Dynamics of human decisions

Previous Article
Average optimal strategies for zero-sum Markov games with poorly known payoff function on one side
JDG Home
This Issue
Next Article
Structure of approximate solutions of dynamic continuous time zero-sum games

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
Related Papers

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.
[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.
[3]	L. Almeida, J. Cruz, H. Ferreira and A. Pinto, Leadership Model,, in, (2011), 53. 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.
[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.
[6]	J. Brida, M. Defesa, M. Faias and A. Pinto, Strategic choice in tourism with differentiated crowding types,, Economics Bulletin, 30 (2010), 1509.
[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.
[8]	G. Mudur, Maths for movies, medicine and markets,, in, (2010).
[9]	A. Pinto, "Game Theory and Duopoly Models,", Interdisciplinary Applied Mathematics Series, (2012).
[10]	A. Pinto, M. Faias and A. Mousa, Resort pricing and bankruptcy,, in, (2011), 567. 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, (2011), 689. 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, ().

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.
[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.
[3]	L. Almeida, J. Cruz, H. Ferreira and A. Pinto, Leadership Model,, in, (2011), 53. 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.
[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.
[6]	J. Brida, M. Defesa, M. Faias and A. Pinto, Strategic choice in tourism with differentiated crowding types,, Economics Bulletin, 30 (2010), 1509.
[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.
[8]	G. Mudur, Maths for movies, medicine and markets,, in, (2010).
[9]	A. Pinto, "Game Theory and Duopoly Models,", Interdisciplinary Applied Mathematics Series, (2012).
[10]	A. Pinto, M. Faias and A. Mousa, Resort pricing and bankruptcy,, in, (2011), 567. 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, (2011), 689. 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, ().

[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]	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
[10]	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
[11]	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
[12]	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
[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]	Janos Kollar. The Nash conjecture for threefolds. Electronic Research Announcements, 1998, 4: 63-73.
[15]	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
[16]	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
[17]	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
[18]	Marcy Barge, Sonja Štimac, R. F. Williams. Pure discrete spectrum in substitution tiling spaces. Discrete & Continuous Dynamical Systems - A, 2013, 33 (2) : 579-597. doi: 10.3934/dcds.2013.33.579
[19]	Pierre Cardaliaguet, Chloé Jimenez, Marc Quincampoix. Pure and Random strategies in differential game with incomplete informations. Journal of Dynamics & Games, 2014, 1 (3) : 363-375. doi: 10.3934/jdg.2014.1.363
[20]	Mathias Staudigl. A limit theorem for Markov decision processes. Journal of Dynamics & Games, 2014, 1 (4) : 639-659. doi: 10.3934/jdg.2014.1.639

Impact Factor:

American Institute of Mathematical Sciences