A Review on Liao’s Dissertation Entitled “The Solutions on Multi-choice Games” and Related Publications
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.
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- Hsiao, Chih-Ru, 1996. "Consistency of the Multi-Choice Shapley Value," MPRA Paper 18504, University Library of Munich, Germany.
- Hsiao, Chih-Ru & Yeh, Yeong-Nan & Mo, Jie-Ping, 1994. "The Potential of Multi-choice Cooperative Games," MPRA Paper 15007, University Library of Munich, Germany.
- Hwang, Yan-An & Liao, Yu-Hsien, 2008. "Potential approach and characterizations of a Shapley value in multi-choice games," Mathematical Social Sciences, Elsevier, vol. 56(3), pages 321-335, November.
- Hart, Sergiu & Mas-Colell, Andreu, 1989. "Potential, Value, and Consistency," Econometrica, Econometric Society, vol. 57(3), pages 589-614, May.
- repec:ebl:ecbull:v:3:y:2007:i:40:p:1-8 is not listed on IDEAS
- Derks, Jean & Peters, Hans, 1993. "A Shapley Value for Games with Restricted Coalitions," International Journal of Game Theory, Springer, vol. 21(4), pages 351-60.
- Yan-An Hwang & Yu-Hsien Liao, 2008. "Potential In Multi-Choice Cooperative Tu Games," Asia-Pacific Journal of Operational Research (APJOR), World Scientific Publishing Co. Pte. Ltd., vol. 25(05), pages 591-611.
- repec:ebl:ecbull:v:3:y:2008:i:43:p:1-7 is not listed on IDEAS
- Yu-Hsien Liao, 2009. "Dividend approach and level consistency for the Derks and Peters value," Economics Bulletin, AccessEcon, vol. 29(2), pages 1054-1062.
- Hsiao, Chih-Ru, 1995. "A note on non-essential players in multi-choice cooperative games," Games and Economic Behavior, Elsevier, vol. 8(2), pages 424-432.
- Hsiao, Chih-Ru, 1995. "A Value for Continuously-Many-Choice Cooperative Games," International Journal of Game Theory, Springer, vol. 24(3), pages 273-92.
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