In many countries, pension funds based on individual accounts have been affected by high operating costs. Contract theory helps to unravel the nature of such problems: managers of pension funds have strong incentives to manipulate market expectations about their capacity through wasteful activities (e.g. promotion). Thus, competition among pension funds entails efficiency loses, due to pension savings attraction efforts, as well as gains, related to investments in asset management skills. Regulations capping fees or costs of pension funds worsen market inefficiency, while a public pension fund competing with private ones improves (at least weekly) it. Taking into account political and commitment constraints affecting public institutions, a quasi-competitive pension scheme - centralizing contribution collection, auctioning the right to manage raised money to competitive fund managers, and affording an opting out choice to households -Pareto-dominates (at least weekly) the market of pension funds.