We use Monte Carlo techniques to simulate an organized prediction competition between a group of a scientific experts acting under the influence of a ``self-governing'' prediction reward algorithm. Our aim is to illustrate the advantages of a specific type of reward distribution rule that is designed to address some of the limitations of traditional forecast scoring rules. The primary extension of this algorithm as compared with standard forecast scoring is that it incorporates measures of both group consensus and question relevance directly into the reward distribution algorithm. Our model of the prediction competition includes parameters that control both the level of bias from prior beliefs and the influence of the reward incentive. The Monte Carlo simulations demonstrate that, within the simplifying assumptions of the the model, experts collectively approach belief in objectively true facts, so long as reward influence is high and the bias stays below a critical threshold. The purpose of this work is to motivate further research into prediction reward algorithms that combine standard forecasting measures with factors like bias and consensus.