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Register a new userEffect of Strategic Grading and Early Offers in Matching Markets
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Added by
Hedyeh Beyhaghi
Publication date
2015
fields
Informatics Engineering
and research's language is
English
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Strategic suppression of grades, as well as early offers and contracts, are well-known phenomena in the matching process where graduating students apply to jobs or further education. In this paper, we consider a game theoretic model of these phenomena introduced by Ostrovsky and Schwarz, and study the loss in social welfare resulting from strategic behavior of the schools, employers, and students. We model grading of students as a game where schools suppress grades in order to improve their students placements. We also consider the quality loss due to unraveling of the matching market, the strategic behavior of students and employers in offering early contracts with the goal to improve the quality. Our goal is to evaluate if strategic grading or unraveling of the market (or a combination of the two) can cause significant welfare loss compared to the optimal assignment of students to jobs. To measure welfare of the assignment, we assume that welfare resulting from a job -- student pair is a separable and monotone function of student ability and the quality of the jobs. Assuming uniform student quality distribution, we show that the quality loss from the above strategic manipulation is bounded by at most a factor of 2, and give improved bounds for some special cases of welfare functions.
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We consider the stability of matchings when individuals strategically submit preference information to a publicly known algorithm. Most pure Nash equilibria of the ensuing game yield a matching that is unstable with respect to the individuals sincere preferences. We introduce a well-supported minimal dishonesty constraint, and obtain conditions under which every pure Nash equilibrium yields a matching that is stable with respect to the sincere preferences. The conditions on the matching algorithm are to be either fully-randomized, or monotonic and independent of non-spouses (INS), an IIA-like property. These conditions are significant because they support the use of algorithms other than the Gale-Shapley (man-optimal) algorithm for kidney exchange and other applications. We prove that the Gale-Shapley algorithm always yields the woman-optimal matching when individuals are minimally dishonest. However, we give a negative answer to one of Gusfield and Irvings open questions: there is no monotonic INS or fully-randomized stable matching algorithm that is certain to yield the egalitarian-optimal matching when individuals are strategic and minimally dishonest. Finally, we show that these results extend to the student placement problem, where women are polyandrous but must be honest but do not extend to the admissions problem, where women are both polyandrous and strategic.
The Arrow-Debreu extension of the classic Hylland-Zeckhauser scheme for a one-sided matching market -- called ADHZ in this paper -- has natural applications but has instances which do not admit equilibria. By introducing approximation, we define the $epsilon$-approximate ADHZ model, and we give the following results. * Existence of equilibrium under linear utility functions. We prove that the equilibrium satisfies Pareto optimality, approximate envy-freeness, and approximate weak core stability. * A combinatorial polynomial-time algorithm for an $epsilon$-approximate ADHZ equilibrium for the case of dichotomous, and more generally bi-valued, utilities. * An instance of ADHZ, with dichotomous utilities and a strongly connected demand graph, which does not admit an equilibrium. Since computing an equilibrium for HZ is likely to be highly intractable and because of the difficulty of extending HZ to more general utility functions, Hosseini and Vazirani proposed (a rich collection of) Nash-bargaining-based matching market models. For the dichotomous-utilities case of their model linear Arrow-Debreu Nash bargaining one-sided matching market (1LAD), we give a combinatorial, strongly polynomial-time algorithm and show that it admits a rational convex program.
Two-sided matching platforms provide users with menus of match recommendations. To maximize the number of realized matches between the two sides (referred here as customers and suppliers), the platform must balance the inherent tension between recommending customers more potential suppliers to match with and avoiding potential collisions. We introduce a stylized model to study the above trade-off. The platform offers each customer a menu of suppliers, and customers choose, simultaneously and independently, either a supplier from their menu or to remain unmatched. Suppliers then see the set of customers that have selected them, and choose to either match with one of these customers or to remain unmatched. A match occurs if a customer and a supplier choose each other (in sequence). Agents choices are probabilistic, and proportional to public scores of agents in their menu and a score that is associated with remaining unmatched. The platforms problem is to construct menus for costumers to maximize the number of matches. This problem is shown to be strongly NP-hard via a reduction from 3-partition. We provide an efficient algorithm that achieves a constant-factor approximation to the expected number of matches.
This paper addresses the paucity of models of matching markets, both one-sided and two-sided, when utility functions of agents are cardinal. The classical Hylland-Zeckhauser scheme cite{hylland}, which is the most prominent such model in economics, can be viewed as corresponding to the linear Fisher model, which is most elementary model in market equilibria. Although HZ is based on the attractive idea of using a pricing mechanism, from the viewpoint of use in applications, it has a serious drawback, namely lack of computational efficiency, due to which solving instances of size even 4 or 5 is difficult. We propose a variety of Nash-bargaining-based models, several of which draw from general equilibrium theory, which has defined a rich collection of market models that generalize the linear Fisher model in order to address more specialized and realistic situations. The Nash bargaining solution satisfies Pareto optimality and symmetry and the allocations it yields are remarkably fair. Furthermore, since the solution is captured via a convex program, it is polynomial time computable. In order to be used in industrial grade applications, we give implementations for these models that are extremely time efficient, solving large instances, with $n = 2000$, in one hour on a PC, even for a two-sided matching market. The idea underlying our work has its origins in Vazirani (2012), which viewed the linear case of the Arrow-Debreu market model as a Nash bargaining game and gave a combinatorial, polynomial time algorithm for finding allocations via this solution concept, rather than the usual approach of using a pricing mechanism.
Modern financial market dynamics warrant detailed analysis due to their significant impact on the world. This, however, often proves intractable; massive numbers of agents, strategies and their change over time in reaction to each other leads to difficulties in both theoretical and simulational approaches. Notable work has been done on strategy dominance in stock markets with respect to the ratios of agents with certain strategies. Perfect knowledge of the strategies employed could then put an individual agent at a consistent trading advantage. This research reports the effects of imperfect oracles on the system - dispensing noisy information about strategies - information which would normally be hidden from market participants. The effect and achievable profits of a singular trader with access to an oracle were tested exhaustively with previously unexplored factors such as changing order schedules. Additionally, the effect of noise on strategic information was traced through its effect on trader efficiency.
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