Externality effects in the formation of societies

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April 2015, 2(3&4): 303-320. doi: 10.3934/jdg.2015007

Externality effects in the formation of societies

Renato Soeiro ^1, , Abdelrahim Mousa ^2, and Alberto A. Pinto ^1,

1.	LIAAD - INESC TEC and Department of Mathematics, Faculty of Science, University of Porto, Rua do Campo Alegre, 687, 4169-007
2.	Department of Mathematics, Faculty of Science, Birzeit University, Palestine

Received March 2015 Revised September 2015 Published November 2015

Abstract
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We study a finite decision model where the utility function is an additive combination of a personal valuation component and an interaction component. Individuals are characterized according to these two components (their valuation type and externality type), and also according to their crowding type (how they influence others). We study how positive externalities lead to type symmetries in the set of Nash equilibria, while negative externalities allow the existence of equilibria that are not type-symmetric. In particular, we show that positive externalities lead to equilibria having a unique partition into a minimum number of societies (similar individuals using the same strategy, see [27]); and negative externalities lead to equilibria with multiple societal partitions, some with the maximum number of societies.

Keywords: polymatrix games, non-market externalities, conformity, social interactions, singleton weighted congestion games., Decision model, type-symmetric equilibria, social congestion, dyadic interactions, pure Nash equilibria.

Mathematics Subject Classification: Primary: 91A06, 91A10, 91A40; Secondary: 91A35, 91A4.

Citation: Renato Soeiro, Abdelrahim Mousa, Alberto A. Pinto. Externality effects in the formation of societies. Journal of Dynamics and Games, 2015, 2 (3&4) : 303-320. doi: 10.3934/jdg.2015007

References:

[1]	L. Almeida, J. Cruz, H. Ferreira and A. A. Pinto, Bayesian-Nash equilibria in theory of planned behaviour, Journal of Difference Equations and Applications, 17 (2011), 1085-1093. doi: 10.1080/10236190902902331.
[2]	A. V. Banerjee, A simple model of herd behavior, The Quarterly Journal of Economics, 107 (1992), 797-817. doi: 10.2307/2118364.
[3]	B. D. Bernheim, A theory of conformity, Journal of Political Economy, 102 (1994), 841-877. doi: 10.1086/261957.
[4]	M. Le Breton and S. Weber, Games of social interactions with local and global externalities, Economics Letters, 111 (2011), 88-90. doi: 10.1016/j.econlet.2011.01.012.
[5]	J. G. Brida, M. J. Such-devesa, M. Faias and A. Pinto, Strategic Choice in Tourism with Differentiated Crowding Types, Economics Bulletin, 30 (2010), 1509-1515.
[6]	W. Brock and S. Durlauf, Discrete choice with social interactions, Review of Economic Studies, 68 (2011), 235-260. doi: 10.1111/1467-937X.00168.
[7]	J. P. Conley and M. Wooders, Taste-homogeneity of optimal jurisdictions in a Tiebout economy with crowding types and endogenous educational investment choices, Ricerche Economiche, 50 (1996), 367-387. doi: 10.1006/reco.1996.0024.
[8]	J. P. Conley and M. H. Wooders, Equivalence of the core and competitive equilibrium in a tiebout economy with crowding types, Journal of Urban Economics, 41 (1997), 421-440. doi: 10.1006/juec.1996.2008.
[9]	J. P. Conley and M. H. Wooders, Tiebout economies with diferential inherent types and endogenously chosen crowding characteristics, Journal of Economic Theory, 98 (2001), 261-294. doi: 10.1006/jeth.2000.2716.
[10]	R. Cooper and A. John, Coordinating coordination failures in keynesian models, The Quarterly Journal of Economics, 103 (1988), 441-463. doi: 10.2307/1885539.
[11]	M. S. Granovetter, The strength of weak ties, American Journal of Sociology, 78 (1973), 1360-1380.
[12]	M. Granovetter, Threshold models of collective action, The American Journal of Sociology, 83 (1978), 1420-1443.
[13]	J. T. Howson, Equilibria of polymatrix games, Management Science, 18 (1972), 312-318.
[14]	H. Konishi, M. Le Breton and S. Weber, Equilibria in a model with partial rivalry, Journal Of Economic Theory, 72 (1997), 225-237. doi: 10.1006/jeth.1996.2203.
[15]	H. Konishi, M. Le Breton and S. Weber, Pure strategy nash equilibrium in a group formation game with positive externalities, Games and Economic Behavior, 21 (1997), 161-182. doi: 10.1006/game.1997.0542.
[16]	I. Milchtaich, Congestion models with player specific payoff functions, Games and Economic Behavior, 13 (1996), 111-124. doi: 10.1006/game.1996.0027.
[17]	L. G. Quintas, A note on polymatrix games, International Journal of Game Theory, 18 (1989), 261-272. doi: 10.1007/BF01254291.
[18]	T. Quint and S. Shubik, A Model of Migration, (1994) Working paper, Cowles Foundation, Yale University.
[19]	P. Ray, Independence of irrelevant alternatives, Econometrica, 41 (1973), 987-991. doi: 10.2307/1913820.
[20]	R. W. Rosenthal, A class of games possessing pure-strategy nash equilibria, International Journal of Game Theory, 2 (1973), 65-67. doi: 10.1007/BF01737559.
[21]	T. C. Schelling, Dynamic models of segregation, Journal of Mathematical Sociology, 1 (1971), 143-186. doi: 10.1080/0022250X.1971.9989794.
[22]	T. C. Schelling, Hockey helmets, concealed weapons, and daylight savings- a study of binary choices with externalities, The journal of Conflict Resolution, 17 (1973), 381-428. doi: 10.1177/002200277301700302.
[23]	R. Soeiro, A. Mousa, T. R. Oliveira and A. A. Pinto, Dynamics of human decisions, Journal of Dynamics and Games, 1 (2014), 121-151. doi: 10.3934/jdg.2014.1.121.
[24]	M. H. Wooders, A tiebout theorem, Mathematical Social Sciences, 18 (1989), 33-55. doi: 10.1016/0165-4896(89)90068-1.
[25]	M. H. Wooders, Equivalence of Lindahl equilibria with participation prices and the core, Economic Theory, 9 (1997), 115-127. doi: 10.1007/BF01213446.
[26]	M. H. Wooders, Multijurisdictional economies, the Tiebout Hypothesis, and sorting, Proceedings of the National Academy of Sciences, 96 (1999), 10585-10587. doi: 10.1073/pnas.96.19.10585.
[27]	M. Wooders, E. Cartwright and R. Selten, Behavioral conformity in games with many players, Games and Economic Behavior, 57 (2006), 347-360. doi: 10.1016/j.geb.2005.09.006.
[28]	M. Wooders and E. Cartwright, Correlated equilibrium, conformity, and stereotyping in social groups, Journal of Public Economic Theory, 16 (2014), 743-766.

show all references

References:

[1]	L. Almeida, J. Cruz, H. Ferreira and A. A. Pinto, Bayesian-Nash equilibria in theory of planned behaviour, Journal of Difference Equations and Applications, 17 (2011), 1085-1093. doi: 10.1080/10236190902902331.
[2]	A. V. Banerjee, A simple model of herd behavior, The Quarterly Journal of Economics, 107 (1992), 797-817. doi: 10.2307/2118364.
[3]	B. D. Bernheim, A theory of conformity, Journal of Political Economy, 102 (1994), 841-877. doi: 10.1086/261957.
[4]	M. Le Breton and S. Weber, Games of social interactions with local and global externalities, Economics Letters, 111 (2011), 88-90. doi: 10.1016/j.econlet.2011.01.012.
[5]	J. G. Brida, M. J. Such-devesa, M. Faias and A. Pinto, Strategic Choice in Tourism with Differentiated Crowding Types, Economics Bulletin, 30 (2010), 1509-1515.
[6]	W. Brock and S. Durlauf, Discrete choice with social interactions, Review of Economic Studies, 68 (2011), 235-260. doi: 10.1111/1467-937X.00168.
[7]	J. P. Conley and M. Wooders, Taste-homogeneity of optimal jurisdictions in a Tiebout economy with crowding types and endogenous educational investment choices, Ricerche Economiche, 50 (1996), 367-387. doi: 10.1006/reco.1996.0024.
[8]	J. P. Conley and M. H. Wooders, Equivalence of the core and competitive equilibrium in a tiebout economy with crowding types, Journal of Urban Economics, 41 (1997), 421-440. doi: 10.1006/juec.1996.2008.
[9]	J. P. Conley and M. H. Wooders, Tiebout economies with diferential inherent types and endogenously chosen crowding characteristics, Journal of Economic Theory, 98 (2001), 261-294. doi: 10.1006/jeth.2000.2716.
[10]	R. Cooper and A. John, Coordinating coordination failures in keynesian models, The Quarterly Journal of Economics, 103 (1988), 441-463. doi: 10.2307/1885539.
[11]	M. S. Granovetter, The strength of weak ties, American Journal of Sociology, 78 (1973), 1360-1380.
[12]	M. Granovetter, Threshold models of collective action, The American Journal of Sociology, 83 (1978), 1420-1443.
[13]	J. T. Howson, Equilibria of polymatrix games, Management Science, 18 (1972), 312-318.
[14]	H. Konishi, M. Le Breton and S. Weber, Equilibria in a model with partial rivalry, Journal Of Economic Theory, 72 (1997), 225-237. doi: 10.1006/jeth.1996.2203.
[15]	H. Konishi, M. Le Breton and S. Weber, Pure strategy nash equilibrium in a group formation game with positive externalities, Games and Economic Behavior, 21 (1997), 161-182. doi: 10.1006/game.1997.0542.
[16]	I. Milchtaich, Congestion models with player specific payoff functions, Games and Economic Behavior, 13 (1996), 111-124. doi: 10.1006/game.1996.0027.
[17]	L. G. Quintas, A note on polymatrix games, International Journal of Game Theory, 18 (1989), 261-272. doi: 10.1007/BF01254291.
[18]	T. Quint and S. Shubik, A Model of Migration, (1994) Working paper, Cowles Foundation, Yale University.
[19]	P. Ray, Independence of irrelevant alternatives, Econometrica, 41 (1973), 987-991. doi: 10.2307/1913820.
[20]	R. W. Rosenthal, A class of games possessing pure-strategy nash equilibria, International Journal of Game Theory, 2 (1973), 65-67. doi: 10.1007/BF01737559.
[21]	T. C. Schelling, Dynamic models of segregation, Journal of Mathematical Sociology, 1 (1971), 143-186. doi: 10.1080/0022250X.1971.9989794.
[22]	T. C. Schelling, Hockey helmets, concealed weapons, and daylight savings- a study of binary choices with externalities, The journal of Conflict Resolution, 17 (1973), 381-428. doi: 10.1177/002200277301700302.
[23]	R. Soeiro, A. Mousa, T. R. Oliveira and A. A. Pinto, Dynamics of human decisions, Journal of Dynamics and Games, 1 (2014), 121-151. doi: 10.3934/jdg.2014.1.121.
[24]	M. H. Wooders, A tiebout theorem, Mathematical Social Sciences, 18 (1989), 33-55. doi: 10.1016/0165-4896(89)90068-1.
[25]	M. H. Wooders, Equivalence of Lindahl equilibria with participation prices and the core, Economic Theory, 9 (1997), 115-127. doi: 10.1007/BF01213446.
[26]	M. H. Wooders, Multijurisdictional economies, the Tiebout Hypothesis, and sorting, Proceedings of the National Academy of Sciences, 96 (1999), 10585-10587. doi: 10.1073/pnas.96.19.10585.
[27]	M. Wooders, E. Cartwright and R. Selten, Behavioral conformity in games with many players, Games and Economic Behavior, 57 (2006), 347-360. doi: 10.1016/j.geb.2005.09.006.
[28]	M. Wooders and E. Cartwright, Correlated equilibrium, conformity, and stereotyping in social groups, Journal of Public Economic Theory, 16 (2014), 743-766.

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