Information plays an important role in financial markets. In this dissertation, first, we consider how traders choose different information. Second, we ask when traders acquire information under competition. Finally, we analyze how ambiguous information affects traders' incentives to trade and reveal their private information. There is information not only about the payoff but also concerning the supply and demand of an asset. In Chapter 1, we study how traders choose to process different information while asset prices are conveying some information. We show that traders decide to process different types of information depends on their initial belief and the informativeness of asset prices. In particular, when the return to each type of information is increasing, traders choose to learn only one type of information. Those who have more precise initial belief about the asset payoff (supply) choose to learn more about the asset payoff (supply). In Chapter 2, we study when traders decide to acquire information under competition. Traders consider two effects of competition in information acquisition: one is that an informed trader's profitability is affected by the presence of another informed trader, the other is the spillover of the information from the informed trader to the uninformed. We show that, when the former effect dominates, then traders tend to acquire information earlier. If the otherwise, then traders tend to delay their information acquisition. In Chapter 3, we study traders' behavior when information is ambiguous, which gives rise to multiple probability models to describe uncertainty. We demonstrate that ambiguity will reduce traders' incentive to trade and reveal their private information. When there is a moderate level of ambiguity, informed traders start to trade randomly, whereas they trade for sure when there is no or a little uncertainty. When ambiguity is sufficiently large, informed traders choose not to trade any more, and no additional information will be revealed in the market.