| Summary: | <p> <b>Chapter 1:</b> The owners of large online platforms, like Airbnb or Amazon Marketplace, are able to affect the probability that a given buyer observes a given seller on their platform. Buyers and sellers therefore interact on a bipartite graph with links between them weighted by the probability of observation. Platform owners are then able to design the network by choosing the observation probabilities. A seller's price is decreasing in their Bonacich centrality. In order to maximise profits, the platform owner connects an entrant to buyers according to a measure of their own centrality in the graph. While a network where buyers observe and trade with all sellers with probability one maximises consumer surplus, such a network does not necessarily maximise the platform's profit. The platform owner faces a trade-off between increasing observability and reducing competition, which explains why buyers tend not to be able to observe all sellers on online platforms. If sellers are identical, increasing seller prominence for any consumer segment increases competition, and profit is maximised when it is randomised across all sellers. </p>
<p><b>Chapter 2:</b> Product ratings and reviews are commonplace on large online platforms, like Airbnb and Amazon Marketplace. One use for these ratings is to order search results. Platform owners are able to choose the extent to which ratings can be used to determine the probability a given seller is observed. Since demand is higher for high-quality products, there is an incentive to increase the probability that highly rated sellers are observed by biasing search results towards them. Biasing search results in this way results in competition being more concentrated, reducing prices. In markets where demand is sensitive to quality, a search process that is biased towards highly rated sellers is more profitable than an environment where matches are random. However, when the variance in idiosyncratic preference is relatively large, the loss in profits associated with missing beneficial matches renders a random match environment more profitable. Whether it is profitable to use ratings as a means of ordering search results therefore depends on the properties of the market(s) in which the platform operates.</p>
<p><b>Chapter 3:</b> Politicians serve two masters: voters and their own party leadership, and allocate effort between tasks that benefit one or the other of these principals. Depending on the extent to which they value the incentives offered by the party leader, a politician may choose to build a reputation either as an effective legislator, increasing their probability of receiving those incentives, or as a representative of the people, increasing their probability of re-election. This framework allows us to analyse the party leader's incentives in the case where they lack commitment power: the legislative benefit affect the probability that politicians are re-elected, and the party leader cannot to take this into account when they are unable to contract with the legislator ex-ante. The party leader therefore suffers from a lack of ability to commit. They may also face second-mover disadvantage because they can only reward the politicians who are re-elected, implying that the effectiveness of their incentive is reducing as the first-best level of legislative effort becomes large. </p>
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