In this paper, we introduce the concept of a multilayer network game in a cooperative setup. We consider the notion of simultaneous contribution of individual players or links to two different networks (say, X and Z). Our model nests both classical network games and bi-cooperative network games. The calculation of the utility of players within a specific network in the presence of an additional/alternative network provides a broader spectrum of real-world decision dynamics. The subsequent challenge involves achieving an optimal distribution of payoffs among the players forming the networks. The link-based rule best fits to our model as it delves into the influence of the alternative links in the network. We have designed an extended Position value to address the complexities arising from scenarios where networks overlap. Further, it is shown that the Position value is uniquely characterized by the Efficiency and Balanced Link Contribution axioms.
