We study a problem where a new, unfamiliar group of agents has to decide how a joint reward should be shared among them. We focus on settings where the share that each agent receives depends on the evaluations of its peers concerning that agent's contribution to the group. We introduce a mechanism to elicit and aggregate evaluations as well as for determining agents' shares. The intuition behind the proposed mechanism is that each agent has its expected share maximized to the extent that it is well evaluated by its peers and that it is truthfully reporting its evaluations. For promoting truthfulness, the proposed mechanism uses a peer-prediction method built on strictly proper scoring rules. Under the assumption that agents are Bayesian decision makers, we show that our mechanism is incentive compatible and budget balanced. We also provide sufficient conditions under which the proposed mechanism is individually rational, resistant to some kinds of collusion, and fair.