Abstract
This paper provides the existence proof for stable sets of a game which may have empty cores. Given the number of licensees of a patented technology which is determined by the patent holder without any production facilities, a game with a coalition structure is formulated with the outcome expected in the subsequent market competition where any cartels are prohibited. Although the core is non-empty if and only if the grand coalition is formed with a condition, we provide, for each permissible coalition structure, the sufficient condition(s) for the existence of von Neumann–Morgenstern stable sets of the game. Under symmetric imputations, there exist stable sets for any permissible coalition structures, and each of those is completely characterized.
| Original language | English |
|---|---|
| Pages (from-to) | 1-12 |
| Number of pages | 12 |
| Journal | Mathematical Social Sciences |
| Volume | 94 |
| DOIs | |
| Publication status | Published - 2018 Jul 1 |
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ASJC Scopus subject areas
- Sociology and Political Science
- Social Sciences(all)
- Psychology(all)
- Statistics, Probability and Uncertainty
Cite this
von Neumann–Morgenstern stable sets of a patent licensing game : The existence proof. / Hirai, Toshiyuki; Watanabe, Naoki.
In: Mathematical Social Sciences, Vol. 94, 01.07.2018, p. 1-12.Research output: Contribution to journal › Article
}
TY - JOUR
T1 - von Neumann–Morgenstern stable sets of a patent licensing game
T2 - The existence proof
AU - Hirai, Toshiyuki
AU - Watanabe, Naoki
PY - 2018/7/1
Y1 - 2018/7/1
N2 - This paper provides the existence proof for stable sets of a game which may have empty cores. Given the number of licensees of a patented technology which is determined by the patent holder without any production facilities, a game with a coalition structure is formulated with the outcome expected in the subsequent market competition where any cartels are prohibited. Although the core is non-empty if and only if the grand coalition is formed with a condition, we provide, for each permissible coalition structure, the sufficient condition(s) for the existence of von Neumann–Morgenstern stable sets of the game. Under symmetric imputations, there exist stable sets for any permissible coalition structures, and each of those is completely characterized.
AB - This paper provides the existence proof for stable sets of a game which may have empty cores. Given the number of licensees of a patented technology which is determined by the patent holder without any production facilities, a game with a coalition structure is formulated with the outcome expected in the subsequent market competition where any cartels are prohibited. Although the core is non-empty if and only if the grand coalition is formed with a condition, we provide, for each permissible coalition structure, the sufficient condition(s) for the existence of von Neumann–Morgenstern stable sets of the game. Under symmetric imputations, there exist stable sets for any permissible coalition structures, and each of those is completely characterized.
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U2 - 10.1016/j.mathsocsci.2018.04.001
DO - 10.1016/j.mathsocsci.2018.04.001
M3 - Article
VL - 94
SP - 1
EP - 12
JO - Mathematical Social Sciences
JF - Mathematical Social Sciences
SN - 0165-4896
ER -