Regulatory distorsions in a competitive banking industry: stockholder commercial versus mutual banks

This paper aims to present a theoretical analysis of strategic competition in retail banking when some of the firms of the industry show profit maximising behaviour (commercial banks) and some other show expense preference conduct (mutual banks). Specifically, we study the impact of imposing a prudential regulation (minimum capital ratio) on those different types of banks. This works build upon recent strategic banking studies ([1],[2] and [3]) which consider, from a mathematical perspective, the competitive behaviour of banking firms in highly liberalized markets but with a regulatory distortion. In order to get this aim, it will be necessary to solve some problems posed in the field of optimisation, particularly on maximisation of functions subjected to some restrictions