Heavy alcohol consumption is known to be a major risk factor for disease and death globally. Various studies have related transmission of alcohol drinking habits with social contacts and peer pressure. Researchers have attempted to model this contact process through dynamical systems. Departing from this approach, this paper adopts a game theory model to study the transmission and prevalence of alcohol drinking habits, based on the concept of an evolutionarily stable population state. The proposed game theoretic model takes into account two scenarios. One deals with populations aged 15+ having two types of individuals: nondrinkers (N) and drinkers (D) whereas the other divides the same populations into nondrinkers (N), moderate drinkers (M) and heavy drinkers (H). In the former case, three types of pairwise interactions are possible between these individuals whereas in the latter, six types. The different possibilities inherent in these types are explained and the payoff matrices representing the interactions and the resulting gain expressions are presented. The game theoretic models are then analyzed and evolutionarily stable population states are computed for a few sets of parameter values. The advantage of this model is that it is found to be beneficial to understand the large time proportions of nondrinkers and drinkers in the population in a simpler manner than the dynamic system models. The work may be further expanded by dividing the existing classes of non-drinking and drinking populations on the basis of other critical aspects also.
| Published in | American Journal of Applied Mathematics (Volume 10, Issue 3) |
| DOI | 10.11648/j.ajam.20221003.15 |
| Page(s) | 111-117 |
| Creative Commons |
This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited. |
| Copyright |
Copyright © The Author(s), 2022. Published by Science Publishing Group |
Game Theoretic Models, Evolutionary Games, Applications of Game Theory, Social Evolution
| [1] | J. A. Andrews, E. Tildesley, H. Hops and F. Li (2002). The influence of peers on young adult substance use. Health Psychol., 21, 341–357. DOI. 10.1037//0278-6133.21.4.349. |
| [2] | A. C. Beal, J. Ausiello and J. M. Perrin (2001). Social influences on health-risk behaviors among minority middle school students. J Adolesc Health, 28, 474-480. DOI. 10.1016/S1054-139X(01)00194-X. |
| [3] | J. J. Beckmeyer and E. H. Weybright (2016). Perceptions of alcohol use by friends compared to peers: Associations with middle adolescents. Subst Abus, 37, 435–440. DOI. 10.1080/08897077.2015.1134754. |
| [4] | B. Benedict (2007). Modeling alcoholism as a contagious disease: How “infected” drinking buddies spread problem drinking. SIAM News, 40. DOI. 10.1.1.555.7480. |
| [5] | B. Borsari and K. B. Carey (2001). Peer influences on college drinking: A review of the research. Journal of Substance Abuse, 13, 391–424. DOI. 10.1016/S0899-3289(01)00098-0. |
| [6] | M. Broom and J. Rychtar. Game-Theoretical Models in Biology. Chapman and Hall/CRC, 2013; p. 520, ISBN 9781439853214. |
| [7] | C. Castillo-Chavez and B. Song, Models for the Transmission Dynamics of Fanatic Behaviors in H. T. Banks and C. Castillo-Chavez (ed.), Bioterrorism: Mathematical Modeling Applications in Homeland Security, SIAM, Philadelphia, 2003. |
| [8] | J. E. Cheadle, K. M. Walsemann and B. J. Goosby (2015). Teen Alcohol Use and Social Networks: The Contributions of Friend Influence and Friendship Selection. J Alcohol Drug Depend, 3, 142-149. DOI. 10.4172/2329-6488.1000224. |
| [9] | R. Cressman. Evolutionary Dynamics and Extensive Form Games. The MIT Press, 2003; p 330, ASIN: B006V99ZV4. |
| [10] | E. van Damme. Stability and Perfection of Nash Equilibria. Springer-Verlag: Berlin Heidelberg, 1991; p 339, DOI: 10.1007/978-3-642-58242-4, ISBN-978-3-642-58242-4. |
| [11] | R. C. M. E. Engels, R. A. Knibbe, H. de Vries, M. J. Drop and G. van Breukelen (2006). Influences of parental and best friends’ smoking and drinking on adolescent use: A longitudinal study. Journal of Applied Social Psychology, 29, 337–361. DOI. 10.1111/j.1559-1816.1999.tb01390.x. |
| [12] | D. Faeh, B. Viswanathan, A. Chiolero, W. Warren and P. Bovet (2006). Clustering of smoking, alcohol drinking and cannabis use in adolescents in a rapidly developing country. BMC Public Health, 6. DOI. 10.1186/1471–2458–6–169. |
| [13] | B. Gonzalez, E. Huerta-Sanchez, A. Ortiz-Nievez, Te. Vazquez-Alvarez and C. Kribs-Zaleta (2003). Am i too fat? Bulimia as an epidemic. Journal of Mathematical Psychology, 47, 515-526. DOI: 10.1016/j.jmp.2003.08.002. |
| [14] | J. W. Graham, G. Marks and W. B. Hansen (1991). Social influence processes affecting adolescent substance use. The Journal of Applied Psychology, 76, 291-298. DOI. 10.1037/0021-9010.76.2.291. |
| [15] | B. F. Grant and D. A. Dawson (1997). Age at onset of alcohol use and its association with DSM-IV alcohol abuse and dependence: results from the national longitudinal alcohol epidemiologic survey. Journal of Substance Abuse, 9, 103–110. DOI. 10.1016/S0899-3289(97)90009-2. |
| [16] | B. F. Grant, F. S. Stinsona and T. C. Harford (2001). Age at onset of alcohol use and DSM-IV alcohol abuse and dependence: A 12-year follow-up. Journal of Substance Abuse, 13, 493–504. DOI. 10.1016/S0899-3289(01)00096-7. |
| [17] | R. Hingson, T. Heeren, M. Winter and H. Wechsler (2005). Magnitude of alcohol-related mortality and morbidity among U.S. college students aged 18-24: Changes from 1998 to 2001. Annu. Rev. Public Health, 26, 259–279. DOI. 10.1146/annurev.publhealth.26.021304.144652. |
| [18] | R. Hingson, T. Heeren, R. C. Zakocs, A. Kopstein and H. Wechsler (2002). Magnitude of alcohol-related mortality and morbidity among U.S. college students ages 18-24. J. Stud. Alcohol, 63, 136–144. DOI. 10.15288/jsa.2002.63.136. |
| [19] | J. Hofbauer and K. Sigmund, Evolutionary Games and Population Dynamics. Cambridge University Press, 1998; p 352, ISBN -10: 052162570X. |
| [20] | K. Kawachi, M. Seki, H. Yoshida, Y. Otake, K. Warashina and H. Ueda (2008). A rumor transmission model with various contact interactions. Journal of Theoretical Biology, 253, 55-60. DOI. 10.1016/j.jtbi.2007.11.024. |
| [21] | S. Ma, H. Huo and X. Meng (2015). Modelling Alcoholism as a Contagious Disease: A Mathematical Model with Awareness Programs and Time Delay. Discrete Dynamics in Nature and Society, 1–25. DOI. 10.1155/2015/260195. |
| [22] | J. L. Manthey, A. Y. Aidoo and K. Y. Ward (2008). Campus drinking: an epidemiological model. Journal of Biological Dynamics, 2, 346–356. DOI. 10.1080/17513750801911169. |
| [23] | J. Maynard Smith and G. R. Price (1973). The logic of animal conflict. Nature, 246, 15–18. DOI. 10.1038/246015a0. |
| [24] | J. Maynard Smith (1974). The theory of games and the evolution of animal conflicts. Journal of Theoretical Biology, 47, 209-221. DOI. 10.1016/0022- 5193(74)90110-6. |
| [25] | A. Mubayi, P. E. Greenwood, C. Castillo-Chavez, P. J. Gruenewald and D. M. Gorman (2010). The impact of relative residence times on the distribution of heavy. drinkers in highly distinct environments. Socio-Economic Planning Sciences, 44, 45-56. DOI. 10.1016/j.seps.2009.02.002. |
| [26] | A. Mubayi, P. Greenwood, X. Wang, C. Castillo-Chavez, D. M. Gorman, P. Gruenewald and R. F. Saltz (2011). Types of Drinkers and Drinking Settings: An Application of a Mathematical Model. Addiction, 106, 749–758. DOI. 10.1111/j.1360-0443.2010.03254.x. |
| [27] | M. P. Mundt, L. Mercken and L. Zakletskaia (2012). Peer selection and influence effects on adolescent alcohol use: a stochastic actor-based model. BMC Pediatrics, 12, 142- 149. DOI. 10.1186/1471-2431-12-115. |
| [28] | S. B. Patten and J. A. Arboleda-Flóez (2004). Epidemic theory and group violence. Psychiatry Psychiatr Epidemiol, 39, 853-856. DOI. 10.1007/s00127-004- 0867-9. |
| [29] | E. A. P. Poelen, R. H. J. Scholte, G. Willemsen, D. I. Boomsma and R. C. M. E. Engels (2007). Drinking by parents, siblings, and friends as predictors of regular alcohol use in adolescents and young adults: A longitudinal twin-family study. Alcohol & Alcoholism, 42, 362–369. DOI. 10.1093/alcalc/agm042. |
| [30] | A. Reifman, G. M. Barnes, B. A. Dintcheff, M. P. Farrell and L. Uhteg (1998). Parental and peer influences on the onset of heavier drinking among adolescents. J. Stud. Alcohol, 59, 311-317. DOI. 10.15288/jsa.1998.59.311. |
| [31] | L. Samuelson, Evolutionary Games and Equilibrium Selection. The MIT Press, 1998; p 328, ISBN 9780262692199. |
| [32] | S. Sharma and G. P. Samanta (2013). Drinking as an Epidemic: A Mathematical Model With Dynamic Behaviour. J. Appl. Math. & Informatics, 31, 1–25. DOI. 10.14317/jami.2013.001. |
| [33] | O. Sharomi and A. B. Gumel (2008). Curtailing smoking dynamics: A mathematical modeling approach, Applied Mathematics and Computation, 195, 475-499. DOI. 10.1016/j.amc.2007.05.012. |
| [34] | V. Tweedle and R. J. Smith (2012). A mathematical model of Bieber Fever: The most infectious disease of our time? Understanding the Dynamics of Emerging and Re-Emerging Infectious Diseases Using Mathematical Models, 157-177. |
| [35] | K. A. Urberg, S. M. Degirmencioglu and C. Pilgrim (1997). Close friend and group influence on adolescent cigarette smoking and alcohol use. Developmental Psychology, 33, 833–844. DOI. 10.1037/0012- 1649.33.5.834. |
| [36] | C. Wang, J. R. Hipp, C. T. Butts, R. Jose and C. M. Lakon (2015). Alcohol Use among Adolescent Youth: The Role of Friendship Networks and Family Factors in Multiple School Studies. PLoS One, 107. DOI. 10.1371/journal.pone.0119965. |
| [37] | R. A. Webster, M. Hunter and J. A. Keats (1994). Peer and parental influences on adolescent’s substance use: a path analysis. International journal of the addictions, 29, 647–657. DOI. 10.3109/10826089409047405. |
| [38] | E. White and C. Comiskey (2007). Heroin epidemics, treatment and ODE modelling, Mathematical Biosciences, 208, 312-324. DOI. 10.1016/j.mbs.2006.10.008. |
| [39] | World Health Organization. Global Status Report on Alcohol and Health 2014. Geneva, 2014; p. 392, ISBN. 978 92 4 069276 3. |
APA Style
Gigi Thomas. (2022). Game Theoretic Approach to the Transmission and Prevalence of Alcohol Drinking Habits. American Journal of Applied Mathematics, 10(3), 111-117. https://doi.org/10.11648/j.ajam.20221003.15
ACS Style
Gigi Thomas. Game Theoretic Approach to the Transmission and Prevalence of Alcohol Drinking Habits. Am. J. Appl. Math. 2022, 10(3), 111-117. doi: 10.11648/j.ajam.20221003.15
AMA Style
Gigi Thomas. Game Theoretic Approach to the Transmission and Prevalence of Alcohol Drinking Habits. Am J Appl Math. 2022;10(3):111-117. doi: 10.11648/j.ajam.20221003.15
Share This Article
Twitter
Linked In
Facebook
Copy
Download@article{10.11648/j.ajam.20221003.15,
author = {Gigi Thomas},
title = {Game Theoretic Approach to the Transmission and Prevalence of Alcohol Drinking Habits},
journal = {American Journal of Applied Mathematics},
volume = {10},
number = {3},
pages = {111-117},
doi = {10.11648/j.ajam.20221003.15},
url = {https://doi.org/10.11648/j.ajam.20221003.15},
eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajam.20221003.15},
abstract = {Heavy alcohol consumption is known to be a major risk factor for disease and death globally. Various studies have related transmission of alcohol drinking habits with social contacts and peer pressure. Researchers have attempted to model this contact process through dynamical systems. Departing from this approach, this paper adopts a game theory model to study the transmission and prevalence of alcohol drinking habits, based on the concept of an evolutionarily stable population state. The proposed game theoretic model takes into account two scenarios. One deals with populations aged 15+ having two types of individuals: nondrinkers (N) and drinkers (D) whereas the other divides the same populations into nondrinkers (N), moderate drinkers (M) and heavy drinkers (H). In the former case, three types of pairwise interactions are possible between these individuals whereas in the latter, six types. The different possibilities inherent in these types are explained and the payoff matrices representing the interactions and the resulting gain expressions are presented. The game theoretic models are then analyzed and evolutionarily stable population states are computed for a few sets of parameter values. The advantage of this model is that it is found to be beneficial to understand the large time proportions of nondrinkers and drinkers in the population in a simpler manner than the dynamic system models. The work may be further expanded by dividing the existing classes of non-drinking and drinking populations on the basis of other critical aspects also.},
year = {2022}
}
TY - JOUR T1 - Game Theoretic Approach to the Transmission and Prevalence of Alcohol Drinking Habits AU - Gigi Thomas Y1 - 2022/06/21 PY - 2022 N1 - https://doi.org/10.11648/j.ajam.20221003.15 DO - 10.11648/j.ajam.20221003.15 T2 - American Journal of Applied Mathematics JF - American Journal of Applied Mathematics JO - American Journal of Applied Mathematics SP - 111 EP - 117 PB - Science Publishing Group SN - 2330-006X UR - https://doi.org/10.11648/j.ajam.20221003.15 AB - Heavy alcohol consumption is known to be a major risk factor for disease and death globally. Various studies have related transmission of alcohol drinking habits with social contacts and peer pressure. Researchers have attempted to model this contact process through dynamical systems. Departing from this approach, this paper adopts a game theory model to study the transmission and prevalence of alcohol drinking habits, based on the concept of an evolutionarily stable population state. The proposed game theoretic model takes into account two scenarios. One deals with populations aged 15+ having two types of individuals: nondrinkers (N) and drinkers (D) whereas the other divides the same populations into nondrinkers (N), moderate drinkers (M) and heavy drinkers (H). In the former case, three types of pairwise interactions are possible between these individuals whereas in the latter, six types. The different possibilities inherent in these types are explained and the payoff matrices representing the interactions and the resulting gain expressions are presented. The game theoretic models are then analyzed and evolutionarily stable population states are computed for a few sets of parameter values. The advantage of this model is that it is found to be beneficial to understand the large time proportions of nondrinkers and drinkers in the population in a simpler manner than the dynamic system models. The work may be further expanded by dividing the existing classes of non-drinking and drinking populations on the basis of other critical aspects also. VL - 10 IS - 3 ER -
Email: