1,720,962 research outputs found
Incentives and Implementation in Allocation Problems with Externalities
Full text linkWe study the implementation of social choice rules in environments with externalities. We prove the impossibility of implementing efficient and α-individually rational rules in dominant strategies. We prove that the α-core is implementable in Nash equilibrium under mild restrictions and discuss the maximality and the minimality of our results. We extend our analysis to weakly efficient rules
Strategic Priority-Based Course Allocation
Full text linkWe present the conditional acceptance mechanism for the course allocation problem. This mechanism combines features of the immediate acceptance and the student optimal stable mechanisms. It implements the set of stable allocations in both Nash and undominated Nash equilibria under substitutable preferences and priorities. We model the post-allocation adjustment mechanism using a repeated version of the mechanism. This repeated mechanism reduces the wastefulness of out-of-equilibrium play and implements the set of stable allocation in Subgame Perfect Nash equilibrium under slot-specific preferences and priorities. Both mechanisms are easily implementable, reduce the complexity of eliciting students' preferences, and mimic the features of the mechanisms currently in use
Games with capacity manipulation: incentives and Nash equilibria
Full text linkArtículo de publicación ISI.Studying the interactions between preference and capacity manipulation
in matching markets, we prove that acyclicity is a necessary and sufficient condition
that guarantees the stability of aNash equilibrium and the strategy-proofness of truthful
capacity revelation under the hospital-optimal and intern-optimal stable rules.We then
introduce generalized games of manipulation in which hospitals move first and state
their capacities, and interns are subsequently assigned to hospitals using a sequential
mechanism. In this setting, we first consider stable revelation mechanisms and introduce
conditions guaranteeing the stability of the outcome. Next, we prove that every
stable non-revelation mechanism leads to unstable allocations, unless restrictions on
the preferences of the agents are introduce
Acyclicity and singleton cores in matching markets
Full text linkArtículo de publicación ISI.The absence of simultaneous cycles is a sufficient condition for the existence of singleton cores. Acyclicity
in the preferences of either side of the market is a minimal condition that guarantees the existence of
singleton core
Notes on Marriage Markets With Weak Externalities
Full text linkWe consider marriage markets with externalities. We focus on weak externalities, that is, markets in which each agent is primarily concerned about her partner. We formalize and prove the claim that weak externalities are not so significant in the marriage market: in this case the ω-core and the α-core coincide and are both non-empty. In addition, we show that, if we allow agents to block matchings without changing their mate, the results do not longer hold
Centralized Course Allocation
Full text linkWe present the renegotiable acceptance mechanism in the context of the multi-unit assignment problem. This mechanism combines features of the immediate and deferred acceptance mechanisms and implements the set of stable matchings in both Nash and undominated Nash equilibria under substitutable priorities. In addition, we prove that under slot-specific priorities, the immediate acceptance mechanism also implements the set of stable matchings in Nash and undominated Nash equilibria. Finally, we present modifications of both mechanisms and show that we can dramatically reduce the complexity of the message space when preferences are responsive
Incentives and Implementation in Marriage Markets with Externalities
Full text linkWe study the implementability of stable correspondences in marriage markets with externalities. We prove that, contrary to what happens in markets without externalities, no stable revelation mechanism makes a dominant strategy for the agents on one side of the market to reveal their preferences. However, the stable correspondence is implementable in Nash equilibrium.We study assignment problems with externalities where agents have expectations about the reactions of other agents to group deviations. We present notions of core consistent with such expectations and identify the largest and smallest cores. We restrict the domain of preferences to study the relationship between essentially single-valued cores and the existence of strategy-proof, individually rational, and efficient mechanisms
Simple Strategies in Multi-unit Assignment Problems
Full text linkThis paper examines strategic behavior in multi-unit assignment problems, employing simple manipulation strategies. Assuming responsive preferences and priorities, we demonstrate that dropping strategies are exhaustive in the immediate acceptance mechanism, while truncation strategies fall short. This finding clarifies the trade-offs among stability, simplicity, and manipulability in assignment mechanisms, with implications for real-world applications, such as course allocation
Coalition Formation Problems With Externalities
Full text linkWe study coalition formation problems with general externalities. We prove that if expectations are not prudent a stable coalitions structure can fail to exist. Under prudent expectations a stable coalition structure exists if the set of admissible coalitions is single-lapping. This assumption also guarantees the existence of a stable and efficient coalition structure. However, under this assumption, the stable set is not a singleton, and no stable and efficient strategy-proof revelation mechanism exists, differently from the case in which agents care only about the coalition they belong to. However, the stable correspondence is implementable in Nash equilibrium
Two-sided strategy-proofness in many-to-many matching markets
Full text linkWe study the existence of group strategy-proof stable rules in many-to-many matching markets under responsiveness of agents’ preferences. We show that when firms have acyclical preferences over workers the set of stable matchings is a singleton, and the worker-optimal stable mechanism is a stable and group strategy-proo frule for firms and workers. Furthermore, acyclicity is the minimal condition guaranteeing the existence of stable and strategy-proof mechanisms in many-to-many matching markets
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