Cost intervention in delinquent networks. (English) Zbl 1537.91056
Summary: This study investigates a novel intervention approach to network games, in which players are delinquents whose payoffs depend on the actions of their network neighbors. The social planner aims to manipulate the delinquency costs of players, seeking to minimize the total delinquency level. We consider two intervention scenarios. First, we consider binary interventions, where the planner can either increase the cost of an offender by a fixed amount; or leave its cost unchanged. The optimal intervention problem involves maximizing a submodular function. We establish a connection between cost and structural intervention in networks. Next, we consider continuous levels of intervention, where the planner can choose how much to increase the cost of an offender. We show that the optimal intervention problem is a tractable convex optimization if the intervention function is concave. We provide a characterization of the optimal intervention which is highly related to players’ centralities in the network. We further discuss the interior solution and apply our result to nested split graphs.
References:
| [1] | Ballester, C.; Calvó-Armengol, A.; Zenou, Y., Who’s who in networks. Wanted: The key player, Econometrica, 74, 5, 1403-1417, 2006 · Zbl 1138.91590 · doi:10.1111/j.1468-0262.2006.00709.x |
| [2] | Ballester, C.; Calvó-Armengol, A.; Zenou, Y., Delinquent networks, J Eur Econ Assoc, 8, 1, 34-61, 2010 · doi:10.1162/jeea.2010.8.1.34 |
| [3] | Bayer, P.; Hjalmarsson, R.; Pozen, D., Building criminal capital behind bars: peer effects in juvenile corrections, Quart J Econ, 124, 105-147, 2009 · doi:10.1162/qjec.2009.124.1.105 |
| [4] | Belhaj, M.; Deroïan, F., Targeting the key player: an incentive-based approach, J Math Econ, 79, 3, 57-64, 2018 · Zbl 1418.91099 · doi:10.1016/j.jmateco.2018.10.001 |
| [5] | Belhaj, M.; Deroïan, F., Group targeting under networked synergies, Games Econom Behav, 118, 3, 29-46, 2019 · Zbl 1429.91193 · doi:10.1016/j.geb.2019.08.003 |
| [6] | Belhaj, M.; Bervoets, S.; Deroïan, F., Efficient networks in games with local complementarities, Theor Econ, 11, 357-380, 2016 · Zbl 1395.91074 · doi:10.3982/TE1742 |
| [7] | Billings, S.; Deming, D.; Ross, S., Partners in Crime, Am Econ J Appl Econ, 11, 1, 126-150, 2019 · doi:10.1257/app.20170249 |
| [8] | Bonacich, P., Power and centrality: a family of measures, Am J Sociol, 92, 5, 1170-1182, 1987 · doi:10.1086/228631 |
| [9] | Corno, L., Homelessness and crime: Do your friends matter?, Econ J, 127, 602, 959-995, 2016 |
| [10] | Damm, A.; Dustmann, C., Does growing up in a high crime neighborhood affect youth criminal behavior?, Am Econ Rev, 104, 6, 1806-32, 2014 · doi:10.1257/aer.104.6.1806 |
| [11] | Demange, G., Optimal targeting strategies in a network under complementarities, Games Econ Behav, 105, 84-103, 2017 · Zbl 1415.91237 · doi:10.1016/j.geb.2017.07.004 |
| [12] | Galeotti, A.; Golub, B.; Goyal, S., Targeting interventions in networks, Econometrica, 88, 6, 2445-2471, 2020 · Zbl 1466.91053 · doi:10.3982/ECTA16173 |
| [13] | Glaser, E.; Sacerdote, B.; Scheinkman, J., Crime and social interactions, Quart J Econ, 111, 508-548, 1996 |
| [14] | Hiller, T., Peer effects in endogenous networks, Games Econom Behav, 105, 349-367, 2017 · Zbl 1415.91238 · doi:10.1016/j.geb.2017.07.010 |
| [15] | Joshi, S.; Mahmud, A., Network formation under multiple sources of externalities, J Public Econ Theory, 18, 148-167, 2016 · doi:10.1111/jpet.12177 |
| [16] | Katz, L., A new status index derived from sociometric analysis, Psychometrika, 18, 39-43, 1953 · Zbl 0053.27606 · doi:10.1007/BF02289026 |
| [17] | König, MD; Tessone, J.; Zenou, Y., Nestedness in networks: a theoretical model and some applications, Theor Econ, 9, 3, 695-752, 2014 · Zbl 1395.90044 · doi:10.3982/TE1348 |
| [18] | Li, X., Designing weighted and directed networks under complementarities, Games Econom Behav, 140, 556-574, 2023 · Zbl 1519.91053 · doi:10.1016/j.geb.2023.04.010 |
| [19] | Ludwig, J.; Greg, D.; Hirschfield, P., Urban poverty and juvenile crime: evidence from a randomized housing-mobility experiment, Quart J Econ, 116, 655-679, 2001 · Zbl 0996.91552 · doi:10.1162/00335530151144122 |
| [20] | Nemhauser, G.; Wolsey, LA; Fisher, ML, An analysis of approximations for maximizing submodular set functions—I, Math Program, 14, 265-294, 1978 · Zbl 0374.90045 · doi:10.1007/BF01588971 |
| [21] | Patacchini, E.; Zenou, Y., The strength of weak ties in crime, Eur Econ Rev, 52, 209-236, 2008 · doi:10.1016/j.euroecorev.2007.09.002 |
| [22] | Poole, G.; Boullion, T., A survey on M-matrices, SIAM Rev, 16, 4, 419-427, 1974 · Zbl 0292.15009 · doi:10.1137/1016079 |
| [23] | Stuart, B.; Talor, E., The effect of social connectedness on crime: evidence from the great migration, Rev Econ Stat, 103, 1, 18-33, 2021 · doi:10.1162/rest_a_00860 |
| [24] | Sun, Y.; Zhao, W.; Zhou, J., Structural interventions in networks, Int Econ Rev, 2023 · Zbl 1533.91086 · doi:10.1111/iere.12639 |
| [25] | Zhou, J.; Chen, Y., Key leaders in social networks, J Econ Theory, 157, 212-235, 2015 · Zbl 1330.91169 · doi:10.1016/j.jet.2015.01.005 |
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
