We study a model of ordered search with learning. Our focus is on settings where an agent knows little about how observable attributes of items map to quality but wants
to avoid missing good discoveries. Knowing only that items with similar attributes have similar qualities, she sequentially decides where to look next or stops searching to take her best discovery to date. We characterize worst-case optimal search procedures. Search effort is ‘inverse-v-shaped’ in search complexity. If there is a sweet-spot in
attribute space, the search path is ‘funnel-shaped’. Optimal search is dynamically consistent and computationally tractable. And the model readily generalizes to limited
consideration sets and multidimensional search.

Many political leaders promise stability during their election campaigns. Several explanations have been offered for the increased support for such politicians, but less is known about future development once they are in office. We develop a model with rationally inattentive voters and investigate how an office-seeking politician designs a political platform in the presence of an incumbent who offers a simple stability policy. We show that this policy, while is not in the best interest of the electorate, also creates negative externalities by encouraging the challenger to propose a more moderate platform, which is sub-optimal. Moreover, the model explains why popular incumbents could benefit from and prefer the high uncertainty and high cost of information.

We study information aggregation in a dynamic trading model with partially informed and strategic or myopic traders, who acquire costly signals in every period. We show that if the acquisition cost is high, very few securities aggregate information always. As the cost decreases, more securities aggregate information, hence the market becomes more efficient. Surprisingly, even when the cost converges to zero, there is a small class of securities that never switches to aggregating information, hence some inefficiency in the market persists. Finally, we study the effect of costly acquisition on the speed of information aggregation and find that, for myopic traders, the only security for which speed is unaffected is the Arrow-Debreu. For any other security, information aggregation can be both faster and slower.