This paper models a circumstance in which there are N conditionally independent experiments, but a decision maker (DM) can only examine at most K of them sequentially. An important feature of the information structure is that those experiments can give each state conclusive signals, and each can only be checked once, i.e. without replacement. I introduce a notion of ``simple strategy'', which allows DM to make decisions at each decision node only depending on partial information of the continuation decision tree. I show that in a 2-state-2-action setting, the optimal strategy is always a simple strategy. The optimal learning strategy also indicates that the DM's strategy may be distorted by some Blackwell-dominated information sources. In the generalized J-state-L-action setting, I give a sufficient and necessary condition under which the optimal strategy is simple when the DM has full learning capacity.

This paper studies one property, independence of irrelevant alternatives (IIA), on the solution concept of strategic games. I focus on the solution concept of rationalizability, and give the necessary and sufficient conditions for IIA to be satisfied in games solved by rationalizability. I discuss two versions of rationalizability in games with complete and incomplete information. In these two circumstances, I focus on supermodular games and give the necessary conditions for IIA to be satisfied in a supermodular game under rationalizability.

This paper explores the trade-off faced by buyers seeking information about products before making a purchase, especially when acquiring more information risks leaking their private information. Different from Chapter 1, which studies a single decision maker's learning problem, this chapter also studies how two agents strategically interact under a bilateral trade market. By allowing the seller to design and sell a menu of experiments, the seller can infer the buyer's private information through this screening mechanism. The seller then sets a monopoly price based on the chosen experiment. Crucially, the seller only observes which experiment the buyer purchases, not the exact realized signal. This study characterizes the seller's first-best outcome and uses it as a benchmark, investigating all conditions under which the seller's first-best outcome can be implemented through the optimal experiment, with a detailed analysis in the binary value case.