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January  2015, 2(1): 1-32. doi: 10.3934/jdg.2015.2.1

Nash Equilibrium in evolutionary competitive models of firms and workers under external regulation

Elvio Accinelli 1, , Bruno Bazzano 2, , Franco Robledo 2, and  Pablo Romero 2,

1. 

Facultad de Economía, Universidad Autónoma San Luis Potosí, Álvaro Obregón 64, Centro Histórico, PC 78000, San Luis Potosí, Mexico
2. 

Facultad de Ingeniería, Universidad de la República, Julio Herrera y Reissig 565, PC 11300, Montevideo, Uruguay, Uruguay, Uruguay

Received  December 2014 Revised  April 2015 Published  June 2015

The object of this paper is to study the labor market using evolutionary game theory as a framework. The entities of this competitive model are firms and workers, with and without external regulation. Firms can either innovate or not, while workers can either be skilled or not. Under the most simple model, called normal model, the economy rests in a poverty trap, where workers are not skilled and firms are not innovative. This Nash equilibria is stable even when both entities follow the optimum strategy in an on-off fashion. This fact suggests the need of an external agent that promotes the economy in order not to fall in a poverty trap.
    Therefore, an evolutionary competitive model is introduced, where an external regulator provides loans to encourage workers to be skilled and firms to be innovative. This model includes poverty traps but also other Nash equilibria, where firms and workers are jointly innovative and skilled.
    The external regulator, in a three-phase process (loans, taxes and inactivity) achieves a common wealth, with a prosperous economy, with innovative firms and skilled workers.
Keywords: external regulator, stochastic dynamics., Nash equilibrium, replicator dynamics, Poverty trap.
Mathematics Subject Classification: Primary: 91A10, 91A05; Secondary: 91A2.
Citation: Elvio Accinelli, Bruno Bazzano, Franco Robledo, Pablo Romero. Nash Equilibrium in evolutionary competitive models of firms and workers under external regulation. Journal of Dynamics and Games, 2015, 2 (1) : 1-32. doi: 10.3934/jdg.2015.2.1
References:
[1]

E. Accinelli, S. London, L. Punzo and E. Sanchez, Dynamic complementarities, efficiency and nash equilibria for populations of firms and workers, Journal of Economics and Econometrics, 53 (2010), 90-110.

[2]

E. Accinelli, S. London, L. F. Punzo and E. J. S. Carrera, Poverty traps, rationality and evolution, Dynamics, Games and Science I, 1 (2011), 37-52. doi: 10.1007/978-3-642-11456-4_4.

[3]

E. Accinelli, S. London and E. Sanchez, A model of imitative behaviour in the population of firms and workers, Technical Report, Department of Economics, University of Siena, 2009.

[4]

C. Azariadis and J. Stachurski, Chapter 5 poverty traps, in Handbook of Economic Growth, Vol. 1 (eds. P. Aghion and S. Durlauf), 2005, 295-384. doi: 10.1016/S1574-0684(05)01005-1.

[5]

C. B. Barrett and B. M. Swallow, Fractal poverty traps, World Development, 34 (2006), 1-15. doi: 10.1016/j.worlddev.2005.06.008.

[6]

G. Dahlquist, A. Bjorck and N. Anderson, Numerical Methods, Reprint edition, Dover Publications, 2003.

[7]

R. Darling and J. Norris, Differential equation approximations for Markov chains, Probability Surveys, 5 (2008), 37-79. doi: 10.1214/07-PS121.

[8]

J. Dormand and P. Prince, A family of embedded Runge-Kutta formulae, Journal of Computational and Applied Mathematics, 6 (1980), 19-26. doi: 10.1016/0771-050X(80)90013-3.

[9]

M. Hirsch and S. Smale, Differential Equations, Dynamical Systems, And Linear Algebra, Acad. Press, 1974.

[10]

J. Maynard Smith and G. R. Price, The logic of animal conflict, Nature, 246 (1973), 15-18. doi: 10.1038/246015a0.

[11]

J. Nash, Non-cooperative games, The Annals of Mathematics, 54 (1951), 286-295. doi: 10.2307/1969529.

[12]

P. Robert, Stochastic Networks and Queues, Springer, 2003. doi: 10.1007/978-3-662-13052-0.

[13]

J. W. Weibull, Evolutionary Game Theory, MIT Press, 1995.

show all references

References:
[1]

E. Accinelli, S. London, L. Punzo and E. Sanchez, Dynamic complementarities, efficiency and nash equilibria for populations of firms and workers, Journal of Economics and Econometrics, 53 (2010), 90-110.

[2]

E. Accinelli, S. London, L. F. Punzo and E. J. S. Carrera, Poverty traps, rationality and evolution, Dynamics, Games and Science I, 1 (2011), 37-52. doi: 10.1007/978-3-642-11456-4_4.

[3]

E. Accinelli, S. London and E. Sanchez, A model of imitative behaviour in the population of firms and workers, Technical Report, Department of Economics, University of Siena, 2009.

[4]

C. Azariadis and J. Stachurski, Chapter 5 poverty traps, in Handbook of Economic Growth, Vol. 1 (eds. P. Aghion and S. Durlauf), 2005, 295-384. doi: 10.1016/S1574-0684(05)01005-1.

[5]

C. B. Barrett and B. M. Swallow, Fractal poverty traps, World Development, 34 (2006), 1-15. doi: 10.1016/j.worlddev.2005.06.008.

[6]

G. Dahlquist, A. Bjorck and N. Anderson, Numerical Methods, Reprint edition, Dover Publications, 2003.

[7]

R. Darling and J. Norris, Differential equation approximations for Markov chains, Probability Surveys, 5 (2008), 37-79. doi: 10.1214/07-PS121.

[8]

J. Dormand and P. Prince, A family of embedded Runge-Kutta formulae, Journal of Computational and Applied Mathematics, 6 (1980), 19-26. doi: 10.1016/0771-050X(80)90013-3.

[9]

M. Hirsch and S. Smale, Differential Equations, Dynamical Systems, And Linear Algebra, Acad. Press, 1974.

[10]

J. Maynard Smith and G. R. Price, The logic of animal conflict, Nature, 246 (1973), 15-18. doi: 10.1038/246015a0.

[11]

J. Nash, Non-cooperative games, The Annals of Mathematics, 54 (1951), 286-295. doi: 10.2307/1969529.

[12]

P. Robert, Stochastic Networks and Queues, Springer, 2003. doi: 10.1007/978-3-662-13052-0.

[13]

J. W. Weibull, Evolutionary Game Theory, MIT Press, 1995.

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