This work consists in simulating a real time interbank gross payment system (RTGS) through a multi-agent model, to analyze the evolution of the liquidity brought by the banks to the system. In this model, each bank chooses the amount of a daily liquidity provided in the system on the basis of costs minimization (costs of liquidity and delaying) by taking into account the liquidity brought by the other banks. Banks agents reasoning is based on a repeated aggregate game of over several payment days where each bank plays against the other banks. For adaptive behaviour we integrate into bank agents a learning classifier system. We carry out then several simulations to follow the system total liquidity evolution as that of each bank agent with varying costs coefficients. The question to be answered is: what are the cash amounts that banks must provide and under what constraints (costs of liquidity and delaying) the system beyond the lack of liquidity (illiquidity)? We find that liquidity e volution depends on costs coefficients.