Estimation of bankruptcy rules with a priori unions for establishing new systems of quotas

• Autores: Alejandro Saavedra Nieves, Paula Saavedra Nieves
• Localización: BEIO, Boletín de Estadística e Investigación Operativa, ISSN 1889-3805, Vol. 39, Nº. 1, 2023
• Idioma: inglés
• Enlaces
  • Texto completo
• Resumen

  • This paper addresses a sampling procedure for estimating extensions of the random arrival rule to those bankruptcy situations where there exist a priori unions. It is based on simple random sampling with replacement and it adapts an estimation method of the Owen value for transferable utility games with a priori unions, especially useful when the set of involved agents is sufficiently large. We analyse the theoretical statistical properties of the resulting estimator as well as we provide some bounds for the incurred error. Its performance is evaluated on two well-studied examples in literature where this allocation rule can be exactly obtained. Finally, we apply this sampling method to provide a new quota system for the milk market in Galicia (Spain) for checking the role of different territorial structures when they are taken as a priori unions. The resulting quotas estimator is also compared with two classical rules in bankruptcy literature.

• Referencias bibliográficas
  • Aumann, R. J. and M. Maschler (1985). ✭✭Game theoretic analysis of a bankruptcy problem from the Talmud✮✮. In: Journal of Economic Theory...
  • Borm, P., L. Carpente, B. Casas-Méndez, and R. Hendrickx (2005). ✭✭The constrained equal awards rule for bankruptcy problems with a priori...
  • Castro, J., D. Gómez, and J. Tejada (2009). ✭✭Polynomial calculation of the Shapley value based on sampling✮✮. In: Computers & Operations...
  • Curiel, I. J., M. Maschler, and S. H. Tijs (1987). ✭✭Bankruptcy games✮✮. In: Zeitschrift f¨ur Operations Research 31.5, A143–A159.
  • Fernández-García, F. R. and J. Puerto-Albandoz (2006). ✭✭Teoria de Juegos Multiobjetivo✮✮. In: Imagraf Impresores SA, Sevilla.
  • Frutos, M. A. de (1999). ✭✭Coalitional manipulations in a bankruptcy problem✮✮. In: Review of Economic Design 4.3, pp. 255–272.
  • González-D´ıaz, J., I. Garc´ıa-Jurado, and M. G. Fiestras-Janeiro (2010). An Introductory Course on Mathematical Game Theory. Vol. 115. Providence:...
  • Hoeffding, W. (1963). ✭✭Probability Inequalities for Sums of Bounded Random Variables✮✮. In: Journal of the American Statistical Association...
  • Maleki, S. (2015). ✭✭Addressing the computational issues of the Shapley value with applications in the smart grid✮✮. PhD thesis. University...
  • Moulin, H. (2002). ✭✭Axiomatic cost and surplus sharing✮✮. In: Handbook of Social Choice and Welfare 1, pp. 289–357.
  • O’Neill, B. (1982). ✭✭A problem of rights arbitration from the Talmud✮✮. In: Mathematical Social Sciences 2.4, pp. 345–371.
  • Owen, G. (1975). ✭✭Multilinear extensions and the Banzhaf value✮✮. In: Naval Research Logistics (NRL) 22.4, pp. 741–750.
  • Owen, G. (1977). ✭✭Values of games with a priori unions✮✮. In: Mathematical Economics and Game Theory. Springer, pp. 76–88.
  • Popoviciu, T. (1935). ✭✭Sur les ´equations alg´ebriques ayant toutes leurs racines r´eelles✮✮. In: Mathematica 9, pp. 129–145.
  • Pulido, M., J. Sánchez-Soriano, and N. Llorca (2002). ✭✭Game theory techniques for university management: an extended bankruptcy model✮✮....
  • R Core Team (2023). R: A Language and Environment for Statistical Computing. R Foundation for Statistical Computing. Vienna, Austria. url:...
  • Saavedra-Nieves, A., I. García-Jurado, and M. G. Fiestras-Janeiro (2018). ✭✭Estimation of the Owen Value Based on Sampling✮✮. In: The Mathematics...
  • Saavedra-Nieves, A. and P. Saavedra-Nieves (2020). ✭✭On systems of quotas from bankruptcy perspective: the sampling estimation of the random...
  • Schmeidler, D. (1969). ✭✭The nucleolus of a characteristic function game✮✮. In: SIAM Journal on Applied Mathematics 17.6, pp. 1163–1170.
  • Shapley, L. S. (1953). ✭✭A value for n-person games✮✮. In: Contributions to the Theory of Games 2.28, pp. 307–317.
  • Thomson, W. (2015). ✭✭Axiomatic and game-theoretic analysis of bankruptcy and taxation problems: an update✮✮. In: Mathematical Social Sciences...