Hsiao, Chih-Ru (2011): A Review on Liao’s Dissertation Entitled “The Solutions on Multi-choice Games” and Related Publications.
Download (149kB) | Preview
In 2007, Liao finished his Ph.d. dissertation(Liao 2007) entitled “The Solutions on Multi-choice Games”. Chapter 1 of the dissertation mainly worked on two special cases of the H&R multi-choice Shapley value. One assumes that the weight function w(j) is a positive constant function for all j 6= 0 with w(0) = 0 and the other one assumes that the weight function w(j) = j for all j. If w(j) ’s are equal for all j > 0 then the formula of H&R multi-choice Shapley value can be significantly simplified to the original formula of the traditional Shapley value for the traditional games. Therefore, as a matter of fact, Definitions 1 and 2 in Chapter 1 of the dissertation  are simply the traditional Shapley value. Hence, in most part of Chapter 1, Liao was just writing “new results” of traditional games in terms of the notations of multi-choice games. Furthermore, the dissertation  did not cited (1994), (1995a) and (1996) which held the original ideas of its main part of chapter 1.
|Item Type:||MPRA Paper|
|Commentary on:||Eprints 0 not found.|
|Original Title:||A Review on Liao’s Dissertation Entitled “The Solutions on Multi-choice Games” and Related Publications|
|English Title:||A Review on Liao’s Dissertation Entitled “The Solutions on Multi-choice Games” and Related Publications|
|Keywords:||Multi-choice TU games, Shapley value, potential, w-consistency|
|Subjects:||C - Mathematical and Quantitative Methods > C7 - Game Theory and Bargaining Theory|
|Depositing User:||Chih-Ru HSIAO|
|Date Deposited:||13. Apr 2011 10:02|
|Last Modified:||12. Feb 2013 17:38|
 WL Chiou, CR Hsiao(2010) A Characterization of the Multi-Choice Shapley Value with Partially Consistent Property, Vol. 14, No. 1, pp.287-318.
 J. Derks and H. Peters(1993), A Shapley value for games with restricted coalitions. International Journal of Game Theory 21,351-360.
 S. Hart, Mas-Colell A (1989) Potential, Value and Consistency. Econometrica 57:589-614
 CR Hsiao(1991) The Shapley Value for Multi-choice Cooperative Games, Ph.D Dissertation submitted to the University of Illinois at Chicago, June, 1991.
 CR Hsiao, Raghavan TES (1992) Monotonicity and Dummy Free Property for Multi-Choice Cooperative Games. International Journal of Game Theory 21:301-312
 CR Hsiao, Raghavan TES (1993) Shapley Value for Multi-choice Cooperative Game(I). Games and Economic Behavior 5:240-256
 CR Hsiao, Y.N. Yeh and J.P. Mo(1994), The Potential of Multi-choice Cooperative Games, Conference Paper. International Mathematics Conference ’94, National Sun Yat-sen University, Kaohsiung, Taiwan, Dec. 2-5, 1994. http://mpra.ub.uni-muenchen.de/15007/1/MPRA002.pdf
 C.R. Hsiao(1995a), A Note on Non-essential Players in Multi-Choice Cooperative Games, Games and Economic Behavior, 8, 424-432.
 C.R. Hsiao(1995b), A Value for Continuously-Many-Choice Cooperative Games, International Journal of Game Theory (1995) 24:273-292
 C.R. Hsiao(1996), Consistency of the Multi-choice Shapley Value, Technical Report, NSC 85-2121-M-031-006(1995-1996), Taiwan. http://mpra.ub.uni-muenchen.de/18504/1/mpra4.pdf
 C.R. Hsiao, Y.H Liao (2008) The Potential and Consistency Property for Multichoice Shapley Value, Taiwanese Journal of Math. 12:2, 545-559.
 Y.A. Hwang and Y.H. Liao(2008a), Potential in multi-choice cooperative TU games, Asia-Pacific Journal of Operational Research(APJOR), vol. 25, issue 05, pages 591- 611.
 Y.A. Hwang and Y.H. Liao(2008b)The solutions for multi-choice games: TU games approach, Economics Bulletin, Vol. 3, No. 43: 1-7
 Y.A. Hwang and Y.H. Liao(2008c), Potential approach and characterizations of a Shapley value in multi-choice games, Mathematical Social Sciences, Volume 56, Issue 3, 321-335.
 Y.A. Hwang and Y.H. Liao(2009a) The consistent value of fuzzy games, Fuzzy Sets and Systems, 160:644-656.
 Y.A. Hwang and Y.H. Liao(2009b) Equivalence theorem, consistency and axiomatizations of a multi-choice values, Journal of Global Optimization, volume 45, Number 4, 597-613.
 Y.H. Liao (1999) Some properties of multi-choice Shapley value. Master Thesis, Department of Mathematics, Soochow University, Taipei Taiwan.
 Y.H. Liao (2007) The Solutions on Multi-choice Games. Dissertation for Ph.d. degree Dong-Hwa University, Hualien Taiwan.
 Y.H. Liao (2007) A Dynamic Approach to a Consistent Value under Plurality-Efficiency. Economics Bulletin, Vol. 3, No. 40 pp. 1-8.  Yu-Hsien Liao (2009) ”Dividend approach and level consistency for the Derks and Peters value”, Economics Bulletin, Vol. 29 no.2 pp. 1054-1062.
 A van den Nouweland, J. Potters, S. Tijs and JM Zarzuelo(1995), Core and related solution concepts for multi-choice games. ZOR-MathematicalMethods of Operations Research 41,289-311.
 H. Peters and H. Zank(2005), The egalitarian solution for multichoice games, Annals of Operations Research 137,399-409
 Shapley LS (1953) A Value for n-person Game. In: Kuhn HW, Tucker AW(eds.) Contributions to the Theory of Games II, Annals of Mathematics Studies 28, Princeton University Press, Princeton, 307-317
- Hsiao, Chih-Ru A Review on Liao’s Dissertation Entitled “The Solutions on Multi-choice Games” and Related Publications. (deposited 13. Apr 2011 10:02) [Currently Displayed]