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The private value of a patent: A cooperative approach

  • Jelnov, Artyom
  • Tauman, Yair

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.

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Article provided by Elsevier in its journal Mathematical Social Sciences.

Volume (Year): 58 (2009)
Issue (Month): 1 (July)
Pages: 84-97

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Handle: RePEc:eee:matsoc:v:58:y:2009:i:1:p:84-97
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  1. Morton I. Kamien & Yair Tauman, 1984. "Fees Versus Royalties and the Private Value of a Patent," Discussion Papers 583, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
  2. Geoffroy de Clippel & Roberto Serrano, 2005. "Marginal Contributions And Externalities In The Value," Economics Working Papers we057339, Universidad Carlos III, Departamento de Economía.
  3. Can Erutku & Yves Richelle, 2007. "Optimal Licensing Contracts and the Value of a Patent," Journal of Economics & Management Strategy, Wiley Blackwell, vol. 16(2), pages 407-436, 06.
  4. Yair Tauman & Naoki Watanabe, 2007. "The Shapley Value of a Patent Licensing Game: the Asymptotic Equivalence to Non-cooperative Results," Economic Theory, Springer, vol. 30(1), pages 135-149, January.
  5. Kamien, Morton I. & Tauman, Yair & Zamir, Shmuel, 1990. "On the value of information in a strategic conflict," Games and Economic Behavior, Elsevier, vol. 2(2), pages 129-153, June.
  6. 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.
  7. Kamien, Morton I., 1992. "Patent licensing," Handbook of Game Theory with Economic Applications, in: R.J. Aumann & S. Hart (ed.), Handbook of Game Theory with Economic Applications, edition 1, volume 1, chapter 11, pages 331-354 Elsevier.
  8. Navarro, Noemi, 2007. "Fair allocation in networks with externalities," Games and Economic Behavior, Elsevier, vol. 58(2), pages 354-364, February.
  9. Kenneth Arrow, 1962. "Economic Welfare and the Allocation of Resources for Invention," NBER Chapters, in: The Rate and Direction of Inventive Activity: Economic and Social Factors, pages 609-626 National Bureau of Economic Research, Inc.
  10. Katz, Michael L & Shapiro, Carl, 1986. "How to License Intangible Property," The Quarterly Journal of Economics, MIT Press, vol. 101(3), pages 567-89, August.
  11. Sen, Debapriya & Tauman, Yair, 2007. "General licensing schemes for a cost-reducing innovation," Games and Economic Behavior, Elsevier, vol. 59(1), pages 163-186, April.
  12. Bolger, E M, 1989. "A Set of Axioms for a Value for Partition Function Games," International Journal of Game Theory, Springer, vol. 18(1), pages 37-44.
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