Interbank Lending Games

TL;DR

This paper models the interbank money market as a strategic game where banks allocate cash to maximize interest income, demonstrating the existence and computability of a unique Nash equilibrium.

Contribution

It introduces a novel game-theoretic model of interbank lending, proving the existence of a unique equilibrium and providing an efficient algorithm for its computation.

Findings

The lending game is an exact potential game with a unique pure strategy Nash equilibrium.

A strongly polynomial-time algorithm is developed to compute the equilibrium.

Best-response dynamics converge to the Nash equilibrium in various scenarios.

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.