The feedback equilibria of a differential game of capitalism.

*(English)*Zbl 0722.90017The paper deals with the workers vs. capitalists differential game originally proposed by K. Lancaster [J. Pol. Econ. 87, 1092-1109 (1973)] and later extended by M. Pohjola [J. Econ. Dyn. Control 6, 173-186 (1983)], T. Basar, A. Haurie and G. Ricci [ibid. 9, 101-125 (1985)] and others. For a discussion of the literature, see M. Pohjola [in: Dynamic games and applications in economics, 7th Annu. Conf., Econ. Dyn. Control, London 1985, Lect. Notes Econ. Math. Syst. 265, 103-133 (1986; Zbl 0586.90109)]. The paper at hand extends the work by Basar, Haurie and Ricci by addressing the question of the existence of a feedback Stackelberg equilibrium and studies the equilibrium path in more detail, for example, convergence to steady state, monotonicity and sensitivity.

Reviewer: S.Jørgensen (Odense)

##### MSC:

91B62 | Economic growth models |

91A23 | Differential games (aspects of game theory) |

91B40 | Labor market, contracts (MSC2010) |

91A40 | Other game-theoretic models |

##### Keywords:

existence of a feedback Stackelberg equilibrium; convergence to steady state; monotonicity; sensitivity
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\textit{K. Shimomura}, J. Econ. Dyn. Control 15, No. 2, 317--338 (1991; Zbl 0722.90017)

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##### References:

[1] | Başar, Tamer; Haurie, Alain, Feedback equilibria in differential games with structural and modal uncertainties, (), 163-201 |

[2] | Başar, Tamer; Haurie, Alain; Ricci, Gianni, On the dominance of capitalists leadership in a ‘feedback-stackelberg’ solution of a differential game model of capitalism, Journal of economic dynamics and control, 9, 101-125, (1985) |

[3] | Başar, Tamer; Olsder, Geert Jan, Dynamic noncooperative game theory, (1982), Academic Press London · Zbl 0479.90085 |

[4] | Hoel, Michael, Distribution and growth as a differential game between workers and capitalists, International economic review, 19, 335-350, (1978) · Zbl 0387.90119 |

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[7] | Lancaster, Kelvin, The dynamic inefficiency of capitalism, Journal of political economy, 87, 1092-1109, (1973) |

[8] | Manning, Richard; Shea, Koon Lam, The limit of union power in the long run, (1988), State University of New York Albany, NY · Zbl 0664.90024 |

[9] | Pohjola, Matti, Nash and Stackelberg solutions in a differential game of capitalism, Journal of economic dynamics and control, 6, 173-186, (1983) · Zbl 0753.90014 |

[10] | Ramsey, Frank P., A mathematical theory of saving, Economic journal, 38, 543-549, (1928) |

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