Prediction markets are incentive-based mechanisms for eliciting and combining the diffused, private beliefs of traders about a future uncertain event such as a political election. Typically prediction markets maintain point estimates of forecast variables; however, exponential-family prediction markets define a class of cost function-based market-making algorithms that maintain a complete, collective belief distribution over the underlying generative process of the event of interest (e.g. the probability density of the winner's vote-share). In this paper, we focus on concretizing a special case of this abstract framework we call the beta-Bernoulli market. We set up a multi-agent simulation of the market ecosystem to experimentally investigate the interaction of this market-making algorithm with a heterogeneous trading population. We design a Bayesian trader model with explicit characterization of this heterogeneity with respect to two independent attributes: how rich a trader's private information is and how much wealth they initially have at their disposal. We are interested in gauging the interplay of the above attributes with the arrival order of traders, particularly in terms of the net profit accrued by different trader types. Our results strongly suggest that early arrival can dominate both wealth and informativeness as a factor in determining trader compensation under a variety of experimental conditions.