Dynamics of human decisions

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January 2014, 1(1): 121-151. doi: 10.3934/jdg.2014.1.121

Dynamics of human decisions

Renato Soeiro ^1, , Abdelrahim Mousa ^1, , Tânia R. Oliveira ^1, 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, Portugal, Portugal, Portugal, Portugal

Received January 2012 Revised November 2012 Published June 2013

Abstract
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We study a dichotomous decision model, where individuals can make the decision yes or no and can influence the decisions of others. We characterize all decisions that form Nash equilibria. Taking into account the way individuals influence the decisions of others, we construct the decision tilings where the axes reflect the personal preferences of the individuals for making the decision yes or no. These tilings characterize geometrically all the pure and mixed Nash equilibria. We show, in these tilings, that Nash equilibria form degenerated hysteresis with respect to the dynamics, with the property that the pure Nash equilibria are asymptotically stable and the strict mixed equilibria are unstable. These hysteresis can help to explain the sudden appearance of social, political and economic crises. We observe the existence of limit cycles for the dynamics associated to situations where the individuals keep changing their decisions along time, but exhibiting a periodic repetition in their decisions. We introduce the notion of altruist and individualist leaders and study the way that the leader can affect the individuals to make the decision that the leader pretends.

Keywords: Dichotomous decision model, pure and mix Nash equilibria..

Mathematics Subject Classification: Primary: 91A35, 91A25; Secondary: 91A8.

Citation: Renato Soeiro, Abdelrahim Mousa, Tânia R. Oliveira, Alberto A. Pinto. Dynamics of human decisions. Journal of Dynamics and Games, 2014, 1 (1) : 121-151. doi: 10.3934/jdg.2014.1.121

References:

[1]	I. Ajzen, Perceived behavioral control, self-Efficacy, locus of control, and the theory of planned behavior, Journal of Applied Social Psychology, 32 (2002), 665-683. doi: 10.1111/j.1559-1816.2002.tb00236.x.
[2]	L. Almeida, J. Cruz, H. Ferreira and A. Pinto, Bayesian-Nash equilibria in theory of planned behavior, Journal of Difference Equations and Applications, 17 (2011), 1085-1093. doi: 10.1080/10236190902902331.
[3]	L. Almeida, J. Cruz, H. Ferreira and A. Pinto, Leadership Model, in "Dynamics, Games and Science I" (eds. M. Peixoto, A. Pinto and D. Rand), Springer Proceedings in Mathematics, Springer-Verlag, Chapter 5, (2011), 53-59. doi: 10.1007/978-3-642-11456-4_5.
[4]	S. Baker, B. Beadnell, M. Gillmore, D. Morrison, B. Huang and S. Stielstra, The theory of reasoned action and the role of external factors on heterosexual mens monogamy and condom use, Journal of Applied Social Psychology, 38 (2008), 97-134.
[5]	J. Brida, M. Defesa, M. Faias and A. Pinto, A tourist's choice model, in "Dynamics, Games and Science I" (eds. M. Peixoto, A. Pinto and D. Rand), Springer Proceedings in Mathematics, Springer-Verlag, Chapter 10, (2011), 159-167. doi: 10.1007/978-3-642-11456-4_10.
[6]	J. Brida, M. Defesa, M. Faias and A. Pinto, Strategic choice in tourism with differentiated crowding types, Economics Bulletin, 30 (2010), 1509-1515.
[7]	J. Conley and M. Wooders, Tiebout economies with differential genetic types and endogenously chosen crowding characteristics, Journal of Economic Theory, 98 (2001), 261-294. doi: 10.1006/jeth.2000.2716.
[8]	G. Mudur, Maths for movies, medicine and markets, in "The Telegraph," Calcutta, India, 2010.
[9]	A. Pinto, "Game Theory and Duopoly Models," Interdisciplinary Applied Mathematics Series, Springer, New York, 2012.
[10]	A. Pinto, M. Faias and A. Mousa, Resort pricing and bankruptcy, in "Dynamics, Games and Science II" (eds. M. Peixoto, A. Pinto and D. Rand), Springer Proceedings in Mathematics, Springer-Verlag, Chapter 39, (2011), 567-573. doi: 10.1007/978-3-642-14788-3_40.
[11]	A. Pinto, A. Mousa, M. Mousa and R. Samarah, Tilings and Bussola for Making Decisions, in "Dynamics, Games and Science I" (eds. M. Peixoto, A. Pinto and D. Rand), Springer Proceedings in Mathematics, Springer-Verlag, Chapter 44, (2011), 689-708. doi: 10.1007/978-3-642-11456-4_44.
[12]	R. Soeiro, A. Mousa and A. Pinto, Influência Das decis oes individuais num mercado competitivo, in "Matemática do Planeta Terra" (eds. F. Costa, J. Buescu and J. T. Pinto), Editora Universitária do Instituto Superior Técnico, IST Press, Lisboa, Aceite para publicação.

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References:

[1]	I. Ajzen, Perceived behavioral control, self-Efficacy, locus of control, and the theory of planned behavior, Journal of Applied Social Psychology, 32 (2002), 665-683. doi: 10.1111/j.1559-1816.2002.tb00236.x.
[2]	L. Almeida, J. Cruz, H. Ferreira and A. Pinto, Bayesian-Nash equilibria in theory of planned behavior, Journal of Difference Equations and Applications, 17 (2011), 1085-1093. doi: 10.1080/10236190902902331.
[3]	L. Almeida, J. Cruz, H. Ferreira and A. Pinto, Leadership Model, in "Dynamics, Games and Science I" (eds. M. Peixoto, A. Pinto and D. Rand), Springer Proceedings in Mathematics, Springer-Verlag, Chapter 5, (2011), 53-59. doi: 10.1007/978-3-642-11456-4_5.
[4]	S. Baker, B. Beadnell, M. Gillmore, D. Morrison, B. Huang and S. Stielstra, The theory of reasoned action and the role of external factors on heterosexual mens monogamy and condom use, Journal of Applied Social Psychology, 38 (2008), 97-134.
[5]	J. Brida, M. Defesa, M. Faias and A. Pinto, A tourist's choice model, in "Dynamics, Games and Science I" (eds. M. Peixoto, A. Pinto and D. Rand), Springer Proceedings in Mathematics, Springer-Verlag, Chapter 10, (2011), 159-167. doi: 10.1007/978-3-642-11456-4_10.
[6]	J. Brida, M. Defesa, M. Faias and A. Pinto, Strategic choice in tourism with differentiated crowding types, Economics Bulletin, 30 (2010), 1509-1515.
[7]	J. Conley and M. Wooders, Tiebout economies with differential genetic types and endogenously chosen crowding characteristics, Journal of Economic Theory, 98 (2001), 261-294. doi: 10.1006/jeth.2000.2716.
[8]	G. Mudur, Maths for movies, medicine and markets, in "The Telegraph," Calcutta, India, 2010.
[9]	A. Pinto, "Game Theory and Duopoly Models," Interdisciplinary Applied Mathematics Series, Springer, New York, 2012.
[10]	A. Pinto, M. Faias and A. Mousa, Resort pricing and bankruptcy, in "Dynamics, Games and Science II" (eds. M. Peixoto, A. Pinto and D. Rand), Springer Proceedings in Mathematics, Springer-Verlag, Chapter 39, (2011), 567-573. doi: 10.1007/978-3-642-14788-3_40.
[11]	A. Pinto, A. Mousa, M. Mousa and R. Samarah, Tilings and Bussola for Making Decisions, in "Dynamics, Games and Science I" (eds. M. Peixoto, A. Pinto and D. Rand), Springer Proceedings in Mathematics, Springer-Verlag, Chapter 44, (2011), 689-708. doi: 10.1007/978-3-642-11456-4_44.
[12]	R. Soeiro, A. Mousa and A. Pinto, Influência Das decis oes individuais num mercado competitivo, in "Matemática do Planeta Terra" (eds. F. Costa, J. Buescu and J. T. Pinto), Editora Universitária do Instituto Superior Técnico, IST Press, Lisboa, Aceite para publicação.

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