Existence of Fractional Solutions in NTU DEA Game

Jing Fu, Shigeo Muto

Abstract

This paper deals with the problem of fairly allocating a certain amount of benefit among individuals or organizations with multiple criteria for their performance evaluation. It is an extension work of our paper on game theoretic approaches to weight assignments in data envelopment analysis (DEA) problems Sek. One of the main conclusions in our previous work is that the core of the TU (transferable utility) DEA game is non-empty if and only if the game is inessential, that is, the evaluation indices are identical for all the criteria for each player. This condition is equivalent to a trivial single-criterion setting, which motivates us to turn to the NTU (non-transferable utility) situation and check the existence of the fractional solutions. In this study, we contribute on showing the existence of a-core, and giving two sufficient conditions such that ß-core exists and is identical to a-core in NTU DEA game. Our discussion is also interesting in light of a direction to improve the robustness of the ß-core existence condition by relaxing the inessential condition in TU DEA game.

References

  1. Calleja, P., Borm, P., and Hendrickx, R. (2005). Multi-issue allocation situations. European Journal of Operations Research, 164:730-747.
  2. Charnes, A., Cooper, W. W., and Rhodes, E. (1978). Measuring the efficiency of decision making units. European Journal of Operational Research, 2:429-444.
  3. Cook, W. D., Tone, K., and Zhu, J. (2014). Data envelopment analysis: Prior to choosing a model. OMEGA, 44:1-4.
  4. Masuzawa, T. (2003). Punishment strategies make the acoalitional game ordinally convex and balanced. International Journal of Game Theory, 32:479-483.
  5. Nakabayashi, K., Sahoo, B. K., and Tone, K. (2009). Fair allocation based on two criteria: a dea game view of “add them up and divide by two”. Journal of the Operations Research Society of Japan, 52:131-146.
  6. Nakabayashi, K. and Tone, K. (2006). Egoist's dilemma: a dea game. OMEGA, 34:135-148.
  7. O'Neil, B. (1982). A problem of rights arbitration from the talmud. Mathematical Social Sciences, 2:345-371.
  8. Scarf, H. (1971). On the existence of a cooperative solution for a general class of n-person games. Journal of Economic Theory, 3:169-181.
  9. Sekine, S., Fu, J., and Muto, S. (2014). Game theoretic approaches to weight assignments in data envelopment analysis problems. Mathematical Problems in Engineering, 2014, Article ID 434252:9 pages.
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Paper Citation


in Harvard Style

Fu J. and Muto S. (2015). Existence of Fractional Solutions in NTU DEA Game . In Proceedings of the International Conference on Operations Research and Enterprise Systems - Volume 1: ICORES, ISBN 978-989-758-075-8, pages 107-115. DOI: 10.5220/0005206701070115


in Bibtex Style

@conference{icores15,
author={Jing Fu and Shigeo Muto},
title={Existence of Fractional Solutions in NTU DEA Game},
booktitle={Proceedings of the International Conference on Operations Research and Enterprise Systems - Volume 1: ICORES,},
year={2015},
pages={107-115},
publisher={SciTePress},
organization={INSTICC},
doi={10.5220/0005206701070115},
isbn={978-989-758-075-8},
}


in EndNote Style

TY - CONF
JO - Proceedings of the International Conference on Operations Research and Enterprise Systems - Volume 1: ICORES,
TI - Existence of Fractional Solutions in NTU DEA Game
SN - 978-989-758-075-8
AU - Fu J.
AU - Muto S.
PY - 2015
SP - 107
EP - 115
DO - 10.5220/0005206701070115