American Institute of Mathematical Sciences

Advanced
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.  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.  doi: 10.1080/10236190902902331.  Google Scholar

[3]

L. Almeida, J. Cruz, H. Ferreira and A. Pinto, Leadership Model,, in, (2011), 53.  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.   Google Scholar

[5]

J. Brida, M. Defesa, M. Faias and A. Pinto, A tourist's choice model,, in, (2011), 159.  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.   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.  doi: 10.1006/jeth.2000.2716.  Google Scholar

[8]

G. Mudur, Maths for movies, medicine and markets,, in, (2010).   Google Scholar

[9]

A. Pinto, "Game Theory and Duopoly Models,", Interdisciplinary Applied Mathematics Series, (2012).   Google Scholar

[10]

A. Pinto, M. Faias and A. Mousa, Resort pricing and bankruptcy,, in, (2011), 567.  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, (2011), 689.  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.  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.  doi: 10.1080/10236190902902331.  Google Scholar

[3]

L. Almeida, J. Cruz, H. Ferreira and A. Pinto, Leadership Model,, in, (2011), 53.  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.   Google Scholar

[5]

J. Brida, M. Defesa, M. Faias and A. Pinto, A tourist's choice model,, in, (2011), 159.  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.   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.  doi: 10.1006/jeth.2000.2716.  Google Scholar

[8]

G. Mudur, Maths for movies, medicine and markets,, in, (2010).   Google Scholar

[9]

A. Pinto, "Game Theory and Duopoly Models,", Interdisciplinary Applied Mathematics Series, (2012).   Google Scholar

[10]

A. Pinto, M. Faias and A. Mousa, Resort pricing and bankruptcy,, in, (2011), 567.  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, (2011), 689.  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

[1]

P. C. Jha, Sugandha Aggarwal, Anshu Gupta, Ruhul Sarker. Multi-criteria media mix decision model for advertising a single product with segment specific and mass media. Journal of Industrial & Management Optimization, 2016, 12 (4) : 1367-1389. doi: 10.3934/jimo.2016.12.1367
[2]

Yannick Viossat. Game dynamics and Nash equilibria. Journal of Dynamics & Games, 2014, 1 (3) : 537-553. doi: 10.3934/jdg.2014.1.537
[3]

Margarida Carvalho, João Pedro Pedroso, João Saraiva. Electricity day-ahead markets: Computation of Nash equilibria. Journal of Industrial & Management Optimization, 2015, 11 (3) : 985-998. doi: 10.3934/jimo.2015.11.985
[4]

Filipe Martins, Alberto A. Pinto, Jorge Passamani Zubelli. Nash and social welfare impact in an international trade model. Journal of Dynamics & Games, 2017, 4 (2) : 149-173. doi: 10.3934/jdg.2017009
[5]

Sheri M. Markose. Complex type 4 structure changing dynamics of digital agents: Nash equilibria of a game with arms race in innovations. Journal of Dynamics & Games, 2017, 4 (3) : 255-284. doi: 10.3934/jdg.2017015
[6]

Alejandra Fonseca-Morales, Onésimo Hernández-Lerma. A note on differential games with Pareto-optimal NASH equilibria: Deterministic and stochastic models†. Journal of Dynamics & Games, 2017, 4 (3) : 195-203. doi: 10.3934/jdg.2017012
[7]

Zhimin Zhang. On a risk model with randomized dividend-decision times. Journal of Industrial & Management Optimization, 2014, 10 (4) : 1041-1058. doi: 10.3934/jimo.2014.10.1041
[8]

Ricardo Borges, Àngel Calsina, Sílvia Cuadrado. Equilibria of a cyclin structured cell population model. Discrete & Continuous Dynamical Systems - B, 2009, 11 (3) : 613-627. doi: 10.3934/dcdsb.2009.11.613
[9]

Sílvia Cuadrado. Stability of equilibria of a predator-prey model of phenotype evolution. Mathematical Biosciences & Engineering, 2009, 6 (4) : 701-718. doi: 10.3934/mbe.2009.6.701
[10]

Emiliano Cristiani, Fabio S. Priuli. A destination-preserving model for simulating Wardrop equilibria in traffic flow on networks. Networks & Heterogeneous Media, 2015, 10 (4) : 857-876. doi: 10.3934/nhm.2015.10.857
[11]

Shangbing Ai. Global stability of equilibria in a tick-borne disease model. Mathematical Biosciences & Engineering, 2007, 4 (4) : 567-572. doi: 10.3934/mbe.2007.4.567
[12]

Theodore Kolokolnikov, Michael J. Ward. Bifurcation of spike equilibria in the near-shadow Gierer-Meinhardt model. Discrete & Continuous Dynamical Systems - B, 2004, 4 (4) : 1033-1064. doi: 10.3934/dcdsb.2004.4.1033
[13]

Semu Mitiku Kassa. Three-level global resource allocation model for HIV control: A hierarchical decision system approach. Mathematical Biosciences & Engineering, 2018, 15 (1) : 255-273. doi: 10.3934/mbe.2018011
[14]

Jian Jin, Weijian Mi. An AIMMS-based decision-making model for optimizing the intelligent stowage of export containers in a single bay. Discrete & Continuous Dynamical Systems - S, 2019, 12 (4&5) : 1101-1115. doi: 10.3934/dcdss.2019076
[15]

Min Tang, Fuying Jing, Xiangrui Chao. A dynamic lot sizing model with production-or-outsourcing decision under minimum production quantities. Journal of Industrial & Management Optimization, 2017, 13 (5) : 1-18. doi: 10.3934/jimo.2019059
[16]

Xue Yan, Heap-Yih Chong, Jing Zhou, Zhaohan Sheng, Feng Xu. Fairness preference based decision-making model for concession period in PPP projects. Journal of Industrial & Management Optimization, 2020, 16 (1) : 11-23. doi: 10.3934/jimo.2018137
[17]

Janos Kollar. The Nash conjecture for threefolds. Electronic Research Announcements, 1998, 4: 63-73.

[18]

William Geller, Bruce Kitchens, Michał Misiurewicz. Microdynamics for Nash maps. Discrete & Continuous Dynamical Systems - A, 2010, 27 (3) : 1007-1024. doi: 10.3934/dcds.2010.27.1007
[19]

Eduard Feireisl, Françoise Issard-Roch, Hana Petzeltová. Long-time behaviour and convergence towards equilibria for a conserved phase field model. Discrete & Continuous Dynamical Systems - A, 2004, 10 (1&2) : 239-252. doi: 10.3934/dcds.2004.10.239
[20]

Abba B. Gumel, Baojun Song. Existence of multiple-stable equilibria for a multi-drug-resistant model of mycobacterium tuberculosis. Mathematical Biosciences & Engineering, 2008, 5 (3) : 437-455. doi: 10.3934/mbe.2008.5.437

 Impact Factor: 

Tools

Metrics

  • PDF downloads (16)
  • HTML views (0)
  • Cited by (3)

Other articles
by authors

[Back to Top]

Copyright © 2019 American Institute of Mathematical Sciences