Coincidence of Myerson allocation rule with Shapley value
Author(s)
Advisor
Koray, SemihDate
2003Publisher
Bilkent University
Language
English
Type
ThesisItem Usage Stats
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Abstract
This thesis studies the coincidence of the Myerson allocation rule in the context
of networks with the Shapley value in the context of transferable utility games. We start
with a value function defined on networks and derive a transferable utility game from
that. We show that without any restrictions on the value function, Myerson allocation
rule may not lead to the same payoff vector as the Shapley value of the derived TU game
for any network. Under the assumption of monotonicity of the value function, we show
the existence of such coincidence and examine the relation of the set of networks
satisfying this coincidence to the set of pairwise stable and strongly stable networks.
Next, we propose a new stability notion and examine the coincidence of the two vectors
under this stability notion. Finally an alternative allocation rule is introduced whose
payoff vector coincide with the Shapley value of the derived transferable utility game on
the set of efficient networks which coincides with the set of strongly stable networks
under this allocation rule.