My research focusses on mechanisms design in economics, mainly related to matching procedures, bankruptcy rules and cost-sharing (and surplus-sharing) problems.
Abstract: Despite the popularity of auction theoretical thinking, it appears that no one has presented an elementary equilibrium analysis of the complete information first-price sealed-bid auction mechanism when the bidding space has a finite grid. This paper aims to remedy that omission. We show that there always exists a "high price equilibrium" which can be considered "the intuitive solution" (an agent with the highest valuation wins the auction bidding at the second-highest valuation). Although there might be other "low price equilibria", we also show that when there are two bidders "the intuitive solution" is the unique limiting equilibrium when the grid size goes to zero and ties are randomly broken.
Abstract: We consider rent seeking contests among at least two agents who might value the prize differently. We capture a wide range of institutional aspects of contests by analyzing a class of contest success functions fulfilling several properties. The main properties are anonymity and a condition on the elasticity of a rent seeker's win probability with respect to her effort. We show the existence of a mixed-strategy equilibrium and establish equilibrium payoffs. In this equilibrium complete rent dissipation holds. Our results imply a partial robustness result for the all-pay auction.
Notes: This paper circulated under the title "All-Pay Auction Equilibria in Contests".
Abstract: This paper provides an analysis of the Minimal Overlap Rule, a solution for bankruptcy problems introduced by O'Neill (1982). We point out that this rule can be understood as a composition of the proposal made by Ibn Ezra and the recommendation given by the Constrained Equal Loss Rule.
By following an interpretation of bankruptcy problems in terms of TU games, we show that the Minimal Overlap Rule is the unique solution for bankruptcy games that satisfies Anonymity and Core Transition Responsiveness. We also provide a characterization based on a (restricted) additivity property.
Abstract: We introduce the serial contest by building on the desirable properties of two prominent contest games. This family of contest games relies both on relative efforts (as Tullock’s proposal) and on absolute effort differences (as difference-form contests). An additional desirable feature is that the serial contest is homogeneous of degree zero in contestants’ efforts. The family is characterized by a parameter representing how sensitive the outcome is to contestants’ efforts. It encompasses as polar cases the (fair) lottery and the (deterministic) all-pay auction. Equilibria have a close relationship to those of the (deterministic) all-pay auction and important properties of the latter hold for the serial contest, too.
Abstract: This paper studies a class of NTU coalition formation games in which every player’s payoff depends only on the members of her coalition. We identify four natural conditions on individuals’ preferences and show that, under each condition, stable (core) allocations exists.
Abstract: This paper explores an old solution for bankruptcy problems, described by Ibn Ezra in the XII century. Particularly, we introduce a new way of extending the Ibn Ezra's proposal, the Generalized Ibn Ezra solution, by imposing that the general distribution principle from which it is inspired remains fixed. In this context, we follow the interpretation of bankruptcy problems in terms of TU games given in O'Neill (1982), and propose the analysis of the Transition Game associated to bankruptcy problems to provide a characterization for the Generalized Ibn Ezra solution.
Abstract: This paper models a contractual process by a sequential mechanism, which mimics matching procedures for many-to-one real-life matching problems. In this framework, we provide a family of mechanisms implementing the student-optimal matching in Subgame Perfect Equilibrium (SPE).
Abstract: This paper explores the existence of stable research teams, when the preferences of each agent depend on the set of researchers who are collaborating. We introduce a property over researchers’ preferences, called top responsiveness, guaranteeing the existence of stable research teams configurations. We also provide a stable mechanism, induced by the so-called top covering algorithm, which is strategy-proof when researchers preferences satisfy top responsiveness. Furthermore, we find that, in this framework, the top covering mechanism is the only strategy-proof mechanism that always selects stable allocations.
Abstract: This paper proposes a cost-sharing rule for the specific case in which the agents’ demands are heterogeneous. We first examine, from a normative point of view, a cost-sharing rule introduced as the axial serial rule (AXS) by Sprumont. We introduce a property, that we call Cost-Based Equal Treatment (CBET), and we demonstrate that the unique rule verifying the Serial Principle (SP) and this property is the AXS rule. We then deal with the analysis of the agents’ strategic behavior when they are allowed to select their own production levels, in which case the total cost is then split, in accordance with the AXS rule. We show that there is only one Nash equilibrium, which is obtained from an iterative elimination of dominated strategies.
Abstract: This paper analyzes simple mechanisms implementing (subselections of) the core correspondence of matching markets. We provide a sequential mechanism which mimics a matching procedure for many-to-one real life matching markets. We show that only core allocations should be attained when agents act strategically when faced with this mechanism. We also provide a second mechanism to implement the core correspondence in Subgame Perfect Equilibrium.
Abstract: This paper studies simple hiring procedures for job markets. We show that when agents act strategically only individually rational outcomes should be expected. Moreover, if agents can form unions, thereby gaining the possibility to commit on the decisions to be chosen, only stable allocations are implemented.
Abstract: This paper analyzes the problem of designing mechanisms to implement efficient solutions in economies with externalities. We provide two simple mechanisms implementing the Pigouvian Social Choice Correspondence in environments in which coalitions can or cannot be formed.
Abstract: We implement the stable correspondence of a job matching market in Subgame Perfect Equilibrium. We use a simple sequential mechanism in which firms propose a salary to each worker (first stage) and, then, each worker accepts at most one proposal (second stage). Moreover, if agents' preferences are additive, this mechanism implements in Subgame Perfect Equilibrium the firms' optimal corre- spondence when firms use undominated strategies. Finally, we construct another simple sequential mechanism where the order of decisions is permuted and which implements the workers' optimal correspondence when agents' preferences are additive.
Abstract: This paper proposes a new axiomatic justification for the employ of the Aumann-Shapley value for non-atomic games in the context of cost sharing.
Abstract: This paper analyzes the possibility of implementing stable outcomes for marriage markets. Our first result shows a contradiction between the use of stable mechanisms and the hypothesis of agents' behavior considered in the Nash equilibrium concept. We analyze the possibility of implementing two sets of stable allocations, by employing two types of mechanisms. The first mechanism is a "now-or-never" choice process that permits us to implement in undominated Nash equilibria the set of all the stable allocations. The second choice process is the classic algorithm in matching theory, the Gale–Shapley mechanism. A reversal property is observed in such a mechanism when agents act strategically. The use of a mechanism which selects the best solution for one side of the market in the absence of strategic behavior yields the best stable solution for the agents on the other side under dominance solvability.
Abstract: Two stability concepts for one-sided matching markets are analyzed: Gale-Shapley stability and ξ-stability. The first one applies best to markets where no status quo allocation is considered, whereas the second one is a solution to be used when property rights are allowed. A common problem of existence is shared by both solution concepts. Hence, we study economic environments where this problem does not exist, and present a family of agents’ preferences for which existence is guaranteed for both Gale-Shapley stable and ξ-stable outcomes.
Abstract: This paper explores the possibility of designing strategy-proof mechanisms yielding satisfactory solutions to the marriage and to the college admissions problem. Our first result is negative. We prove that no strategy-proof mechanism can always choose marriages that are individually rational and Pareto efficient. This strengthens a result by Roth (1982) showing that strategy-proof mechanisms cannot always select stable marriages. The result also applies, a fortiori, to college admissions. Since finding difficulties with strategy-proofness is quite an expected result, we then address a second question which is classical within the incentives literature. Are there restrictions on the preferences of agents under which strategy-proof and stable mechanisms do exist? We identify a nontrivial restriction on the domain of preferences, to be called top dominance, under which there exist strategy-proof and stable mechanisms for both types of matching problems. The mechanisms turn out to be exactly those that derive from the most classical algorithms in the literature; namely, the women's optimal, the men's optimal and the student's optimal. Finally, top dominance is shown to be essentially necessary, as well as sufficient, for the existence of strategy-proof stable matching mechanisms.
Abstract: This paper studies, from a theoretical point of view, the assignament of workers to different departments within a firm: our first contribution to this analysis pertains to a non-traditional modelling of workers' preferences, as they can rank different tasks and can even reject some potential jobs. In this context we characterice a set of conditions that insure the existence of stable allocations, and illustrate that concerning assignments encompasses both the existence of a conflic process among groups and an agreement within members of each group. Finally, we study incentive problems in this type of models: In general agents will not report their true types. Hence, we study truth-telling mechanisms, and we obtain some positive results.
Abstract: This work proposes a novel way to finance the public services in order to reach three objectives:
(1) a (full) public access to the service;
(2) a diversity of the service to be supplied; and
(3) to provide the service at the lowest cost.
The analyzed system, inspired in a proposal by Ibn Ezra, is studied by a (non-cooperative) game theoretical point of view.
Abstract: This paper proposes an strategic analysis of mechanisms assigning workers to firms. We point out that the emply of these mechanisms guarantee the market' stability.
We study two types of mechanisms. The first one is related to the case in which agents in a side of the market have an active role by searching a job, whereas the other side is mostly passive because its agents just receive offers. The second type of mechanisms is very related to a centralized process in which both workers and firms propose their offers and an employment office decides whcih contracts should be signed.
Abstract: We propose a new procurement procedure which allocates shares of the total amount to be procured depending on the bids of suppliers. Among the properties of the mechanism are:
(i) Bidders have an incentive to participate in the procurement procedure, as equilibrium payoffs are strictly positive.
(ii) The mechanism allows to vary the extent to which affirmative action objectives, like promoting local industries, are pursued.
(iii) Surprisingly, even accomplishing affirmative action goals, procurement expenditures might be lower than under a classical auction format.
Abstract: This paper proposes the notion of ε-stability to conciliate Pareto efficiency and fairness. We propose the employ of a centralized procedure, the Exchanging Places Mechanism. It endows students according with the Gale and Shapley students optimal stable matching as tentative allocation and allows the student to trade their positions. We show that the final allocation is ε-stable, i.e. efficient, fair and immune to any justifiable objection that students can formulate.
Abstract: As it is known, there is no rule satisfying Additivity in the complete domain of bankruptcy problems. This paper proposes a notion of partial Additivity in this context, to be called µ-additivity. We find that µ-additivity, together with two quite compelling axioms, anonymity and continuity, identify the Minimal Overlap rule, introduced by Neill (1982).
Abstract: This paper proposes a way to allocate students to schools such that conciliates Pareto efficiency and stability. Taking as a starting point the recent reform proposed by the Boston School Committee, we propose a marginal modification to reach our objective redefine how students are prioritize. Our proposal is to allow schools to prioritize only a small set of students an then use a common priority order for the rest. Under this condition we propose a score based priority ranking that makes the output of the new Boston Mechanism Pareto efficient and stable.
Abstract: This paper proposes a reform for school allocation procedures in order to help integration policies reach their objective. For this purpose, we suggest the use of a natural two-step mechanism. The (stable) first step is introduced as an adaptation of the deferred-acceptance algorithm designed by Gale and Shapley (1962), when students are divided into two groups. The (efficient) second step captures the idea of exchanging places inherent to Gale's Top Trading Cycle. This latter step could be useful for Municipal School Boards when implementing some integration policies.
Abstract: Despite the popularity of auction theoretical thinking, it appears that no one has presented an elementary equilibrium analysis of the complete information first-price sealed-bid auction mechanism when the bidding space has a finite grid. This paper aims to remedy that omission. We show that there always exists a "high price equilibrium'' which can be considered "the intuitive solution'' (an agent with the highest valuation wins the auction bidding at the second-highest valuation). Although there might be other "low price equilibria'', we also show that when there are two bidders "the intuitive solution'' is the unique limiting equilibrium when the grid size goes to zero and ties are randomly broken.
