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Splitting Games: Nash Equilibrium and the Optimisation Problem

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  • Ana Paula Martins

Abstract

This research states the stylised n players’ splitting problem as a mathematical programme, relying on definitions of the values of the game and problem stationarity to generate tractable reduced forms, and derives the known solutions after pertaining first-order conditions. Boundary constraints are introduced. Distinction between FOC’s of optimising behavior and equilibrium fitness is provided. Finally, the formal proof of the internal insufficiency of the usual approach to determine the equilibrium is advanced, and the imposing additional conditions – affecting cross multipliers – required for model solving forwarded. Two types of protocols were staged: alternate offers – Rubinstein’s like – and synchronised ones.

Suggested Citation

  • Ana Paula Martins, 2010. "Splitting Games: Nash Equilibrium and the Optimisation Problem," Journal of Economics and Econometrics, Economics and Econometrics Society, vol. 53(1), pages 1-28.
  • Handle: RePEc:eei:journl:v:53:y:2010:i:1:p:1-28
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    1. Rubinstein, Ariel, 1982. "Perfect Equilibrium in a Bargaining Model," Econometrica, Econometric Society, vol. 50(1), pages 97-109, January.
    2. Kancs, d'Artis & Kielyte, Julda, 2010. "European Integration and Labour Migration," European Integration online Papers (EIoP), European Community Studies Association Austria (ECSA-A), vol. 14, November.
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    5. Ana Paula Martins, 2012. "On Depth and Retrospect: “I Forget, and Forgive – but I Discount”," Journal of Economics and Econometrics, Economics and Econometrics Society, vol. 55(3), pages 1-45.
    6. Ana Paula Martins, 2010. "Splitting Games: Nash Equilibrium and the Optimisation Problem," Journal of Economics and Econometrics, Economics and Econometrics Society, vol. 53(1), pages 1-28.
    7. Nash, John, 1953. "Two-Person Cooperative Games," Econometrica, Econometric Society, vol. 21(1), pages 128-140, April.
    8. Ana Paula Martins, 2010. "Frontier Techniques: Contrasting the Performance of (Single-)Truncated Order Regression Methods and Replicated Moments," Journal of Economics and Econometrics, Economics and Econometrics Society, vol. 53(2), pages 75-93.
    9. d’Artis Kancs & Julda Kielyte, 2002. "Migration in the Enlarged European Union: Empirical Evidence for Labour Mobility in the Baltic States," EERI Research Paper Series EERI_RP_2002_04, Economics and Econometrics Research Institute (EERI), Brussels.
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    12. D’Artis Kancs, 2005. "Can we use NEG models to predict migration flows? An example of CEE accession countries," Migration Letters, Migration Letters, vol. 2(1), pages 32-63, April.
    13. Kancs, D’Artis & Kielyte, Julda, 2010. "Education in the East, Emigrating to the West?," European Review, Cambridge University Press, vol. 18(2), pages 133-154, May.
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    16. Julda Kielyte, 2008. "Estimating Panel Data Models in the Presence of Endogeneity and Selection," Journal of Economics and Econometrics, Economics and Econometrics Society, vol. 51(2), pages 1-19.
    17. Perry Motty & Reny Philip J., 1993. "A Non-cooperative Bargaining Model with Strategically Timed Offers," Journal of Economic Theory, Elsevier, vol. 59(1), pages 50-77, February.
    18. Ana Paula Martins, 2006. "On Simple Conditions for Mixed Equilibria in Dualistic Models. Part II: Degree of Coverage," EERI Research Paper Series EERI_RP_2006_04, Economics and Econometrics Research Institute (EERI), Brussels.
    19. Ana Paula Martins, 2002. "Reconciling the Nash and Kalai-Smorodinsky Cooperative Solutions: Generalized Maximands of CES Form," EERI Research Paper Series EERI_RP_2002_05, Economics and Econometrics Research Institute (EERI), Brussels.
    20. Ana Paula Martins, 2006. "On Simple Conditions for Mixed Equilibria in Dualistic Models. Part I: Degree of Mobility," EERI Research Paper Series EERI_RP_2006_03, Economics and Econometrics Research Institute (EERI), Brussels.
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    Cited by:

    1. William H. Greene & Ana P. Martins, 2013. "Striking Features of the Labor Market: Empirical Evidence," Journal of Economics and Econometrics, Economics and Econometrics Society, vol. 56(2), pages 25-53.
    2. Ana Paula Martins, 2011. "Compliance with the Institutional Wage in Dualistic Models," Journal of Economics and Econometrics, Economics and Econometrics Society, vol. 54(2), pages 93-126.
    3. James Anderson, 2001. "Migration, FDI, and the Margins of Trade," EERI Research Paper Series EERI_RP_2001_05, Economics and Econometrics Research Institute (EERI), Brussels.
    4. Ana Paula Martins, 2010. "Frontier Techniques: Contrasting the Performance of (Single-)Truncated Order Regression Methods and Replicated Moments," Journal of Economics and Econometrics, Economics and Econometrics Society, vol. 53(2), pages 75-93.
    5. Kancs, d'Artis & Kielyte, Julda, 2010. "European Integration and Labour Migration," European Integration online Papers (EIoP), European Community Studies Association Austria (ECSA-A), vol. 14, November.
    6. Ana Paula Martins, 2010. "Splitting Games: Nash Equilibrium and the Optimisation Problem," Journal of Economics and Econometrics, Economics and Econometrics Society, vol. 53(1), pages 1-28.
    7. William H. Greene & Ana P. Martins, 2013. "Striking Features of the Labor Market: Theory," Journal of Economics and Econometrics, Economics and Econometrics Society, vol. 56(2), pages 1-24.
    8. William H. Greene & Ana P. Martins, 2002. "Striking Features of the Labor Market," EERI Research Paper Series EERI RP 2002/08, Economics and Econometrics Research Institute (EERI), Brussels.

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    More about this item

    Keywords

    Non-Cooperative N-Person Games; Infinite Horizon.;

    JEL classification:

    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
    • C78 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Bargaining Theory; Matching Theory
    • C44 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics - - - Operations Research; Statistical Decision Theory
    • H56 - Public Economics - - National Government Expenditures and Related Policies - - - National Security and War
    • D74 - Microeconomics - - Analysis of Collective Decision-Making - - - Conflict; Conflict Resolution; Alliances; Revolutions
    • D31 - Microeconomics - - Distribution - - - Personal Income and Wealth Distribution
    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
    • C62 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Existence and Stability Conditions of Equilibrium

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