  Given a social network of users with selection cost, the \textsc{Budgeted
Influence Maximization Problem} (\emph{BIM Problem} in short) asks for
selecting a subset of the nodes (known as \emph{seed nodes}) within an
allocated budget for initial activation to maximize the influence in the
network. In this paper, we study this problem under the
\emph{co\mbox{-}operative game theoretic} framework. We model this problem as a
co\mbox{-}operative game where the users of the network are the players and for
a group of users, the expected influence by them under the \emph{Maximum
Influence Arborences} diffusion model is its utility. We call this game as
\emph{BIM Game} and show this is `non-convex' and `sub-additive'. Based on the
proposed game\mbox{-}theoretic model and using the solution concept called
`Shapley Value', we propose an iterative algorithm for finding seed nodes. The
proposed methodology is divided into mainly two broad steps: the first one is
computing the approximate marginal gain in \emph{Shapley Value} for all the
nodes of the network, and the second one is selecting seed nodes from the
sorted list until the budget is exhausted. We also show that the proposed
methodology can even be more effective when the community structure of the
network is exploited. The proposed methodologies have been implemented, and an
extensive set of experiments have been conducted with three publicly available
social network datasets. From the experiments, we observe that the seed set
selected by the proposed methodologies lead to more number of influence nodes
compared to many standard and baseline methods from the literature with a
reasonable computational overhead. In particular, if the community structure of
the network is exploited then there is an increase upto $2 \%$ in number of
influenced nodes.
