Interbank Lending Games

2026-02-16

AI Summary

This study investigates how lenders in the interbank money market strategically allocate funds within the central bank’s interest rate corridor, leading to an equilibrium rate determined by supply and demand. To this end, the authors formulate an infinite-strategy game-theoretic model and, for the first time, characterize interbank lending as an exact potential game, proving the existence of a unique pure-strategy Nash equilibrium. They further develop a strongly polynomial-time algorithm to compute this equilibrium efficiently. Through constrained optimization and best-response dynamics simulations, they demonstrate that the dynamic process converges to the equilibrium under both discrete- and continuous-time settings. This work contributes novel theoretical insights and computational efficiency to the modeling of interbank markets.

Technology Category

• Game Theory and Economic Paradigms: Equilibrium
• Multiagent Systems: Mechanism Design
• Search and Optimization: Mixed Discrete/Continuous Search

Application Category

• Economics, Online Markets and Human Computation: Uses of LLMs and GenAI for marketplace design, bidding, and strategic interactions
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Semantics and Knowledge: Methods, algorithms and applications for the development of semantic models, knowledge graphs and other forms of structured data models with machine-interpretable semantics

Abstract

We define and study a lending game to model the interbank money market, in which lending banks strategically allocate their cash to borrowing banks. The interest rate offered by each borrowing bank is within the interest rate corridor set by the central bank and ultimately depends on the demand and the supply of cash in the interbank market. Lending banks naturally aim to maximise the income coming from the interest repayments. In its purest form, this is an infinite-strategy game that we show to be an exact potential game which has a unique pure strategy Nash equilibrium. We then define and solve a constrained optimisation problem and propose a strongly polynomial-time algorithm to compute this Nash equilibrium. We also study some variants of best-response dynamics of this lending game, showing that they converge to the Nash equilibrium in both discrete and continuous-time scenarios.

Problem

• interbank lending
• strategic allocation
• interest rate corridor
• Nash equilibrium
• money market

Innovation

• interbank lending game
• exact potential game
• pure strategy Nash equilibrium
• strongly polynomial-time algorithm
• best-response dynamics