Interbank lending is often portrayed as the financial system’s emergency plumbing: when one bank faces a sudden wave of withdrawals, another can provide the liquidity needed to keep payments flowing and prevent a temporary shock from becoming a crisis. But a new theoretical study suggests that the same connections designed to make banks safer can also encourage them to hold fewer reserves, depend more heavily on their partners and create networks that eventually become less efficient as they grow. The research, published in Risk Sciences, examines how banks decide both how much liquidity to keep on their own balance sheets and whether to join an interbank credit network. Its central finding is a paradox with major implications for financial stability: cooperation can reduce individual exposure to liquidity shocks, yet widespread reliance on cooperation can weaken the system that makes cooperation possible.
The researchers model a bank that must balance two competing objectives. Holding reserves provides protection against unexpected deposit withdrawals, but idle money generally earns less than funds invested through lending or other profitable activities. A bank that keeps a large reserve is better positioned to meet immediate claims from depositors, but it may sacrifice returns. A bank that lends more aggressively can increase expected profits, yet it becomes vulnerable if withdrawals arrive faster or in greater volume than anticipated. In the model, each bank first chooses its reserve level while considering the possibility of a liquidity shock. It then evaluates whether joining a network of banks that can lend to one another would produce better outcomes than remaining financially independent. This two-stage structure allows the study to capture an important feature of banking markets: institutions choose both their individual safety margins and the relationships that may substitute for those margins.
The model focuses on liquidity withdrawals, represented as a sudden demand for cash that can force a bank to liquidate assets or seek assistance. A bank with reserves greater than the withdrawal can survive without outside help. A bank whose reserves are insufficient may rely on credit from connected institutions, provided those partners have enough liquidity available and are willing to lend. If support cannot be obtained, the bank may fail. This framework does not treat interbank links as automatically beneficial. Each connection can provide insurance against an isolated shock, but it can also transmit stress when several institutions need cash at the same time. The outcome depends on the interaction between reserve choices, the distribution of deposits across banks, the structure of the network and the incentives created by access to shared liquidity.
The most striking mechanism identified by the researchers is a form of strategic free-riding. Once a bank knows that it can obtain assistance from other institutions, it may reduce its own reserve holdings. That decision can be individually rational: reserves are costly because they represent funds that could otherwise generate income. Yet when many banks make the same calculation, the network’s collective safety cushion becomes thinner. Each institution benefits from the protection provided by others while attempting to avoid bearing the full cost of maintaining liquidity. The result is a tension between private incentives and system-wide resilience. Risk-sharing can lower the expected damage from a shock for an individual bank, but free-riding can reduce the reserves available to absorb shocks across the network, potentially increasing the probability of failures and lowering expected profits.
According to the analysis, the relationship between network size and market performance is not simply positive or negative. When only a relatively small number of banks are connected, adding participants can improve outcomes because the benefits of diversification and liquidity sharing are substantial. A withdrawal affecting one institution may be met by several partners whose reserves remain intact, reducing the need for costly asset sales or emergency intervention. As the network expands, however, the incentive to economize on individual reserves becomes stronger. Every additional connection can make a bank feel less responsible for maintaining its own liquidity, while the number of institutions that may simultaneously seek support also increases. The model therefore produces a rise-and-fall pattern in expected profits: performance improves at first, reaches a peak and then declines as free-riding begins to dominate risk-sharing.
This result points to an optimal range of connectivity rather than a universal case for larger and denser networks. The study finds that relatively small networks can be Pareto optimal, meaning that no participating bank can be made better off without making at least one other participant worse off. In practical terms, a compact network may deliver enough insurance to manage isolated withdrawals while limiting the erosion of individual reserves. A much larger network can appear safer because more institutions are linked, but its apparent strength may be misleading if every bank has reduced its own liquidity buffer. Network size, in this view, is not a measure of resilience by itself. The quality of resilience depends on whether institutions retain sufficient capacity to withstand stress before drawing on their partners.
The researchers also examine networks containing banks of different sizes. Traditional views of interbank relationships might suggest that institutions with similar deposit bases and balance sheets would have the strongest reasons to connect. The model instead indicates that smaller and larger banks may both benefit from forming links even when their deposit sizes differ considerably. A large bank may provide liquidity because it has greater reserves or more diversified funding, while a smaller bank may value access to that support because it is more exposed to a localized withdrawal shock. Such relationships can help explain core-periphery structures in banking, in which a relatively small number of highly connected institutions occupy the center of the network and interact with many smaller banks around them. The same structure, however, can concentrate risk if peripheral institutions become dependent on central providers or if central banks are hit by demands from many partners at once.
The findings also raise questions about the role of government guarantees. When banks believe that authorities will protect depositors, creditors or major institutions during a crisis, they may perceive the consequences of failure as less severe. That implicit safety net can encourage greater risk-taking, lower reserve holdings and more extensive interbank connections. Such behavior may remain profitable during calm periods, when liquidity can be obtained easily, but it can amplify instability during a systemic shock. The researchers argue that capital requirements and related safeguards should be designed with these strategic incentives in mind. Regulation that focuses only on the balance sheet of each bank may miss the way one institution’s reserve decision affects the behavior and vulnerability of its partners. Requirements that preserve adequate buffers could reduce free-riding and prevent large networks from becoming excessively interconnected.
The study is theoretical and relies on computational modeling rather than observations from a particular banking crisis, so it does not claim that every interbank network has the same ideal size or that connections inevitably increase danger. Its contribution is to show how market efficiency can emerge from a trade-off between insurance and incentives. Interbank lending remains a potentially valuable mechanism for absorbing unexpected liquidity withdrawals, especially when shocks are limited and partners are sufficiently strong. But the model warns that connectivity can produce diminishing returns when banks treat shared liquidity as a substitute for prudent reserve management. For policymakers, the message is clear: a safer financial network is not necessarily the one with the most links. It may be the one in which banks share risk while still maintaining enough independent liquidity to survive when everyone needs help at the same time. The research offers a mathematical explanation for why cooperation can stabilize markets at one scale and destabilize them at another, turning the architecture of interbank finance into a critical question for the future of banking regulation.
Subject of Research: Not applicable
Article Title: Interbank network and market efficiency
Web References: https://doi.org/10.1016/j.risk.2026.100059
References: Yu, T., He, X.-Z. (Tony), & Zhang, N. “Interbank network and market efficiency.” Risk Sciences. DOI: 10.1016/j.risk.2026.100059
Image Credits: Yu, T., He, X.-Z. (Tony), & Zhang, N.
Keywords: interbank lending, banking networks, liquidity risk, financial stability, free-riding, bank reserves, market efficiency, core-periphery networks, capital requirements, computational modeling
