Amrit Daswaney will present the General Exam "Fair and Efficient Allocation of Indivisible Goods via Pseudomarkets with Price Floors" on May 2nd, 10 am - 12 pm. Friend Center 005. Committee: Mark Braverman (adviser), Matt Weinberg, Fedor Sandomirskiy. Abstract: The combinatorial assignment problem involves allocating m indivisible goods to n agents without any monetary transfers such that the resulting allocation is Pareto efficient and each agent is (approximately) envy-free. This problem models many practical settings of interest: from assigning courses to students to allocating truckloads of food to food banks. A classical route, pioneered by Varian (1974) and extended by Hylland and Zeckhauser (1979), is to search for a Competitive Equilibrium from Equal Incomes (CEEI): endow every agent with one unit of artificial currency and find prices so that when each agent buys their favourite affordable bundle, the market clears (i.e., supply equals demand for all goods). With indivisible goods, however, a CEEI need not exist: in a two-agent, one-good instance any price makes either both agents or neither demand the good. Budish (2011) restores existence by introducing an arbitrarily small budget inequality between agents. The rationale behind introducing this budget inequality is to use these small differences to break ties between otherwise identical agents. However, our first result shows they can legitimize highly unequal outcomes, allowing agents with negligibly higher budgets to potentially leverage this advantage across multiple goods. To mitigate this, we introduce price floors and define a CEEI-with-price-floors mechanism. Our second result proves that this concept is equivalent to a discrete analogue of Varian (1974)'s coalition fairness: in the replica economy, no coalition can seize the bundle of another coalition with the same total endowment and make all of its members better off. The equivalence echoes the Debreu–Scarf core-equivalence theorem (1963). Crucially, whenever a CEEI-with-floors can be proved to exist for a structured domain (e.g., additive values, bounded numbers of agents), an EFX allocation exists for that very domain, providing a concrete pathway toward resolving this long standing open problem in fair division. Our third result establishes the existence of CEEI-with-floors when (i) n = 2 agents or (ii) n agents have identical valuations. If time permits, we will also discuss alternative combinatorial and randomized techniques that have been applied to the problem.