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A Review on Liao’s Dissertation Entitled “The Solutions on Multi-choice Games” and Related Publications


  • Hsiao, Chih-Ru


In 2007, Liao finished his Ph.d. dissertation[18](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 [18] 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 [18] did not cited [7](1994), [8](1995a) and [10](1996) which held the original ideas of its main part of chapter 1.

Suggested Citation

  • Hsiao, Chih-Ru, 2011. "A Review on Liao’s Dissertation Entitled “The Solutions on Multi-choice Games” and Related Publications," MPRA Paper 30260, University Library of Munich, Germany.
  • Handle: RePEc:pra:mprapa:30260

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    References listed on IDEAS

    1. repec:ebl:ecbull:v:3:y:2008:i:43:p:1-7 is not listed on IDEAS
    2. Hsiao, Chih-Ru, 1995. "A Value for Continuously-Many-Choice Cooperative Games," International Journal of Game Theory, Springer;Game Theory Society, vol. 24(3), pages 273-292.
    3. 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.
    4. Derks, Jean & Peters, Hans, 1993. "A Shapley Value for Games with Restricted Coalitions," International Journal of Game Theory, Springer;Game Theory Society, vol. 21(4), pages 351-360.
    5. repec:ebl:ecbull:v:3:y:2007:i:40:p:1-8 is not listed on IDEAS
    6. 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.
    7. Hart, Sergiu & Mas-Colell, Andreu, 1989. "Potential, Value, and Consistency," Econometrica, Econometric Society, vol. 57(3), pages 589-614, May.
    8. Yu-Hsien Liao, 2009. "Dividend approach and level consistency for the Derks and Peters value," Economics Bulletin, AccessEcon, vol. 29(2), pages 1054-1062.
    9. Hsiao, Chih-Ru, 1996. "Consistency of the Multi-Choice Shapley Value," MPRA Paper 18504, University Library of Munich, Germany.
    10. 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.
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    More about this item


    Multi-choice TU games; Shapley value; potential; w-consistency;

    JEL classification:

    • C7 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory

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