Strategic Priority-Based Course Allocation

We 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

Coalition Formation Problems With Externalities

We 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

Notes on Marriage Markets With Weak Externalities

We 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

Incentives and Implementation in Allocation Problems with Externalities

We 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

Centralized Course Allocation

We 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

We 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

Notes on marriage markets with weak externalities

We 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 nonempty. In addition, we show that, if we allow agents to block matchings without changing their mate, the results do not longer hold