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Splitting Games: Nash Equilibrium and the Optimisation Problem

  • Ana Paula Martins

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.

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Article provided by Economics and Econometrics Society in its journal Journal of Economics and Econometrics.

Volume (Year): 53 (2010)
Issue (Month): 1 ()
Pages: 1-28

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Handle: RePEc:eei:journl:v:53:y:2010:i:1:p:1-28
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  1. 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.
  2. 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.
  3. d’Artis Kancs, 2005. "Can we use NEG models to predict migration flows? An example of CEE accession countries," EERI Research Paper Series EERI_RP_2005_01, Economics and Econometrics Research Institute (EERI), Brussels.
  4. d'Artis Kancs & Julda Kielyte, 2010. "Education in the East, Emigrating to the West?," EERI Research Paper Series EERI_RP_2010_01, Economics and Econometrics Research Institute (EERI), Brussels.
  5. Nash, John, 1953. "Two-Person Cooperative Games," Econometrica, Econometric Society, vol. 21(1), pages 128-140, April.
  6. Ana Paula Martins, 2010. "Frontier Techniques: Contrasting the Performance of (Single-) Truncated Order Regression Methods and Replicated Moments," EERI Research Paper Series EERI_RP_2010_37, Economics and Econometrics Research Institute (EERI), Brussels.
  7. Martin J. Osborne & Ariel Rubinstein, 2005. "Bargaining and Markets," Levine's Bibliography 666156000000000515, UCLA Department of Economics.
  8. d’Artis Kancs, 2006. "The economic geography of labour migration: Competition, competitiveness and development," EERI Research Paper Series EERI_RP_2006_01, Economics and Econometrics Research Institute (EERI), Brussels.
  9. Ana Paula Martins, 2007. "On Depth and Retrospect: “I Forget, and Forgive – but I Discount”," EERI Research Paper Series EERI_RP_2007_07, Economics and Econometrics Research Institute (EERI), Brussels.
  10. 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.
  11. 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.
  12. 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.
  13. 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.
  14. Ariel Rubinstein, 2010. "Perfect Equilibrium in a Bargaining Model," Levine's Working Paper Archive 661465000000000387, David K. Levine.
  15. Busch, Lutz-Alexander & Wen, Quan, 1995. "Perfect Equilibria in Negotiation Model," Econometrica, Econometric Society, vol. 63(3), pages 545-65, May.
  16. 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.
  17. Sakovics Jozsef, 1993. "Delay in Bargaining Games with Complete Information," Journal of Economic Theory, Elsevier, vol. 59(1), pages 78-95, February.
  18. 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.
  19. JÕzsef SÂkovics & Clara PonsatÎ, 1998. "Rubinstein bargaining with two-sided outside options," Economic Theory, Springer, vol. 11(3), pages 667-672.
  20. Nash, John, 1950. "The Bargaining Problem," Econometrica, Econometric Society, vol. 18(2), pages 155-162, April.
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