2,557 research outputs found
Private Matchings and Allocations
We consider a private variant of the classical allocation problem: given k
goods and n agents with individual, private valuation functions over bundles of
goods, how can we partition the goods amongst the agents to maximize social
welfare? An important special case is when each agent desires at most one good,
and specifies her (private) value for each good: in this case, the problem is
exactly the maximum-weight matching problem in a bipartite graph.
Private matching and allocation problems have not been considered in the
differential privacy literature, and for good reason: they are plainly
impossible to solve under differential privacy. Informally, the allocation must
match agents to their preferred goods in order to maximize social welfare, but
this preference is exactly what agents wish to hide. Therefore, we consider the
problem under the relaxed constraint of joint differential privacy: for any
agent i, no coalition of agents excluding i should be able to learn about the
valuation function of agent i. In this setting, the full allocation is no
longer published---instead, each agent is told what good to get. We first show
that with a small number of identical copies of each good, it is possible to
efficiently and accurately solve the maximum weight matching problem while
guaranteeing joint differential privacy. We then consider the more general
allocation problem, when bidder valuations satisfy the gross substitutes
condition. Finally, we prove that the allocation problem cannot be solved to
non-trivial accuracy under joint differential privacy without requiring
multiple copies of each type of good.Comment: Journal version published in SIAM Journal on Computation; an extended
abstract appeared in STOC 201
Approximately Stable, School Optimal, and Student-Truthful Many-to-One Matchings (via Differential Privacy)
We present a mechanism for computing asymptotically stable school optimal
matchings, while guaranteeing that it is an asymptotic dominant strategy for
every student to report their true preferences to the mechanism. Our main tool
in this endeavor is differential privacy: we give an algorithm that coordinates
a stable matching using differentially private signals, which lead to our
truthfulness guarantee. This is the first setting in which it is known how to
achieve nontrivial truthfulness guarantees for students when computing school
optimal matchings, assuming worst- case preferences (for schools and students)
in large markets
Competition and Resource Sensitivity in Marriage and Roommate Markets
We consider one-to-one matching markets in which agents can either be matched as pairs or remain single. In these so-called roommate markets agents are consumers and resources at the same time. We investigate two new properties that capture the effect newcomers have on incumbent agents. Competition sensitivity focuses on newcomers as additional consumers and requires that some incumbents will suffer if competition is caused by newcomers. Resource sensitivity focuses on newcomers as additional resources and requires that this is beneficial for some incumbents. For solvable roommate markets, we provide the first characterizations of the core using either competition or resource sensitivity. On the domain of all roommate markets, we obtain two associated impossibility results.core; matching; competition sensitivity; resource sensitivity; roommate market
Competition and Resource Sensitivity in Marriage and Roommate Markets
We consider one-to-one matching markets in which agents can either be matched as pairs or remain single. In these so-called roommate markets agents are consumers and resources at the same time. We investigate two new properties that capture the effect a newcomer has on incumbent agents. Competition sensitivity focuses on the newcomer as additional consumer and requires that some incumbents will suffer if competition is caused by a newcomer. Resource sensitivity focuses on the newcomer as additional resource and requires that this is beneficial for some incumbents. For solvable roommate markets, we provide the first characterizations of the core using either competition or resource sensitivity. On the domain of all roommate markets, we obtain two associated impossibility results.Core, Matching, Competition Sensitivity, Resource Sensitivity, Roommate Market.
Competition and Resource Sensitivity in Marriage and Roommate Markets
We consider one-to-one matching markets in which agents can either be matched as pairs or remain single. In these so-called roommate markets agents are consumers and resources at the same time. We investigate two new properties that capture the effect a newcomer has on incumbent agents. Competition sensitivity focuses on the newcomer as additional consumer and requires that some incumbents will suffer if competition is caused by a newcomer. Resource sensitivity focuses on the newcomer as additional resource and requires that this is beneficial for some incumbents. For solvable roommate markets, we provide the first characterizations of the core using either competition or resource sensitivity. On the class of all roommate markets, we obtain two associated impossibility results.microeconomics ;
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