My research is in market design, and combines ideas from theory and experiments in mechanism design, game theory, resource allocation, matching, and social choice.
Improving Transparency in School Admissions: Theory and experiment
with Rustamdjan Hakimov, 2022
Working paper: SSRN
This paper was previously circulated under the title "Transparency in Centralised Allocation: Theory and Experiment", first online March 2020.
(Mentioned here on Al Roth's Market Design blog)
Students participating in centralised admissions procedures do not typically have access to the information used to determine their matched school, such as other students’ preferences or school priorities. This can lead to doubts about whether their matched schools were computed correctly (the ‘Verifiability Problem’) or, at a deeper level, whether the promised admissions procedure was even used (the ‘Transparency Problem’). In a general centralised admissions model that spans many popular applications, we show how these problems can be addressed by providing appropriate feedback to students, even without disclosing sensitive private information like other students’ preferences or school priorities. In particular, we show that the Verifiability Problem can be solved by (1) publicly communicating the minimum scores required to be matched to a school (‘cutoffs’); or (2) using ‘predictable’ preference elicitation procedures that convey rich ‘experiential’ information. In our main result, we show that the Transparency Problem can be solved by using cutoffs and predictable procedures together. We find strong support for these solutions in a laboratory experiment, and show how they can be simply implemented for popular school admissions applications involving top trading cycles, and deferred and immediate acceptance.
We show that the first-price auction with no reserve price is the essentially unique mechanism that is non-bossy, individually rational, and efficient in equilibrium. The first-price auction with optimal reserve price is the essentially unique mechanism that is non-bossy, individually rational, and revenue maximizing.
In some labour markets, firms and workers are constrained to match with each other via intermediaries that mutually connect them. We study these markets via a model that synthesises tripartite matching with a `trading network' feature, by formulating a simple agency game in which intermediaries first make offers to connected firms and workers, and then firms and workers accept at most one of these offers. We identify restrictions on preferences of intermediaries that restore stability and side-optimality to equilibrium outcomes of the agency game. Our results shed light on the implicit restrictions imposed on clearinghouses in standard two-sided matching models. They also have implications for the design of decentralised recruitment markets.
We present a new characterisation of the agent-proposing deferred acceptance (APDA) rule (Gale and Shapley, 1962) in models of school choice. This is based on the notion of `influence', introduced in Raghavan (2018), that agents may have on each other's welfare under bossy allocation rules. When priorities are substitutable, we show that the APDA rule is the unique strategy-proof, bossy, and unanimous allocation rule to satisfy weak mutual-best and three influence-related properties: acyclicity, positivity, and displacement. This result contributes to the literature on strategy-proofness for agents of the APDA rule, and is also the first characterisation in terms of bossiness.
We consider a model in which projects are to be assigned to agents based on their preferences, and where projects have capacities, i.e., can each be assigned to a minimum and maximum number of agents. The extreme cases of our model are the social choice model (the same project is assigned to all agents) and the house allocation model (each project is assigned to at most one agent). We propose a natural extension of the dictatorial rule (social choice model) and the serial priority rule (house allocation model) to cover the intermediate cases, and call it the strong serial priority rule. We show that, when minimum and maximum capacities are common to all projects, a strong serial priority rule is characterised by the axioms of strategy-proofness, group-non-bossiness, limited influence, unanimity, and neutrality. Our result thus provides a bridge between the characterisations in Gibbard (1973), Satterthwaite (1975) and Svensson (1999). We also provide an independent characterisation of the serial priority rule in the house allocation model, and demonstrate some new relations between the axioms.
A house allocation rule should be flexible in its response to changes in agents’ preferences. We propose a specific notion of this flexibility. An agent is said to be swap-sovereign over a pair of houses at a profile of preferences if the rule assigns her one of the houses at that profile and assigns her the other house when she instead reports preferences that simply swap the positions of the two houses. A pair of agents is said to be mutually swap-sovereign over their assignments at a profile if the rule exchanges their assignments when they together report such ‘swap preferences’. An allocation rule is individually swap-flexible if any pair of houses has a swap-sovereign agent, and is mutually swap-flexible if any pair of houses has either a swap-sovereign agent or mutually swap-sovereign agents. We show for housing markets that the top-trading-cycles rule is the unique strategy-proof, individually rational and mutually swap-flexible rule. In house allocation problems, we show that queue-based priority rules are uniquely strategy-proof, individually swap-flexible and envy non-bossy. Varying the strength of non-bossiness, we characterise the important subclasses of sequential priority rules (additionally non-bossy) and serial priority rules (additionally pair-non-bossy and pair-sovereign).
We reinterpret the `bossiness' of a private-goods allocation rule (Satterthwaite and Sonneschein, 1981) as the ability of an agent to `influence' another's welfare with no change to her own welfare. We propose simple conditions on (1) which agents may have influence (`acyclicity' and `preservation'), and (2) the welfare consequences of influence (`positivity' and `oppositeness'). We apply these conditions to three well-known bossy rules: the `Vickrey rule' in single-object auctions (Vickrey, 1961) (acyclic, positive), the `doctor-optimal stable rule' in matching with contracts (Hatfield and Milgrom, 2005) (acyclic, positive, preserving) and `generalised absorbing top-trading cycles (GATTC) rules' in housing markets with indifferences in preferences (Aziz and Keijzer, 2011) (acyclic, opposite, preserving). Under mild restrictions, we show how the nature of influence under a strategy-proof rule determines whether or not it satisfies `weak group-strategy-proofness' (requires acyclicity and either positivity or preservation), `weak Maskin monotonicity' (acyclicity and positivity) and `Pareto-efficiency' (acyclicity and oppositeness). In addition, we propose an influence-related generalisation of the`efficiency-adjusted deferred acceptance mechanism' in school choice (Kesten, 2010), and characterise influence for strategy-proof GATTC rules in housing markets.
Despite encouraging signs, India’s retail market remains largely off-limits to large international retailers like Wal-Mart and Carrefour. Opposition to liberalising foreign direct investment in this sector raises concerns about employment losses, unfair competition resulting in large-scale exit of incumbent domestic retailers and infant industry arguments to protect the organised domestic retail sector that is at a nascent stage. Based on international evidence, we suggest that allowing entry by large international retailers into the Indian market may help tackle inflation especially in food prices. Moreover, technical know-how from foreign firms, such as warehousing technologies and distribution systems, can improve supply chain efficiency in India, in particular for agricultural produce. Better linkages between demand and supply have the potential to improve the price signals that farmers receive and also serve to enhance agricultural and other exports.