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A Conjecture of Shapley and Shubik on Competitive Outcomes in the Cores of NTU Market Games

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  • Qin, Cheng-Zhong

Abstract

It is shown that for every NTU market game, there is a market that represents the game whose competitive payoff vectors completely fill up the inner core of the game. It is also shown that for every NTU market game and for any point in its inner core, there is a market that represents the game and further has the given inner core point as its unique competitive payoff vector. The results prove a conjecture of Shapley and Shubik.

Suggested Citation

  • Qin, Cheng-Zhong, 1993. "A Conjecture of Shapley and Shubik on Competitive Outcomes in the Cores of NTU Market Games," International Journal of Game Theory, Springer;Game Theory Society, vol. 22(4), pages 335-344.
  • Handle: RePEc:spr:jogath:v:22:y:1993:i:4:p:335-44
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    Cited by:

    1. Sonja Brangewitz & Jan-Philip Gamp, 2014. "Competitive outcomes and the inner core of NTU market games," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 57(3), pages 529-554, November.
    2. Sun, Ning & Trockel, Walter & Yang, Zaifu, 2008. "Competitive outcomes and endogenous coalition formation in an n-person game," Journal of Mathematical Economics, Elsevier, vol. 44(7-8), pages 853-860, July.
    3. Cheng-Zhong Qin & Martin Shubik, 2012. "Selecting a unique competitive equilibrium with default penalties," Journal of Economics, Springer, vol. 106(2), pages 119-132, June.
    4. Brangewitz, Sonja & Gamp, Jan-Philip, 2014. "Competitive outcomes and the core of TU market games," Center for Mathematical Economics Working Papers 454, Center for Mathematical Economics, Bielefeld University.
    5. repec:spr:etbull:v:5:y:2017:i:2:d:10.1007_s40505-017-0115-6 is not listed on IDEAS
    6. Inoue, Tomoki, 2013. "Representation of non-transferable utility games by coalition production economies," Journal of Mathematical Economics, Elsevier, vol. 49(2), pages 141-149.
    7. Qin, Cheng-Zhong & Shapley, Lloyd S. & Shimomura, Ken-Ichi, 2006. "The Walras core of an economy and its limit theorem," Journal of Mathematical Economics, Elsevier, vol. 42(2), pages 180-197, April.
    8. Page Jr., Frank H. & Wooders, Myrna, 2009. "Strategic basins of attraction, the path dominance core, and network formation games," Games and Economic Behavior, Elsevier, vol. 66(1), pages 462-487, May.
    9. Brangewitz, Sonja & Gamp, Jan-Philip, 2013. "Asymmetric Nash bargaining solutions and competitive payoffs," Economics Letters, Elsevier, vol. 121(2), pages 224-227.
    10. Inoue, Tomoki, 2011. "Representation of TU games by coalition production economies," Center for Mathematical Economics Working Papers 430, Center for Mathematical Economics, Bielefeld University.

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