This dissertation presents three essays on digital platforms and market manipulation, and investigates the economic impact of social media platforms on manipulation and coordination in the financial markets, as well as their influence on marketing and business models. This first essay, "Media Trading Groups and Short Selling Manipulation", models how chatroom traders, forming a coalition via social media platforms, influence the stock price in the presence of large and strategic short sellers. The economic consequences of this dynamic game are studied in a micro-founded quasi-competitive equilibrium framework, which is new to the literature. Various equilibrium phenomena arise, including price bubbles, short squeezes, forced liquidations, and precautionary savings by the large trader. Media groups discipline the large trader's incentive to short sell, but it can either increase or decrease market efficiency. Additionally, it uniformly improves social welfare under the belief-neutral welfare criterion. The second essay, "Index Design: Hedging and Manipulation", studies optimal index design to both facilitate hedging and alleviate illegal manipulation in a competitive equilibrium paradigm, modified to deal with manipulation. Specifically, a large trader is trading both derivatives and assets, and effectively hides her trades behind the competitive market clearing mechanism. Unlike the strategic game paradigm, a volume-weighted average pricing (VWAP) index both introduces basis risk and encourages manipulation because of the additional randomness in volume weight and the greater price impact enjoyed by the large trader. In contrast, an equal-weighted average pricing (EWAP) index both preserves market completeness and discourages manipulation. The third essay, "A Model of Influencer Economy", studies an influencer economy in which brand owners and sellers depend on influencers to attract consumers (who cares about influencer affinity as well as product quality), while competing in both influencer and product markets. As technologies governing marketing outreach improve, the equilibrium features non-monotonicities in influencer market concentration, payoffs, and distributional inequality. Influencer heterogeneity and horizontal product differentiation are substitutes; small style differences complement vertical product differentiation while large differences substitute. Moreover, assortative matching between sellers and influencers occurs under endogenous influence, with the maximum horizontal differentiation principle recovered in the limit of costless style selection. Meanwhile, the sellers' bargaining power counteracts the influencers' tendency to over-invest in influence power and they jointly determine the direction and magnitude of the sub-optimal acquisition. Finally, regulations for balanced seller-influencer matching can encourage seller competition under single dimensional seller-influencer heterogeneity. But uni-directional exclusivity contracts are welfare-improving for sufficiently differentiated products and uncongested influencers' markets.