“School Choice: Nash Implementation of Stable Matchings through Rank-Priority Mechanisms” (2021) Journal of Mathematical Economics, Article 102496 (joint with Paula Jaramillo and Flip Klijn).
We consider school choice problems (Abdulkadiroğlu and Sönmez, 2003) where students are assigned to public schools through a centralized assignment mechanism. We study the family of so-called rank-priority mechanisms, each of which is induced by an order of rank-priority pairs. Following the corresponding order of pairs, at each step, a rank-priority mechanism considers a rank-priority pair and matches an available student to an unfilled school if the student and the school rank and prioritize each other in accordance with the rank-priority pair. The Boston or immediate acceptance mechanism is a particular rank-priority mechanism. Our first main result is a characterization of the subfamily of rank-priority mechanisms that Nash implement the set of stable matchings (Theorem 1). Our second main result is a strong impossibility result: under incomplete information, no rank-priority mechanism implements the set of stable matchings (Theorem 2).
“The Core of Roommate Problems: Size and Rank-fairness within Matched Pairs” (2019) International Journal of Game Theory, 48, 157–179 (joint with Paula Jaramillo and Flip Klijn).
This paper deals with roommate problems (Gale and Shapley, Am Math Mon 69(1):9–15, 1962) that are solvable, i.e., have a non-empty core (set of stable matchings). We study rank-fairness within pairs of stable matchings and the size of the core by means of maximal and average rank gaps. We provide upper bounds in terms of maximal and average disagreements in the agents’ rankings. Finally, we show that most of our bounds are tight.
“Corrigendum to “Characterizations of Pareto-efficient, fair, and strategy-proof allocation rules in queueing problems” [Games Econ. Behav. 68 (1) (2010) 220–232]” (2019) Games and Economic Behavior, 118, 491 –492 (joint with Eve Ramaekers).
“Allocation Rules for Networks” (2014) Social Choice and Welfare, 43(4), 877–892 (joint with Rahmi Ilkiliç)
When allocating a resource, geographical, and infrastructural constraints have to be taken into account. We study the problem of distributing a resource through a network from sources endowed with the resource to citizens with claims. A link between a source and a citizen depicts the possibility of a transfer from the source to the citizen. Given the endowments at each source, the claims of citizens, and the network, the question is how to allocate the available resources among the citizens. We consider a simple allocation problem that is free of network constraints, where the total amount can be freely distributed. The simple allocation problem is a claims problem where the total amount of claims is greater than what is available. We focus on resource monotonic and anonymous bilateral principles satisfying a regularity condition and extend these principles to allocation rules on networks. We require the extension to preserve the essence of the bilateral principle for each pair of citizens in the network. We call this condition pairwise robustness with respect to the bilateral principle. We provide an algorithm and show that each bilateral principle has a unique extension which is pairwise robust (Theorem 1). Next, we consider a Rawlsian criteria of distributive justice and show that there is a unique “Rawls fair” rule that equals the extension given by the algorithm (Theorem 2). Pairwise robustness and Rawlsian fairness are two sides of the same coin, the former being a pairwise and the latter a global requirement on the allocation given by a rule. We also show as a corollary that any parametric principle can be extended to an allocation rule (Corollary 1). Finally, we give applications of the algorithm for the egalitarian, the proportional, and the contested garment bilateral principles (Example 1).
“Asymmetrically Fair Rules for an Indivisible Good Problem with a Budget Constraint” (2014) Social Choice and Welfare, 43(3), 603–633 (joint with Paula Jaramillo and Flip Klijn).
We study a particular restitution problem where there is an indivisible good (land or property) over which two agents have rights: the dispossessed agent and the owner. A third party, possibly the government, seeks to resolve the situation by assigning rights to one and compensate the other. There is also a maximum amount of money available for the compensation. We characterize a family of asymmetrically fair rules that are immune to strategic behavior, guarantee minimal welfare levels for the agents, and satisfy the budget constraint.
“Exhaustiveness of Truncation and Dropping Strategies in Many-to-Many Matching Markets” (2014) Social Choice and Welfare, 42(4), 793–811 (joint with Paula Jaramillo and Flip Klijn).
We consider two-sided many-to-many matching markets in which each worker may work for multiple firms and each firm may hire multiple workers. We study individual and group manipulations in centralized markets that employ (pairwise) stable mechanisms and that require participants to submit rank order lists of agents on the other side of the market. We are interested in simple preference manipulations that have been reported and studied in empirical and theoretical work: truncation strategies, which are the lists obtained by removing a tail of least preferred partners from a preference list, and the more general dropping strategies, which are the lists obtained by only removing partners from a preference list (i.e., no reshuffling). We study when truncation/dropping strategies are exhaustive for a group of agents on the same side of the market, i.e., when each match resulting from preference manipulations can be replicated or improved upon by some truncation/dropping strategies. We prove that for each stable mechanism, dropping strategies are exhaustive for each group of agents on the same side of the market (Theorem 1), i.e., independently of the quotas. Then, we show that for each stable mechanism, truncation strategies are exhaustive for each agent with quota 1 (Theorem 2). Finally, we show that this result cannot be extended neither to individual manipulations when the agent’s quota is larger than 1 (even when all other agents’ quotas equal 1—Example 1), nor to group manipulations (even when all quotas equal 1—Example 2).
7. "Equilibria under Deferred Acceptance: Dropping Strategies, Filled Positions, and Welfare” (2013) Games and Economic Behavior, 82(1), 693–701 (joint with Paula Jaramillo and Flip Klijn).
We study many-to-one matching markets where hospitals have responsive preferences over students. We study the game induced by the student-optimal stable matching mechanism. We assume that students play their weakly dominant strategy of truth-telling. Roth and Sotomayor (1990) showed that equilibrium outcomes can be unstable. We prove that any stable matching is obtained in some equilibrium. We also show that the exhaustive class of dropping strategies does not necessarily generate the full set of equilibrium outcomes. Finally, we find that the ‘rural hospital theorem’ cannot be extended to the set of equilibrium outcomes and that welfare levels are in general unrelated to the set of stable matchings. Two important consequences are that, contrary to one-to-one matching markets, (a) filled positions depend on the equilibrium that is reached and (b) welfare levels are not bounded by the optimal stable matchings (with respect to the true preferences).
8. “Characterizations of Pareto-efficient, fair, and strategy-proof allocation rules in queueing problems” (2010) Games and Economic Behavior, 68 (1), 220–232 (joint with Eve Ramaekers).
A set of agents with possibly different waiting costs have to receive the same service one after the other. Efficiency requires to maximize total welfare. Fairness requires to treat equal agents equally. One must form a queue, set up monetary transfers to compensate agents having to wait, and not a priori arbitrarily exclude agents from positions. As one may not know agents' waiting costs, they may have no incentive to reveal them. We identify the only rule satisfying Pareto-efficiency, equal treatment of equals in welfare or symmetry, and strategy-proofness. It satisfies stronger axioms, as no-envy and anonymity. Further, its desirability extends to related problems. To obtain these results, we prove that a rule, single-valued or not, satisfies queue-efficiency and strategy-proofness if and only if it always selects efficient queues and sets transfers à la Groves [Groves, T., 1973. Incentives in teams. Econometrica 41, 617–631]. This holds in other problems, provided the domain of quasi-linear preferences is rich enough.
1. “School Choice: Nash Implementation of Stable Matchings through Rank-Priority Mechanisms” (2017) Barcelona GSE Working Papers Series no 957 (joint with Paula Jaramillo and Flip Klijn).
2. “Rank Gaps and the Size of the Core for Roommate Problems” (2017) Barcelona GSE Working Papers Series no 956 (joint with Paula Jaramillo and Flip Klijn).
3. “Equilibria under Deferred Acceptance: Dropping Strategies, Filled Positions, and Welfare” (2013) Barcelona GSE Working Papers Series no 686, Universidad del Rosario, Facultad de Economía, Documento Trabajo # 136, Universidad de los Andes,Documentos CEDE # 23 (joint with Paula Jaramillo and Flip Klijn).
4. “Exhaustiveness of Truncation and Dropping Strategies in Many-to-Many Matching Markets” (2012) Barcelona GSE Working Papers Series no 632, Universidad del Rosario, Facultad de Economía, Documento Trabajo # 123, Universidad de los Andes, Documentos CEDE # 36 (joint with Paula Jaramillo and Flip Klijn).
5. “Asymmetrically Fair Rules for an Indivisible Good Problem with a Budget Constraint” (2012) Barcelona GSE Working Papers Series no 610, Universidad del Rosario, Facultad de Economía, Documento Trabajo # 119, Universidad de los Andes, Documentos CEDE # 05 (joint with Paula Jaramillo and Flip Klijn).
6. “Allocation Rules for Networks” (2012) Universidad del Rosario, Facultad de Economía, Documento Trabajo # 118 (joint with Rahmi Ilkiliç).
7. “Characterizations of Pareto-efficient, Fair, and Strategy-proof Allocation Rules in Queueing Problems” (2008) CORE Discussion Papers 2008-084, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE) (joint with Eve Ramaekers).
8. “An Impossibility in Sequencing Problems” (2008) METEOR Research Memorandum, 40 (joint with Eve Ramaekers).
9. “Consistency and the Sequential Equal Contributions Rule for Airport Problems” (2008) METEOR Research Memorandum, 39 (joint with Youngsub Chun and Chun-Hsien Yeh).