Consider a seller that intends to auction some item. The seller can invest money and effort in advertising in different market segments in order to recruit n bidders to the auction. Alternatively, the seller can have a much cheaper and focused marketing operation and recruit the same number of bidders from a single market segment. Which marketing operation should the seller choose?

Seed fundraising for ventures often takes place by sequentially approaching potential contributors, whose decisions are observed by other contributors. The fundraising succeeds when a target number of investments is reached. When a single investment suffices, this setting resembles the classic information cascades model. However, when more than one investment is needed, the solution is radically different and exhibits surprising complexities. We analyze a setting where contributors' levels of information are i.i.d. draws from a known distribution, and find strategies in equilibrium for all. We show that participants rely on social insurance,i.e., invest despite having unfavorable private information, relying on future player strategies to protect them from loss. Delegationis an extreme form of social insurance where a contributor will unconditionally invest, effectively delegating the decision to future players. In typical fundraising, early contributors will invest unconditionally, stopping when the target is "close enough", thus de factodelegating the business of determining fundraising success or failure to the last contributors.

We consider a setting where in a known future time, a certain continuous random variable will be realized. There is a public prediction that gradually converges to its realized value, and an expert that has access to a more accurate prediction. Our goal is to study when should the expert reveal his information, assuming that his reward is based on a logarithmic market scoring rule (i.e., his reward is proportional to the gain in log-likelihood of the realized value). Our contributions are: (1) we characterize the expert's optimal policy and show that it is threshold based. (2) we analyze the expert's asymptotic expected optimal reward and show a tight connection to the Law of the Iterated Logarithm, and (3) we give an efficient dynamic programming algorithm to compute the optimal policy.

Online reputation systems collect, maintain and disseminate reputations as a summary numerical score of past interactions of an establishment with its users. As reputation systems, including web search engines, gain in popularity and become a common method for people to select sought services, a dynamical system unfolds: Experts' reputation attracts the potential customers. The experts' expertise affects the probability of satisfying the customers. This rate of success in turn influences the experts' reputation. We consider here several models where each expert has innate, constant, but unknown level of expertise and a publicly known, dynamically varying, reputation.