this is related to the customer value, weither it's retention of existing customer or attracting new ones. Here is I would proceed :
1. Understand the root cause / trigger of such action
- Is credit card fee an important criteria in customer's choice over the different banks ?
- Are current client living for new bank offering zero fee ?
- Is the bank trying to gain market share and developp its customer database by attracting new customer with this type of offer ?
2. Evaluate the customer value by identiying the different revenu generated per customer
- Recurrent revenues : credit card fees, insurances, agios, commission over exchange rate, etc.
- Project related revenues : loan interests (car, real estate, consuming, etc.)
3. Run the economics of reducing credit cards fees
- Compare the loss of credit card fees revenues on the customer databse over the value generated by new / retained customers
Hope this helps