TY - JOUR

T1 - The private value of a patent

T2 - A cooperative approach

AU - Jelnov, Artyom

AU - Tauman, Yair

PY - 2009/7

Y1 - 2009/7

N2 - 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.

AB - 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.

KW - Game theory

KW - Patent licensing

KW - Shapley value

UR - http://www.scopus.com/inward/record.url?scp=67349198093&partnerID=8YFLogxK

U2 - 10.1016/j.mathsocsci.2009.01.005

DO - 10.1016/j.mathsocsci.2009.01.005

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AN - SCOPUS:67349198093

SN - 0165-4896

VL - 58

SP - 84

EP - 97

JO - Mathematical Social Sciences

JF - Mathematical Social Sciences

IS - 1

ER -