In this paper, we present an evolutionary trust game to investigate the formation of trust in the so-called sharing economy from a population perspective. To the best of our knowledge, this is the first attempt to model trust in the sharing economy using the evolutionary game theory framework. Our sharing economy trust model consists of four types of players: a trustworthy provider, an untrustworthy provider, a trustworthy consumer, and an untrustworthy consumer. Through systematic simulation experiments, five different scenarios with varying proportions and types of providers and consumers were considered. Our results show that each type of players influences the existence and survival of other types of players, and untrustworthy players do not necessarily dominate the population even when the temptation to defect (i.e., to be untrustworthy) is high. Our findings may have important implications for understanding the emergence of trust in the context of sharing economy transactions.