Multiple equilibrium overnight rates in a dynamic interbank market game

We analyse a two-period model of the interbank market, i.e. the market where banks trade liquidity. We assume that banks do not take the interbank interest rate as given, but instead negotiate on interest rates and transaction volumes with each other. The solution concept applied is the Shapley value. We show that there are a multiplicity of average equilibrium interest rates of the first period so that the average interest rate in this period does not convey any information on the expected liquidity situation on the interbank market. As the banks control not only the transaction volumes, but also the interest rates, they can leave the interest rates constant and adjust the transaction volumes when, for example, a liquidity deficit becomes more likely.