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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

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 & 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.  Google Scholar

[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.  Google Scholar

[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.  Google Scholar

[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. Google Scholar

[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.  Google Scholar

[6]

J. Brida, M. Defesa, M. Faias and A. Pinto, Strategic choice in tourism with differentiated crowding types, Economics Bulletin, 30 (2010), 1509-1515. Google Scholar

[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.  Google Scholar

[8]

G. Mudur, Maths for movies, medicine and markets, in "The Telegraph," Calcutta, India, 2010. Google Scholar

[9]

A. Pinto, "Game Theory and Duopoly Models," Interdisciplinary Applied Mathematics Series, Springer, New York, 2012. Google Scholar

[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.  Google Scholar

[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.  Google Scholar

[12]

R. Soeiro, A. Mousa and A. Pinto, Influência Das decis oes individuais num mercado competitivo,, in, ().   Google Scholar

show all references

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.  Google Scholar

[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.  Google Scholar

[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.  Google Scholar

[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. Google Scholar

[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.  Google Scholar

[6]

J. Brida, M. Defesa, M. Faias and A. Pinto, Strategic choice in tourism with differentiated crowding types, Economics Bulletin, 30 (2010), 1509-1515. Google Scholar

[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.  Google Scholar

[8]

G. Mudur, Maths for movies, medicine and markets, in "The Telegraph," Calcutta, India, 2010. Google Scholar

[9]

A. Pinto, "Game Theory and Duopoly Models," Interdisciplinary Applied Mathematics Series, Springer, New York, 2012. Google Scholar

[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.  Google Scholar

[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.  Google Scholar

[12]

R. Soeiro, A. Mousa and A. Pinto, Influência Das decis oes individuais num mercado competitivo,, in, ().   Google Scholar

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