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 non-cooperative 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.

中文翻译：

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银行博弈——ATM网络成本分摊的双形博弈理论框架

自动柜员机 (ATM) 在世界经济中发挥着重要作用，因为它们促进了金融交易，从而促进了良好的交流和消费。 ATM 交易费用用于支付网络运行成本，这些费用通常由银行和提款机运营商等成员结算。在本文中，我们开发了一种新颖的双形博弈论模型，供成员优化投资 ATM 网络并分摊成本。这种双形博弈既包括用于交换费用共享的合作博弈论机制，也包括用于模拟成员也希望最大化其效用这一事实的非合作对应机制。虽然拟议的合作框架适用于一般 ATM 网络，但由于数据的可访问性以及该网络目前正在经历的显着稳定性问题（主流已广泛提及），我们将案例研究重点放在英国 ATM 网络上。媒体。在技​​术方面，我们证明了纯纳什均衡的存在，并且可以有效地计算。我们还表明，在某些设置下，Shapley 分配属于核心，因此它不仅对所有成员公平，而且还能带来稳定的 ATM 网络。此外，我们还表明，在社会福利方面，沙普利价值分配在现行机制中占主导地位。最后，我们使用完整英国 ATM 网络的真实数据提供数值分析和管理见解。