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Register a new userStable Matching Mechanisms are Not Obviously Strategy-Proof
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Added by
Yannai A. Gonczarowski
Publication date
2015
fields
Informatics Engineering
and research's language is
English
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Many two-sided matching markets, from labor markets to school choice programs, use a clearinghouse based on the applicant-proposing deferred acceptance algorithm, which is well known to be strategy-proof for the applicants. Nonetheless, a growing amount of empirical evidence reveals that applicants misrepresent their preferences when this mechanism is used. This paper shows that no mechanism that implements a stable matching is obviously strategy-proof for any side of the market, a stronger incentive property than strategy-proofness that was introduced by Li (2017). A stable mechanism that is obviously strategy-proof for applicants is introduced for the case in which agents on the other side have acyclical preferences.
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Consider the problem of implementing a revenue-optimal, Bayesian Incentive Compatible auction when buyers values are drawn from distributions $times_i D_i$ on a particular instance $vec{v}$. Optimal single-dimensional mechanisms are local: in order to allocate the item correctly on a particular valuation profile $vec{v}$, only $tilde{O}(1)$ bits are needed from each player (specifically, their Myerson virtual value [Mye81]), rather than the entire distribution. We show that optimal multi-dimensional mechanisms are not local: in order to allocate the item correctly on a particular valuation profile $vec{v}$, one still needs to know (essentially) the entire distribution. Specifically, if the distributions have support-size $n$, then $Omega(n)$ bits are necessary from each bidder. We show that this phenomenon already occurs with just two bidders, even when one bidder is single-dimensional, and even when the other bidder is barely multi-dimensional. More specifically, the multi-dimensional bidder is inter-dimensional from the FedEx setting with just two days [FGKK16].
We study variants of the stable marriage and college admissions models in which the agents are allowed to express weak preferences over the set of agents on the other side of the market and the option of remaining unmatched. For the problems that we address, previous authors have presented polynomial-time algorithms for computing a Pareto-stable matching. In the case of college admissions, these algorithms require the preferences of the colleges over groups of students to satisfy a technical condition related to responsiveness. We design new polynomial-time Pareto-stable algorithms for stable marriage and college admissions that correspond to strategyproof mechanisms. For stable marriage, it is known that no Pareto-stable mechanism is strategyproof for all of the agents; our algorithm provides a mechanism that is strategyproof for the agents on one side of the market. For college admissions, it is known that no Pareto-stable mechanism can be strategyproof for the colleges; our algorithm provides a mechanism that is strategyproof for the students.
Facility location problems often permit facilities to be located at any position. But what if this is not the case in practice? What if facilities can only be located at particular locations like a highway exit or close to a bus stop? We consider here the impact of such constraints on the location of facilities on the performance of strategy proof mechanisms for locating facilities.We study four different performance objectives: the total distance agents must travel to their closest facility, the maximum distance any agent must travel to their closest facility, and the utilitarian and egalitarian welfare.We show that constraining facilities to a limited set of locations makes all four objectives harder to approximate in general.
An important feature of many real world facility location problems are capacity limits on the facilities. We show here how capacity constraints make it harder to design strategy proof mechanisms for facility location, but counter-intuitively can improve the guarantees on how well we can approximate the optimal solution.
In this paper, we investigate stable matching in structured networks. Consider case of matching in social networks where candidates are not fully connected. A candidate on one side of the market gets acquaintance with which one on the heterogeneous side depends on the structured network. We explore four well-used structures of networks and define the social circle by the distance between each candidate. When matching within social circle, we have equilibrium distinguishes from each other since each social networks topology differs. Equilibrium changes with the change on topology of each network and it always converges to the same stable outcome as complete information algorithm if there is no block to reach anyone in agents social circle.
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