Skip to main content

Stable profit sharing in a patent licensing game: general bargaining outcomes

Abstract

By considering coalition structures formed by an external licensor of a patented technology and oligopolistic firms, we investigate licensing agreements that can be reached as bargaining outcomes under those coalition structures. The following results hold in a generalized patent licensing game. The core for a coalition structure is always empty, unless the grand coalition forms. We give a necessary and sufficient condition for the nonemptiness of the core (for the grand coalition). If the number of licensees that maximizes licensees’ total surplus is greater than the number of existing non-licensees, each symmetric bargaining set for a coalition structure is a singleton, and the optimal number of licensees that maximizes the licensor’s revenue is uniquely determined.

This is a preview of subscription content, access via your institution.

References

  • Aumann RJ, Drèze M (1974) Cooperative games with coalition structures. Int J Game Theory 3: 217–237

    Article  Google Scholar 

  • Aumann RJ, Maschler M (1964) The bargaining set for cooperative games. In: Dresher M, Shaply LS, Tucker AW (eds) Advances in game theory. Princeton University Press, Princeton, pp 443–476

    Google Scholar 

  • Davis M, Maschler M (1965) The kernel of a cooperative game. Naval Res Logist Q 12: 223–259

    Article  Google Scholar 

  • Davis M, Maschler M (1967) Existence of stable payoff configurations for cooperative games. In: Schubik M (eds) Essays in Mathematical Economics in honor of Oskar Morgenstern. Princeton University Press, Princeton, pp 39–52 (abstract appeared in 1963 in Bulletin of American Mathematical Society 69, 106–108)

    Google Scholar 

  • Driessen T, Muto S, Nakayama M (1992) A cooperative game of information trading: the core, the nucleolus and the kernel. ZOR Methods Models Oper Res 36: 55–72

    Article  Google Scholar 

  • Kamien MI, Oren SS, Tauman Y (1992) Optimal licensing of cost-reducing innovation. J Math Econ 21: 483–508

    Article  Google Scholar 

  • Kamien MI, Tauman Y (1984) The private value of a patent: a game theoretic analysis. J Econ Suppl 4: 93–118

    Google Scholar 

  • Kamien MI, Tauman Y (1986) Fees versus royalties and the private value of a patent. Q J Econ 101: 471–491

    Article  Google Scholar 

  • Kamien MI, Tauman Y, Zhang I (1988) Optimal license fees for a new product. Math Soc Sci 16: 77–106

    Article  Google Scholar 

  • Katz ML, Shapiro C (1985) On the licensing of innovation. Rand J Econ 16: 504–520

    Article  Google Scholar 

  • Katz ML, Shapiro C (1986) How to license intangible property. Q J Econ 101: 567–589

    Article  Google Scholar 

  • Maschler M, Peleg B (1966) A Characterization, existence proof and dimension bounds for the kernel. Pac J Math 18: 289–328

    Google Scholar 

  • Muto S (1987) Possibility of relicensing and patent protection. Euro Econ Rev 31: 927–945

    Article  Google Scholar 

  • Muto S (1990) Resale-proofness and coalition-proof Nash equilibria. Games Econ Behav 2: 337–361

    Article  Google Scholar 

  • Muto S (1993) On licensing policies in Bertrand competition. Games Econ Behav 5: 257–267

    Article  Google Scholar 

  • Muto S, Nakayama M, Potters J, Tijs S (1989) On Big Boss games. Econ Stud Quart 39: 303–321

    Google Scholar 

  • Nakayama M, Quintas L (1991) Stable payoffs in resale-proof trades of information. Games Econ Behav 3: 339–349

    Article  Google Scholar 

  • Peleg B (1967) Existence theorem of for the bargaining set \({\mathcal{M}_{1}^{i}}\) . In: Schubik M (eds) Essays in Mathematical Economics in honor of Oskar Morgenstern. Princeton University Press, Princeton, pp 53–56 (the abstract appeared in 1963 in Bulletin of American Mathematical Society 69, 109–110)

    Google Scholar 

  • Schmeidler D (1969) The nucleolus of a characteristic function game. SIAM J Appl Math 17: 1163–1170

    Article  Google Scholar 

  • Sempere-Monerris J, Vannetelbosch J (2001) The relevance of bargaining for the licensing of a cost-reducing innovation. Bull Econ Res 53: 101–115

    Article  Google Scholar 

  • Sen D (2005) Fee versus royalty reconsidered. Games Econ Behav 53: 141–147

    Article  Google Scholar 

  • Sen D, Tauman Y (2007) General licensing schemes for a cost-reducing innovations. Games Econ Behav 59: 163–186

    Article  Google Scholar 

  • Shapley L, Schubik M (1967) Ownership and the production function. Q J Econ LXXXI: 88–111

    Article  Google Scholar 

  • Tauman Y, Watanabe N (2007) The Shapley value of a patent licensing game: the asymptotic equivalence to non-cooperative results. Econ Theory 30: 135–149

    Article  Google Scholar 

  • Thrall RM, Lucas WF (1963) n-person games in partition function form. Naval Res Ligist Q 10: 281–298

    Article  Google Scholar 

  • Watanabe N, Muto S (2006) Licensing agreements as bargaining outcomes: general results and two examples. Adv Math Econ 8: 433–447

    Article  Google Scholar 

  • Watanabe N, Tauman Y (2003) Asymptotic properties of the Shapley value of a patent licensing game. mimeo., Kyoto University

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Naoki Watanabe.

Additional information

The authors wish to thank the chief editor, anonymous referees, and participants in the 10th DC (Japan), the 3rd ICMA, and the 17th Stony Brook conference for helpful comments and suggestions. Thanks are extended to Ryo Kawasaki for editing English. They are partially supported by the MEXT Grant-in-Aid for 21 Century COE Program, Grant-in-Aid 18730517 (Watanabe), and Grant-in-Aid 16310107 (Muto).

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Watanabe, N., Muto, S. Stable profit sharing in a patent licensing game: general bargaining outcomes. Int J Game Theory 37, 505–523 (2008). https://doi.org/10.1007/s00182-008-0130-9

Download citation

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00182-008-0130-9

Keywords

  • Licensing
  • Coalition structure
  • Bargaining set
  • Core

JEL Classification

  • C71
  • D45
  • D43