Optimal Two-Part Tariff Licensing under Returns to Scale

A. Karakitsiou, A. Mavrommati


In this study we investigate a two-part tariff licensing contract that enables an incumbent innovator to license a cost reducing innovation in a Cournot duopoly characterized by non-constant returns to scale. We identify the optimal two-part tariff licensing contract based on the cost reduction imposed by the use of the new technology and the market parameter.


Patent Licensing; Royalty; Ad-valorem; two tarrif, Cournot Duopoly; Game Theory

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Arrow, K.J. 1962. “Economic welfare and the allocation of resources for invention”, in R. Nelson (Ed.), The rate and direction of inventive activity: Economic and social factors, Princeton University pp.609--625

Bousquet, A., Cremer, H., Ivaldi, M. and Wolkovicz, M. (1998). “Risk sharing in licensing”, International Journal of Industrial Organization, Vol. 16, pp 535-554.

Colombo, S. and Filippini, L. 2014. “Patent Licensing with Bertrand Competitors”, The Manchester School DOI: 10.1111/manc.12050.

Fauli-Oller, R. and Sandonis, J. 2002. “Welfare Reducing Licensing”, Games and Economic Behavior, Vol. 41, pp. 192-205.

Filippini, L. 2005. “Licensing Contract in a Stackelberg Model”, The Manchester School, Vol. 73, pp. 582-598.

Kamien, M. 1992. “Patent Licensing”, in R. J. Aumann and S. Hart (eds), Handbook of Game Theory, Amsterdam, Elsevier Science, 1, pp. 331--354.

Kamien, M., Oren, S. and Tauman, Y. 1992. “Optimal licensing of cost reducing innovation”, Journal of Mathematical Economics, Vol. 21, pp. 483-508.

Kamien, M.I., and Tauman, Y. 1986. “Fees versus royalties and the private value of a patent” Quarterly Journal of Economics, Vol. 101, pp. 471-491.

Kamien, M.I. and Tauman, Y. 2002. “Patent licensing: the inside story”, The Manchester School, Vol. 70, pp. 7-15.

Karakitsiou, A. and Mavrommati, A. 2013. “Ad-valorem and Royalty Licensing Under Decreasing Returns to Scale”, Asian Journal of Business and Management, Vol. 1, pp. 14-20.

Katz, M. and Shapiro, C. 1986. “How to License Intangible Property”, Quarterly Journal of Economics, Vol. 101, pp. 567-590.

Kitagawa, T., Masuda, Y. and Umezawa, M. 2014. “Patent strength and optimal two-part tariff licensing with a potential rival”, Economic Letters, Vol. 123, pp. 227-231

Rostoker, M. 1984. “A survey of corporate licensing”, IDEA, Vol.24, pp. 59-92.

San Martin, M. and Saracho, A.I. 2010. “Royalty licensing”, Economics Letters, Vol. 107, pp. 284--287.

San Martin, M. and Saracho, A.I. 2014, “Optimal Two-part Tariff Licensing Mechanisms”, The Manchester School, DOI: 10.1111/manc.12059.

Sen, D. and Tauman, Y. 2007. “General Licensing Schemes for a Cost reducing Innovation”, Games and Economic Behaviour, Vol. 59, pp. 163-186.

Sen, D. and Stamatopoulos G. 2009. “Technology transfer under returns to scale”, The Manchester School, Vol. 77, pp. 337-365.

Wang, X.H. 1998. “Fee versus royalty licensing in a Cournot duopoly model”, Economics Letters, Vol. 60, pp. 55-62.

Wang, X. H. 2002. “Fee versus royalty licensing in a differentiated Cournot duopoly”, Journal of Economics and Business, Vol. 54, pp.253-266.

Wang, X. H. and Yang, B. Z. 1999. “On Licensing under Bertrand Competition”, Australian Economic Papers, Vol. 38, pp. 106-119.


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