segregation in Australian communities, Societies, 4 (2014), 3044. doi: 10.3390/soc4010030. 
[41] 
R. Riolo, The Effects of TagMediated Selection of Partners in Evolving Populations Playing the Iterated Prisoner's Dilemma, Technical report, Santa Fe Institute, Santa Fe, NM, 1997. 
[42] 
R. L. Riolo, M. D. Cohen and R. Axelrod, Evolution of cooperation without reciprocity, Nature, 414 (2001), 441443. doi: 10.1038/35106555. 
[43] 
F. C. Santos, J. M. Pacheco and T. Lenaerts, Cooperation prevails when individuals adjust their social ties, PLoS Computational Biology, 2 (2006), e140. doi: 10.1371/journal.pcbi.0020140. 
[44] 
M. Semyonov and A. Tyree, Community segregation and the costs of ethnic subordination, Social Forces, 59 (1981), 649666. 
[45] 
E. S. Stewart, UK dispersal policy and onward migration: Mapping the current state of knowledge, Journal of Refugee Studies, 25 (2012), 2549. doi: 10.1093/jrs/fer039. 
[46] 
A. Szolnoki and M. Perc, Competition of tolerant strategies in the spatial public goods game, New Journal of Physics, 18 (2016), 083021. doi: 10.1088/13672630/18/8/083021. 
[47] 
UNHCR, Global trends: Forced displacement in 2017, Technical report, The UN Refugee Agency, The United Nations, 2018, http://www.unhcr.org/5b27be547.pdf. 
[48] 
Q. Wang, H. Wang, Z. Zhang, Y. Li, Y. Liu and M. Perc, Heterogeneous investments promote cooperation in evolutionary public goods games, Physica A, 502 (2018), 570575. 
[49] 
D. J. Watts and S. H. Strogatz, Collective dynamics of 'smallworld' networks, Nature, 393 (1998), 440442. 
[50] 
G. Weisbuch, G. Deffuant, F. Amblard and J.P. Nadal, Meet, discuss, and segregate, Complexity, 7 (2002), 5563. doi: 10.1002/cplx.10031. 
[51] 
J. S. White, R. Hamad, X. Li, S. Basu, H. Ohlsson, J. Sundquist and K. Sundquist, Longterm effects of neighbourhood deprivation on diabetes risk: Quasiexperimental evidence from a refugee dispersal policy in Sweden, The Lancet Diabetes and Endocrinology, 4 (2016), 517524. doi: 10.1016/S22138587(16)300092. 
Symbol  Description  default values 
 attitude  1 to 1 
 maximal utility through ingroup connection  
 maximal utility through outgroup connection  
 sensitivity to attitude difference  
 attitude adjustment timescale  
 cost of adding connections  
 total population  
 guest population  
 host population  
Symbol  Description  default values 
 attitude  1 to 1 
 maximal utility through ingroup connection  
 maximal utility through outgroup connection  
 sensitivity to attitude difference  
 attitude adjustment timescale  
 cost of adding connections  
 total population  
 guest population  
 host population  
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