This paper provides a simple two-period, game theoretic set-up with heterogeneous agents to analyse individual selection of a pension scheme by different categories of agents. Agents have been differentiated according to their income variability. We describe Bayesian equilibria and provide examples to illustrate. The design of a pension scheme requires the consent of all the population. and we have shown that differences of volatility of income contribute to the divergence regarding the decision of a pension investment alternative. We also provide support for the subsistence of unfunded scheme in economies with demographic aging and with promising returns in funded alternatives.