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

Externality effects in the formation of societies

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

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.
Citation: Renato Soeiro, Abdelrahim Mousa, Alberto A. Pinto. Externality effects in the formation of societies. Journal of Dynamics & 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.  doi: 10.1080/10236190902902331.  Google Scholar

[2]

A. V. Banerjee, A simple model of herd behavior,, The Quarterly Journal of Economics, 107 (1992), 797.  doi: 10.2307/2118364.  Google Scholar

[3]

B. D. Bernheim, A theory of conformity,, Journal of Political Economy, 102 (1994), 841.  doi: 10.1086/261957.  Google Scholar

[4]

M. Le Breton and S. Weber, Games of social interactions with local and global externalities,, Economics Letters, 111 (2011), 88.  doi: 10.1016/j.econlet.2011.01.012.  Google Scholar

[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.   Google Scholar

[6]

W. Brock and S. Durlauf, Discrete choice with social interactions,, Review of Economic Studies, 68 (2011), 235.  doi: 10.1111/1467-937X.00168.  Google Scholar

[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.  doi: 10.1006/reco.1996.0024.  Google Scholar

[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.  doi: 10.1006/juec.1996.2008.  Google Scholar

[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.  doi: 10.1006/jeth.2000.2716.  Google Scholar

[10]

R. Cooper and A. John, Coordinating coordination failures in keynesian models,, The Quarterly Journal of Economics, 103 (1988), 441.  doi: 10.2307/1885539.  Google Scholar

[11]

M. S. Granovetter, The strength of weak ties,, American Journal of Sociology, 78 (1973), 1360.   Google Scholar

[12]

M. Granovetter, Threshold models of collective action,, The American Journal of Sociology, 83 (1978), 1420.   Google Scholar

[13]

J. T. Howson, Equilibria of polymatrix games,, Management Science, 18 (1972), 312.   Google Scholar

[14]

H. Konishi, M. Le Breton and S. Weber, Equilibria in a model with partial rivalry,, Journal Of Economic Theory, 72 (1997), 225.  doi: 10.1006/jeth.1996.2203.  Google Scholar

[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.  doi: 10.1006/game.1997.0542.  Google Scholar

[16]

I. Milchtaich, Congestion models with player specific payoff functions,, Games and Economic Behavior, 13 (1996), 111.  doi: 10.1006/game.1996.0027.  Google Scholar

[17]

L. G. Quintas, A note on polymatrix games,, International Journal of Game Theory, 18 (1989), 261.  doi: 10.1007/BF01254291.  Google Scholar

[18]

T. Quint and S. Shubik, A Model of Migration,, (1994) Working paper, (1994).   Google Scholar

[19]

P. Ray, Independence of irrelevant alternatives,, Econometrica, 41 (1973), 987.  doi: 10.2307/1913820.  Google Scholar

[20]

R. W. Rosenthal, A class of games possessing pure-strategy nash equilibria,, International Journal of Game Theory, 2 (1973), 65.  doi: 10.1007/BF01737559.  Google Scholar

[21]

T. C. Schelling, Dynamic models of segregation,, Journal of Mathematical Sociology, 1 (1971), 143.  doi: 10.1080/0022250X.1971.9989794.  Google Scholar

[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.  doi: 10.1177/002200277301700302.  Google Scholar

[23]

R. Soeiro, A. Mousa, T. R. Oliveira and A. A. Pinto, Dynamics of human decisions,, Journal of Dynamics and Games, 1 (2014), 121.  doi: 10.3934/jdg.2014.1.121.  Google Scholar

[24]

M. H. Wooders, A tiebout theorem,, Mathematical Social Sciences, 18 (1989), 33.  doi: 10.1016/0165-4896(89)90068-1.  Google Scholar

[25]

M. H. Wooders, Equivalence of Lindahl equilibria with participation prices and the core,, Economic Theory, 9 (1997), 115.  doi: 10.1007/BF01213446.  Google Scholar

[26]

M. H. Wooders, Multijurisdictional economies, the Tiebout Hypothesis, and sorting,, Proceedings of the National Academy of Sciences, 96 (1999), 10585.  doi: 10.1073/pnas.96.19.10585.  Google Scholar

[27]

M. Wooders, E. Cartwright and R. Selten, Behavioral conformity in games with many players,, Games and Economic Behavior, 57 (2006), 347.  doi: 10.1016/j.geb.2005.09.006.  Google Scholar

[28]

M. Wooders and E. Cartwright, Correlated equilibrium, conformity, and stereotyping in social groups,, Journal of Public Economic Theory, 16 (2014), 743.   Google Scholar

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.  doi: 10.1080/10236190902902331.  Google Scholar

[2]

A. V. Banerjee, A simple model of herd behavior,, The Quarterly Journal of Economics, 107 (1992), 797.  doi: 10.2307/2118364.  Google Scholar

[3]

B. D. Bernheim, A theory of conformity,, Journal of Political Economy, 102 (1994), 841.  doi: 10.1086/261957.  Google Scholar

[4]

M. Le Breton and S. Weber, Games of social interactions with local and global externalities,, Economics Letters, 111 (2011), 88.  doi: 10.1016/j.econlet.2011.01.012.  Google Scholar

[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.   Google Scholar

[6]

W. Brock and S. Durlauf, Discrete choice with social interactions,, Review of Economic Studies, 68 (2011), 235.  doi: 10.1111/1467-937X.00168.  Google Scholar

[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.  doi: 10.1006/reco.1996.0024.  Google Scholar

[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.  doi: 10.1006/juec.1996.2008.  Google Scholar

[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.  doi: 10.1006/jeth.2000.2716.  Google Scholar

[10]

R. Cooper and A. John, Coordinating coordination failures in keynesian models,, The Quarterly Journal of Economics, 103 (1988), 441.  doi: 10.2307/1885539.  Google Scholar

[11]

M. S. Granovetter, The strength of weak ties,, American Journal of Sociology, 78 (1973), 1360.   Google Scholar

[12]

M. Granovetter, Threshold models of collective action,, The American Journal of Sociology, 83 (1978), 1420.   Google Scholar

[13]

J. T. Howson, Equilibria of polymatrix games,, Management Science, 18 (1972), 312.   Google Scholar

[14]

H. Konishi, M. Le Breton and S. Weber, Equilibria in a model with partial rivalry,, Journal Of Economic Theory, 72 (1997), 225.  doi: 10.1006/jeth.1996.2203.  Google Scholar

[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.  doi: 10.1006/game.1997.0542.  Google Scholar

[16]

I. Milchtaich, Congestion models with player specific payoff functions,, Games and Economic Behavior, 13 (1996), 111.  doi: 10.1006/game.1996.0027.  Google Scholar

[17]

L. G. Quintas, A note on polymatrix games,, International Journal of Game Theory, 18 (1989), 261.  doi: 10.1007/BF01254291.  Google Scholar

[18]

T. Quint and S. Shubik, A Model of Migration,, (1994) Working paper, (1994).   Google Scholar

[19]

P. Ray, Independence of irrelevant alternatives,, Econometrica, 41 (1973), 987.  doi: 10.2307/1913820.  Google Scholar

[20]

R. W. Rosenthal, A class of games possessing pure-strategy nash equilibria,, International Journal of Game Theory, 2 (1973), 65.  doi: 10.1007/BF01737559.  Google Scholar

[21]

T. C. Schelling, Dynamic models of segregation,, Journal of Mathematical Sociology, 1 (1971), 143.  doi: 10.1080/0022250X.1971.9989794.  Google Scholar

[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.  doi: 10.1177/002200277301700302.  Google Scholar

[23]

R. Soeiro, A. Mousa, T. R. Oliveira and A. A. Pinto, Dynamics of human decisions,, Journal of Dynamics and Games, 1 (2014), 121.  doi: 10.3934/jdg.2014.1.121.  Google Scholar

[24]

M. H. Wooders, A tiebout theorem,, Mathematical Social Sciences, 18 (1989), 33.  doi: 10.1016/0165-4896(89)90068-1.  Google Scholar

[25]

M. H. Wooders, Equivalence of Lindahl equilibria with participation prices and the core,, Economic Theory, 9 (1997), 115.  doi: 10.1007/BF01213446.  Google Scholar

[26]

M. H. Wooders, Multijurisdictional economies, the Tiebout Hypothesis, and sorting,, Proceedings of the National Academy of Sciences, 96 (1999), 10585.  doi: 10.1073/pnas.96.19.10585.  Google Scholar

[27]

M. Wooders, E. Cartwright and R. Selten, Behavioral conformity in games with many players,, Games and Economic Behavior, 57 (2006), 347.  doi: 10.1016/j.geb.2005.09.006.  Google Scholar

[28]

M. Wooders and E. Cartwright, Correlated equilibrium, conformity, and stereotyping in social groups,, Journal of Public Economic Theory, 16 (2014), 743.   Google Scholar

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