We theoretically and experimentally examine the implications of trusting behavior arising under sequential and simultaneous designs. In this institutional design problem, player A makes an investment choice, and player B decides whether to share the investment gains with player A. In the sequential design, the level of investment is observable, allowing for more sophisticated strategic behavior by player A than is possible in the simultaneous design. Intuition thus suggests that the sequential design would be more efficient, but this conclusion is premature. Theoretically, we show that in certain circumstances the simultaneous design may actually result in a more efficient outcome than the sequential design. In our experiment, we compare the two designs not only in terms of outcomes but also in terms of perceived cooperation levels, which represent a proxy for trust in the institution itself. Although the outcomes of the two designs differ in predictable ways, i.e., the investment levels as well as the sharing rates are both significantly higher in the sequential design, we do not find corresponding differences in the perceived cooperation levels. We conjecture that this happens because in the sequential design a substantially higher exposure by player A is necessary to induce cooperation by player B. Our data strongly support this conjecture