  A network game assigns a level of collectively generated wealth to every
network that can form on a given set of players. A variable network game
combines a network game with a network formation probability distribution,
describing certain restrictions on network formation. Expected levels of
collectively generated wealth and expected individual payoffs can be formulated
in this setting.
  We investigate properties of the resulting expected wealth levels as well as
the expected variants of well-established network game values as allocation
rules that assign to every variable network game a payoff to the players in a
variable network game. We establish two axiomatizations of the Expected Myerson
Value, originally formulated and proven on the class of communication
situations, based on the well-established component balance, equal bargaining
power and balanced contributions properties. Furthermore, we extend an
established axiomatization of the Position Value based on the balanced link
contribution property to the Expected Position Value.
