Mobile opportunistic networks are characterized by unpredictable mobility, heterogeneity of contact rates and lack of global information. Successful delivery of messages at low costs and delays in such networks is thus challenging. Most forwarding algorithms avoid the cost associated with flooding the network by forwarding only to nodes that are likely to be good relays, using a quality metric associated with nodes. However it is non-trivial to decide whether an encountered node is a good relay at the moment of encounter. Thus the problem is in part one of online inference of the quality distribution of nodes from sequential samples, and has connections to optimal stopping theory. Based on these observations we develop a new strategy for forwarding, which we refer to as delegation forwarding. We analyse two variants of delegation forwarding and show that while naive forwarding to high contact rate nodes has cost linear in the population size, the cost of delegation forwarding is propo...