Is there any reason to store any information on those "credit cards" other than the card ID itself?
there will be 3 to 5 players exchanging money between eachother and the bank.
That's the description we really have. Do those players have to be able to exchange peer to peer, or only through a reader? In the first case you need "smart" cards that can store info, communicate with each other, have batteries, etc. In the second case a passive RFID is enough, as all the accounting is done in the reader itself.