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on Economic Design |
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Issue of 2020‒05‒11
ten papers chosen by Guillaume Haeringer, Baruch College and Alex Teytelboym, University of Oxford |
| By: | Orhan Ayg\"un; Bertan Turhan |
| Abstract: | We study a school choice problem under affirmative action policies where authorities reserve a certain fraction of the slots at each school for specific student groups, and where students have preferences not only over the schools they are matched to but also the type of slots they receive. Such reservation policies might cause waste in instances of low demand from some student groups. To propose a solution to this issue, we construct a family of choice functions, dynamic reserves choice functions, for schools that respect within-group fairness and allow the transfer of otherwise vacant slots from low-demand groups to high-demand groups. We propose the cumulative offer mechanism (COM) as an allocation rule where each school uses a dynamic reserves choice function and show that it is stable with respect to schools' choice functions, is strategy-proof, and respects improvements. Furthermore, we show that transferring more of the otherwise vacant slots leads to strategy-proof Pareto improvement under the COM. |
| Date: | 2020–05 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2005.01103&r=all |
| By: | Nadja Stroh-Maraun (Paderborn University) |
| Abstract: | There are a number of school choice problems in which students are heterogeneous according to the number of seats they occupy at the school they are assigned to. We propose a weighted school choice problem by assigning each student a so-called weight and extend the top trading cycles algorithm to fit to this extension. We call the new mechanism the weighted TTC and show that it is strategy-proof and results in a Pareto efficient matching. Therefore, the TTC is robust towards the introduction of weights. Nevertheless, it is more complex to guarantee each student a seat at a school, as the extension introduces a trade-off between weights and priorities. |
| Keywords: | Matching, School Choice, College Admission Problems, Top Trading Cycles, Pareto Efficiency, Strategy-Proofness |
| JEL: | C78 D47 |
| Date: | 2020–05 |
| URL: | http://d.repec.org/n?u=RePEc:pdn:dispap:64&r=all |
| By: | Britta Hoyer (Paderborn University); Nadja Stroh-Maraun (Paderborn University) |
| Abstract: | There are a number of college admissions problems in which students are heterogeneous according to the space they occupy at the college they are allocated to. To deal with this source of heterogeneity we propose a weighted college admissions problem by assigning each student a so-called weight. The existence of stable matchings is not ensured in weighted college admissions problems. To find a stable matching, if it exists, we propose a new algorithm, the deferred acceptance algorithm with gaps (DAG). It results in stable matchings if existing and cycles otherwise. Moreover, we show how to restore stability. |
| Keywords: | Matching, School Choice, College Admissions Problems, Deferred Acceptance Algorithm, Stability, DAG, Gaps |
| JEL: | C78 D47 |
| Date: | 2020–05 |
| URL: | http://d.repec.org/n?u=RePEc:pdn:dispap:63&r=all |
| By: | Mithun Chakraborty; Ayumi Igarashi; Warut Suksompong; Yair Zick |
| Abstract: | We introduce and analyze new envy-based fairness concepts for agents with weights that quantify their entitlements in the allocation of indivisible items. We propose two variants of weighted envy-freeness up to one item (WEF1): strong, where the envy can be eliminated by removing an item from the envied agent's bundle, and weak, where the envy can be eliminated either by removing an item as in the strong version or by replicating an item from the envied agent's bundle in the envying agent's bundle. We prove that for additive valuations, an allocation that is both Pareto optimal and strongly WEF1 always exists; however, an allocation that maximizes the weighted Nash social welfare may not be strongly WEF1 but always satisfies the weak version of the property. Moreover, we establish that a generalization of the round-robin picking sequence algorithm produces in polynomial time a strongly WEF1 allocation for an arbitrary number of agents; for two agents, we can efficiently achieve both strong WEF1 and Pareto optimality by adapting the adjusted winner procedure. Our work exhibits several aspects in which weighted fair division is richer and more challenging than its unweighted counterpart. |
| Date: | 2019–09 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:1909.10502&r=all |
| By: | Niclas Boehmer; Edith Elkind |
| Abstract: | In the multidimensional stable roommate problem, agents have to be allocated to rooms and have preferences over sets of potential roommates. We study the complexity of finding good allocations of agents to rooms under the assumption that agents have diversity preferences [Bredereck et al., 2019]: each agent belongs to one of the two types (e.g., juniors and seniors, artists and engineers), and agents' preferences over rooms depend solely on the fraction of agents of their own type among their potential roommates. We consider various solution concepts for this setting, such as core and exchange stability, Pareto optimality and envy-freeness. On the negative side, we prove that envy-free, core stable or (strongly) exchange stable outcomes may fail to exist and that the associated decision problems are NP-complete. On the positive side, we show that these problems are in FPT with respect to the room size, which is not the case for the general stable roommate problem. Moreover, for the classic setting with rooms of size two, we present a linear-time algorithm that computes an outcome that is core and exchange stable as well as Pareto optimal. Many of our results for the stable roommate problem extend to the stable marriage problem. |
| Date: | 2020–04 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2004.14640&r=all |
| By: | Ricardo Martínez (Department of Economic Theory and Economic History, University of Granada.); Juan D Moreno Ternero (Department of Economics, Universidad Pablo de Olavide.) |
| Abstract: | We consider the problem of randomly allocating indivisible units of a resource among agents with conflicting claims on the available amount. In the two-agent case, we characterize three focal rules combining axioms reflecting principles of compensation and sacrifice: probabilistic uniform awards, probabilistic uniform losses and probabilistic concede-and-divide. In the general case of n agents, the two uniform rules are characterized adding the axiom of consistency. There is, however, no consistent extension of probabilistic concede-and-divide. |
| Keywords: | rationing, resource allocation, axioms, probabilistic, discrete goods. |
| JEL: | D63 C71 |
| Date: | 2020–04–18 |
| URL: | http://d.repec.org/n?u=RePEc:gra:wpaper:20/03&r=all |
| By: | Kerman, Toygar (RS: GSBE other - not theme-related research, General Economics 1 (Micro)); Herings, P. Jean-Jacques (RS: GSBE Theme Data-Driven Decision-Making, RS: GSBE Theme Conflict & Cooperation, General Economics 1 (Micro)); Karos, Dominik (RS: GSBE Theme Conflict & Cooperation, General Economics 1 (Micro)) |
| Abstract: | A Sender wants to persuade multiple Receivers with homogeneous preferences and a common belief about the state of the world to vote in favor of a proposal. Prior to the vote Sender commits to a communication strategy which sends private, potentially correlated, signals to Receivers that are contingent on the true state of the world. While Sender benefits from using private messages rather than public communication if Receivers vote sincerely, under the optimal communication strategy, sincere voting is not in any Receiver’s best interest. If the proposal does not require unanimous agreement, Sender’s optimal communication strategy after which sincere voting indeed constitutes a Bayes-Nash equilibrium is such that no voter is ever pivotal. |
| JEL: | C72 D72 D82 D83 |
| Date: | 2020–02–20 |
| URL: | http://d.repec.org/n?u=RePEc:unm:umagsb:2020004&r=all |
| By: | Kunimoto, Takashi (School of Economics, Singapore Management University); Saran, Rene (University of Cincinnati) |
| Abstract: | A social choice function (SCF) is robustly implementable in rationalizable strate-gies if every rationalizable strategy profile on every type space results in outcomes consistent with it. First, we establish an equivalence between robust implementation in rationalizable strategies and “weak rationalizable implementation”. Second, using the equivalence result, we identify weak robust monotonicity as a necessary and al-most sufficient condition for robust implementation in rationalizable strategies. This exhibits a contrast with robust implementation in interim equilibria, i.e., every equilib-rium on every type space achieves outcomes consistent with the SCF. Bergemann and Morris (2011) show that strict robust monotonicity is a necessary and almost sufficient condition for robust implementation in interim equilibria. We argue that strict robust monotonicity is strictly stronger than weak robust monotonicity, which further implies that, within general mechanisms, robust implementation in rationalizable strategies is more permissive than robust implementation in interim equilibria. The gap between robust implementation in rationalizable strategies and that in interim equilibria stems from the strictly stronger nonemptiness requirement inherent in the latter concept. |
| Keywords: | Ex post incentive compatibility; rationalizability; interim equilibrium; robust implementation; weak rationalizable implementation; weak robust monotonicity |
| JEL: | C72 D78 D80 |
| Date: | 2020–04–14 |
| URL: | http://d.repec.org/n?u=RePEc:ris:smuesw:2020_010&r=all |
| By: | Damien Challet (MICS - Mathématiques et Informatique pour la Complexité et les Systèmes - CentraleSupélec); Nikita Gourianov (Department of Physics [Oxford] - University of Oxford [Oxford]) |
| Abstract: | We first investigate static properties of opening and closing auctions such as typical auction volume relative to daily volume and order value distributions. We then show that the indicative match price is strongly mean-reverting because the imbalance is, which we link to strategic behavior. Finally, we investigate how the final auction price reacts to order placement, especially conditional on imbalance improving or worsening events and find a large difference between the opening and closing auctions, emphasizing the role of liquidity and simultaneous trading in the pre-open or open-market order book. |
| Keywords: | Auctions,US equities,Linear response,Imbalance,Liquidity |
| Date: | 2019 |
| URL: | http://d.repec.org/n?u=RePEc:hal:journl:hal-01702726&r=all |
| By: | Abhinandan Dalal; Diganta Mukherjee; Subhrajyoty Roy |
| Abstract: | Tea auctions across India occur as an ascending open auction, conducted online. Before the auction, a sample of the tea lot is sent to potential bidders and a group of tea tasters. The seller's reserve price is a confidential function of the tea taster's valuation, which also possibly acts as a signal to the bidders. In this paper, we work with the dataset from a single tea auction house, J Thomas, of tea dust category, on 49 weeks in the time span of 2018-2019, with the following objectives in mind: $\bullet$ Objective classification of the various categories of tea dust (25) into a more manageable, and robust classification of the tea dust, based on source and grades. $\bullet$ Predict which tea lots would be sold in the auction market, and a model for the final price conditioned on sale. $\bullet$ To study the distribution of price and ratio of the sold tea auction lots. $\bullet$ Make a detailed analysis of the information obtained from the tea taster's valuation and its impact on the final auction price. The model used has shown various promising results on cross-validation. The importance of valuation is firmly established through analysis of causal relationship between the valuation and the actual price. The authors hope that this study of the properties and the detailed analysis of the role played by the various factors, would be significant in the decision making process for the players of the auction game, pave the way to remove the manual interference in an attempt to automate the auction procedure, and improve tea quality in markets. |
| Date: | 2020–05 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2005.02814&r=all |