Even when there is a potential danger of opportunism, economic agents often initiate contracts or engage in trust. Considering a world with two types of agents, opportunists and non-opportunists, interacting under incomplete information, this article develops a simple two-stage game theoretic model to show how trust and cooperation can emerge in a one-shot interaction, even in the absence of a supporting incentive mechanism. Two classic paradigms are considered: the prisoner's dilemma and the game of chicken. In the context of the prisoner's dilemma, trust depends on the exogenous probability of having a non-opportunist partner, while in the game of chicken trust is purely a function of the payoffs. Contrary to intuition, a high ratio of non-opportunistic agents in the population does not favor contract initiation in the game of chicken and a strong presence of opportunists does not act as an impediment to respecting commitments.