Game of banks - biform game theoretical framework for automated teller machine network cost sharing

Automated teller machines (ATM) play a major role in the world economy as they enable financial transactions and hence good exchanges and consumption. ATM transaction fees are incurred to cover the cost of running the network and these are often settled among the members including banks and cash machine operators. In this paper, we develop a novel biform game theoretic model for members to optimally invest in the ATM network and to share the cost. This biform game includes both a cooperative game theory mechanism for interchange fee sharing and a noncooperative counterpart to model the fact that members also wish to maximize their utilities. While the proposed coopetition framework is applicable to general ATM networks, we focus the case study on the UK ATM network thanks to the accessibility of the data in addition to the notable stability issues that the network is currently experiencing as has been widely featured by the mainstream media. On the technical side, we prove the existence of a pure Nash equilibrium, which can be computed efficiently. We also show that, under some settings, the Shapley allocation belongs to the core and hence it is not only fair to all members but also leads to a stable ATM network. In addition, we show that the Shapley value allocation dominates the current mechanism in terms of social welfare. Finally, we provide numerical analysis and managerial insights using real data on the complete UK ATM network.