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The private value of a patent: A cooperative approach

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  • Jelnov, Artyom
  • Tauman, Yair

Abstract

We consider a game in coalitional form played by the firms of a Cournot industry and an outside patent holder of a cost-reducing innovation. The worth of a coalition of players is the total Cournot profit of the active firms within this coalition. The number of firms that a coalition activates is determined by the Nash equilibrium of the game played by the coalition and its complement, where the strategy of each is the number of firms to be activated. Only firms in a coalition containing the patent holder are allowed to use the new technology. We prove that when the industry size increases indefinitely, the Shapley value of the patent holder approximates the payoff he obtains in a standard non-cooperative setup where he has the entire bargaining power. We also examine a partition game which considers for every coalition all structures of its complement, namely all partitions of the complement into sub-coalitions. The coalition and every sub-coalition of the complement simultaneously decide how many of their firms to be activated. We prove a similar equivalence result for an extension of the Shapley value from coalitional games to partition games.

Suggested Citation

  • Jelnov, Artyom & Tauman, Yair, 2009. "The private value of a patent: A cooperative approach," Mathematical Social Sciences, Elsevier, vol. 58(1), pages 84-97, July.
  • Handle: RePEc:eee:matsoc:v:58:y:2009:i:1:p:84-97
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    References listed on IDEAS

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    9. Macho-Stadler, Ines & Perez-Castrillo, David & Wettstein, David, 2007. "Sharing the surplus: An extension of the Shapley value for environments with externalities," Journal of Economic Theory, Elsevier, vol. 135(1), pages 339-356, July.
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    Cited by:

    1. Borm, Peter & Ju, Yuan & Wettstein, David, 2015. "Rational bargaining in games with coalitional externalities," Journal of Economic Theory, Elsevier, vol. 157(C), pages 236-254.
    2. Eric Bahel & Christian Trudeau, 2013. "A discrete cost sharing model with technological cooperation," International Journal of Game Theory, Springer;Game Theory Society, vol. 42(2), pages 439-460, May.
    3. BHATTACHARYA, Sudipto & D’ASPREMONT, Claude & GURIEV, Sergei & SEN, Debapriya, 2012. "Cooperation in R&D: patenting, licensing and contracting," CORE Discussion Papers 2012055, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    4. Inés Macho-Stadler & David Pérez-Castrillo & David Wettstein, 2017. "Extensions of the Shapley value for Environments with Externalities," Working Papers 1002, Barcelona Graduate School of Economics.
    5. Elias Carayannis & Igor Dubina & Alina Ilinova, 2015. "Licensing in the Context of Entrepreneurial University Activity: an Empirical Evidence and a Theoretical Model," Journal of the Knowledge Economy, Springer;Portland International Center for Management of Engineering and Technology (PICMET), vol. 6(1), pages 1-12, March.
    6. Yair Tauman & Debrapiya Sen, 2012. "Patents and Licenses," Department of Economics Working Papers 12-05, Stony Brook University, Department of Economics.
    7. Kishimoto, Shin & Watanabe, Naoki, 2017. "The kernel of a patent licensing game: The optimal number of licensees," Mathematical Social Sciences, Elsevier, vol. 86(C), pages 37-50.
    8. Kishimoto, Shin, 2013. "Stable bargaining outcomes in patent licensing: A cooperative game approach without side payments," Mathematical Social Sciences, Elsevier, vol. 66(3), pages 183-195.
    9. Shin Kishimoto & Naoki Watanabe, "undated". "The Kernel of a Patent Licensing Game," Working Papers e75, Tokyo Center for Economic Research.
    10. Kishimoto, Shin & Watanabe, Naoki & Muto, Shigeo, 2011. "Bargaining outcomes in patent licensing: Asymptotic results in a general Cournot market," Mathematical Social Sciences, Elsevier, vol. 61(2), pages 114-123, March.

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