TY - JOUR
T1 - On the existence of population-monotonic solutions on the domain of quasi-convex games
AU - Hokari, Toru
AU - Uchida, Seigo
PY - 2017/1/1
Y1 - 2017/1/1
N2 - On the domain of convex games, the Shapley value and the Dutta–Ray solutions are two well-known solutions that satisfy population-monotonicity. The existence of a population-monotonic solution on the domain of quasi-convex games has been an open question. In this note, we show that in general, no convex combination of the above two solutions can be extended to the domain of quasi-convex games in such a way that preserves population-monotonicity and efficiency.
AB - On the domain of convex games, the Shapley value and the Dutta–Ray solutions are two well-known solutions that satisfy population-monotonicity. The existence of a population-monotonic solution on the domain of quasi-convex games has been an open question. In this note, we show that in general, no convex combination of the above two solutions can be extended to the domain of quasi-convex games in such a way that preserves population-monotonicity and efficiency.
KW - Dutta–Ray solution
KW - Population-monotonicity
KW - Quasi-convex games
KW - Shapely value
KW - TU-games
UR - http://www.scopus.com/inward/record.url?scp=85009168189&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=85009168189&partnerID=8YFLogxK
U2 - 10.1016/j.orl.2016.12.008
DO - 10.1016/j.orl.2016.12.008
M3 - Article
AN - SCOPUS:85009168189
SN - 0167-6377
VL - 45
SP - 90
EP - 92
JO - Operations Research Letters
JF - Operations Research Letters
IS - 1
ER -