Abstract
In network games under a cooperative framework, the position value is a link-based allocation rule. It is obtained from the Shapley value of an associated cooperative game where the links in the network are considered players. The Shapley value of each of the links is then divided equally among the players who form those links. The inherent assumption is that the value is indifferent to the weights of the players in the network. Depending on how central a player is in the network or their ability to form links with other players, etc., players can be considered to have weights. Thus, in such situations, dividing the Shapley value equally among the players can be an overly simplistic notion. We propose a generalized version of the position value, that is, the weighted position value, that allocates the Shapley shares proportionally to the players’ weights. These weights for the players are exogenously given. We provide two axiomatic characterizations of our value. Finally, a bidding mechanism is formulated to show that any subgame-perfect Nash equilibrium (SPNE) of this mechanism coincides with the weighted position value.
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