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.

翻译：本文定义并研究了一种用于模拟银行间货币市场的借贷博弈，其中贷款银行策略性地将现金分配给借款银行。每家借款银行提供的利率均处于中央银行设定的利率走廊内，并最终取决于银行间市场的现金供需状况。贷款银行自然以最大化利息还款收入为目标。在最纯粹的形式下，这是一个无限策略博弈，我们证明其为一个精确势博弈，且存在唯一的纯策略纳什均衡。随后，我们定义并求解了一个约束优化问题，并提出一种强多项式时间算法来计算该纳什均衡。我们还研究了该借贷博弈若干最优响应动态的变体，证明其在离散与连续时间场景下均收敛至纳什均衡。