We consider a platform in a two-sided market with unit-supply sellers and unit-demand buyers. Each buyer can transact with a subset of sellers it knows off platform and another seller that the platform recommends. Given the choice of sellers, transactions and prices form a competitive equilibrium. The platform selects one seller for each buyer, and charges a fixed percentage of prices to all transactions that it recommends. The platform seeks to maximize total revenue. We show that the platform's problem is NP-hard, even when each buyer knows at most two buyers off platform. Finally, when each buyer values all sellers equally and knows only one buyer off platform, we provide a polynomial time algorithm that optimally solves the problem.

We model the role of an online platform disrupting a market with unit-demand buyers and unit-supply sellers. Each seller can transact with a subset of the buyers whom she already knows, as well as with any additional buyers to whom she is introduced by the platform. Given these constraints on trade, prices and transactions are induced by a competitive equilibrium. The platform's revenue is proportional to the total price of all trades between platform-introduced buyers and sellers.

We introduce the theoretical study of a Platform Equilibrium in a market with unit-demand buyers and unit-supply sellers. Each seller can join a platform and transact with any buyer or remain off-platform and transact with a subset of buyers whom she knows. Given the constraints on trade, prices form a competitive equilibrium and clears the market. The platform charges a transaction fee to all on-platform sellers, in the form of a fraction of on-platform sellers' price. The platform chooses the fraction to maximize revenue. A Platform Equilibrium is a Nash equilibrium of the game where each seller decides whether or not to join the platform, balancing the effect of a larger pool of buyers to trade with, against the imposition of a transaction fee.

We study the behavior of an economic platform (e.g., Amazon, Uber Eats, Instacart) under shocks, such as COVID-19 lockdowns, and the effect of different regulation considerations. To this end, we develop a multi-agent simulation environment of a platform economy in a multi-period setting where shocks may occur and disrupt the economy. Buyers and sellers are heterogeneous and modeled as economically-motivated agents, choosing whether or not to pay fees to access the platform. We use deep reinforcement learning to model the fee-setting and matching behavior of the platform, and consider two major types of regulation frameworks: (1) taxation policies and (2) platform fee restrictions. We offer a number of simulated experiments that cover different market settings and shed light on regulatory tradeoffs. Our results show that while many interventions are ineffective with a sophisticated platform actor, we identify a particular kind of regulation—fixing fees to the optimal, no-shock fees while still allowing a platform to choose how to match buyers and sellers—as holding promise for promoting the efficiency and resilience of the economic system.