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Indeterminacy and history dependence of strategically interacting players

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  • Wirl, Franz

Abstract

This paper considers a finite number of agents populating Krugman’s (1991) labor market. The objective is to investigate whether the much emphasized indeterminate outcome is due to the assumption of uncountable many agents, each of measure 0. It is shown that this result extends to n players each with strategic leverage if the social reference includes the own action. This multiplicity results in an open loop setting, which renders in almost all other cases a unique intertemporal Nash equilibrium. Finally, the cooperative solution exhibits non-standard features: the possibility of converging to the (stationary inferior) agricultural equilibrium and that is due to an unstable node while an unstable spiral can render the unique outcome of full industrialization.

Suggested Citation

  • Wirl, Franz, 2016. "Indeterminacy and history dependence of strategically interacting players," Economics Letters, Elsevier, vol. 145(C), pages 19-24.
    • Handle: RePEc:eee:ecolet:v:145:y:2016:i:c:p:19-24
    DOI: 10.1016/j.econlet.2016.05.006
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    References listed on IDEAS

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    1. Wirl, Franz, 2007. "Do multiple Nash equilibria in Markov strategies mitigate the tragedy of the commons?," Journal of Economic Dynamics and Control, Elsevier, vol. 31(11), pages 3723-3740, November.
    2. W. Davis Dechert & Kazuo Nishimura, 2012. "A Complete Characterization of Optimal Growth Paths in an Aggregated Model with a Non-Concave Production Function," Springer Books, in: John Stachurski & Alain Venditti & Makoto Yano (ed.), Nonlinear Dynamics in Equilibrium Models, edition 127, chapter 0, pages 237-257, Springer.
    3. Tsutsui, Shunichi & Mino, Kazuo, 1990. "Nonlinear strategies in dynamic duopolistic competition with sticky prices," Journal of Economic Theory, Elsevier, vol. 52(1), pages 136-161, October.
    4. Dieter Grass & Jonathan P. Caulkins & Gustav Feichtinger & Gernot Tragler & Doris A. Behrens, 2008. "Optimal Control of Nonlinear Processes," Springer Books, Springer, number 978-3-540-77647-5, June.
    5. Wirl, Franz & Feichtinger, Gustav, 2006. "History versus expectations: Increasing returns or social influence?," Journal of Behavioral and Experimental Economics (formerly The Journal of Socio-Economics), Elsevier, vol. 35(5), pages 877-888, October.
    6. Skiba, A K, 1978. "Optimal Growth with a Convex-Concave Production Function," Econometrica, Econometric Society, vol. 46(3), pages 527-539, May.
    7. Rowat, Colin, 2007. "Non-linear strategies in a linear quadratic differential game," Journal of Economic Dynamics and Control, Elsevier, vol. 31(10), pages 3179-3202, October.
    8. Wagener, F. O. O., 2003. "Skiba points and heteroclinic bifurcations, with applications to the shallow lake system," Journal of Economic Dynamics and Control, Elsevier, vol. 27(9), pages 1533-1561, July.
    9. Paul Krugman, 1991. "History versus Expectations," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 106(2), pages 651-667.
    10. Dockner Engelbert J. & Van Long Ngo, 1993. "International Pollution Control: Cooperative versus Noncooperative Strategies," Journal of Environmental Economics and Management, Elsevier, vol. 25(1), pages 13-29, July.
    11. Hartl, Richard F., 1987. "A simple proof of the monotonicity of the state trajectories in autonomous control problems," Journal of Economic Theory, Elsevier, vol. 41(1), pages 211-215, February.
    12. Jonathan P. Caulkins & Gustav Feichtinger & Dieter Grass & Richard F. Hartl & Peter M. Kort & Andreas J. Novak & Andrea Seidl & Franz Wirl, 2014. "A Dynamic Analysis of Schelling’s Binary Corruption Model: A Competitive Equilibrium Approach," Journal of Optimization Theory and Applications, Springer, vol. 161(2), pages 608-625, May.
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    Cited by:

    1. Akihiko Yanase & Ngo Van Long & Ngo Van Long, 2020. "Trade Costs and Strategic Investment in Infrastructure in a Dynamic Global Economy with Symmetric Countries," CESifo Working Paper Series 8707, CESifo.
    2. Eigruber, Markus & Wirl, Franz, 2024. "Market equilibrium strategies under learning by doing and spillovers," Energy Economics, Elsevier, vol. 131(C).

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    More about this item

    Keywords

    Krugman’s labor market; Stability; History and expectation dependence; Differential game;
    All these keywords.

    JEL classification:

    • C73 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Stochastic and Dynamic Games; Evolutionary Games
    • D92 - Microeconomics - - Micro-Based Behavioral Economics - - - Intertemporal Firm Choice, Investment, Capacity, and Financing
    • J61 - Labor and Demographic Economics - - Mobility, Unemployment, Vacancies, and Immigrant Workers - - - Geographic Labor Mobility; Immigrant Workers

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