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on Economic Design |
| By: | Gagan Aggarwal; Anupam Gupta; Andres Perlroth; Grigoris Velegkas |
| Abstract: | We study a setting where agents use no-regret learning algorithms to participate in repeated auctions. \citet{kolumbus2022auctions} showed, rather surprisingly, that when bidders participate in second-price auctions using no-regret bidding algorithms, no matter how large the number of interactions $T$ is, the runner-up bidder may not converge to bidding truthfully. Our first result shows that this holds for \emph{general deterministic} truthful auctions. We also show that the ratio of the learning rates of the bidders can \emph{qualitatively} affect the convergence of the bidders. Next, we consider the problem of revenue maximization in this environment. In the setting with fully rational bidders, \citet{myerson1981optimal} showed that revenue can be maximized by using a second-price auction with reserves.We show that, in stark contrast, in our setting with learning bidders, \emph{randomized} auctions can have strictly better revenue guarantees than second-price auctions with reserves, when $T$ is large enough. Finally, we study revenue maximization in the non-asymptotic regime. We define a notion of {\em auctioneer regret} comparing the revenue generated to the revenue of a second price auction with truthful bids. When the auctioneer has to use the same auction throughout the interaction, we show an (almost) tight regret bound of $\smash{\widetilde \Theta(T^{3/4})}.$ If the auctioneer can change auctions during the interaction, but in a way that is oblivious to the bids, we show an (almost) tight bound of $\smash{\widetilde \Theta(\sqrt{T})}.$ |
| Date: | 2024–11 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2411.09517 |
| By: | Adriana Amieva; Agust\'in Bonifacio; Pablo Neme |
| Abstract: | We examine the problem of assigning teachers to public schools over time when teachers have tenured positions and can work simultaneously in multiple schools. To do this, we investigate a dynamic many-to-many school choice problem where public schools have priorities over teachers and teachers hold substitutable preferences over subsets of schools. We introduce a new concept of dynamic stability that recognizes the tenured positions of teachers and we prove that a dynamically stable matching always exists. We propose the Tenured-Respecting Deferred Acceptance $(TRDA)$ mechanism, which produces a dynamically stable matching that is constrained-efficient within the class of dynamically stable matchings and minimizes unjustified claims. To improve efficiency beyond this class, we also propose the Tenured-Respecting Efficiency-Adjusted Deferred Acceptance $(TREADA)$ mechanism, an adaptation of the Efficiency-Adjusted Deferred Acceptance mechanism to our dynamic context. We demonstrate that the outcome of the $TREADA$ mechanism Pareto-dominates any dynamically stable matching and achieves efficiency when all teachers consent. Additionally, we examine the issue of manipulability, showing that although the $TRDA$ and $TREADA$ mechanisms can be manipulated, they remain non-obviously dynamically manipulable under specific conditions on schools' priorities. |
| Date: | 2024–11 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2411.07851 |
| By: | Terence Highsmith |
| Abstract: | Caseworkers in foster care systems seek to place waiting children in the most suitable homes. Furthermore, social work guidelines prioritize heterogeneous attributes of children and homes when deliberating placements. We use insights from market design and dynamic matching to characterize a class of dynamically envy-free mechanisms that incentivize expedient placements when children and homes arrive to the market over time and homes may accept or decline placements. The mechanisms have robustness against justified envy and costly patience. We analyze strategic incentives and efficiency properties of dynamic envy-freeness. Finally, we conduct empirical simulations that affirm that our mechanisms drastically increase placements and reduce waiting costs while maintaining robustness to prediction error versus a naive mechanism that always sequentially runs Deferred Acceptance. Practitioners can implement our mechanisms through assigning priority to child-home matches. |
| Date: | 2024–11 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2411.09817 |
| By: | Mira Frick; Ryota Iijima; Yuhta Ishii |
| Abstract: | A multi-product monopolist faces a buyer who is privately informed about his valuations for the goods. As is well-known, optimal mechanisms are in general complicated, while simple mechanisms -- such as pure bundling or separate sales -- can be far from optimal and do not admit clear-cut comparisons. We show that this changes if the monopolist observes sufficiently rich data about the buyer's valuations: Now, pure bundling always outperforms separate sales; moreover, there is a sense in which pure bundling performs essentially as well as the optimal mechanism. To formalize this, we characterize how fast the corresponding revenues converge to the first-best revenue as the monopolist's data grows rich: Pure bundling achieves the same convergence rate to the first-best as optimal mechanisms; in contrast, the convergence rate under separate sales is suboptimal. |
| Date: | 2024–11 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2411.06312 |
| By: | Yiding Feng; Yaonan Jin |
| Abstract: | A large proportion of the Bayesian mechanism design literature is restricted to the family of regular distributions $\mathbb{F}_{\tt reg}$ [Mye81] or the family of monotone hazard rate (MHR) distributions $\mathbb{F}_{\tt MHR}$ [BMP63], which overshadows this beautiful and well-developed theory. We (re-)introduce two generalizations, the family of quasi-regular distributions $\mathbb{F}_{\tt Q-reg}$ and the family of quasi-MHR distributions $\mathbb{F}_{\tt Q-MHR}$. All four families together form the following hierarchy: $\mathbb{F}_{\tt MHR} \subsetneq (\mathbb{F}_{\tt reg} \cap \mathbb{F}_{\tt Q-MHR}) \subsetneq \mathbb{F}_{\tt Q-reg}$ and $\mathbb{F}_{\tt Q-MHR} \subsetneq (\mathbb{F}_{\tt reg} \cup \mathbb{F}_{\tt Q-MHR}) \subsetneq \mathbb{F}_{\tt Q-reg}$. The significance of our new families is manifold. First, their defining conditions are immediate relaxations of the regularity/MHR conditions (i.e., monotonicity of the virtual value functions and/or the hazard rate functions), which reflect economic intuition. Second, they satisfy natural mathematical properties (about order statistics) that are violated by both original families $\mathbb{F}_{\tt reg}$ and $\mathbb{F}_{\tt MHR}$. Third but foremost, numerous results [BK96, HR09a, CD15, DRY15, HR14, AHN+19, JLTX20, JLQ+19b, FLR19, GHZ19b, JLX23, LM24] established before for regular/MHR distributions now can be generalized, with or even without quantitative losses. |
| Date: | 2024–11 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2411.03583 |
| By: | Elacqua, Gregory; Kutscher, Macarena; Nascimento, Danielle |
| Abstract: | The potential efficacy of centralized school choice systems in reducing inequalities in access to high-quality schools may be hindered by informational frictions. In this paper, we experimentally evaluate a low-cost information intervention in the centralized school admission system (Matrícula Digital) of Recife, Brazil. The intervention modified how school vacancies were initially displayed on the application platform: the treatment group first saw schools listed by quality; the control group first saw them ordered by proximity to the student's home, i.e., the default order. We focus on students applying to first grade, the level with the highest participation rate since all pupils entering the municipal school system must go through this process. We find no overall effect of the school ordering change on the quality of the schools selected. However, when we restrict our analysis to students who live near at least one of the top three schools on the list, we observe a significant positive effect. This effect weakens as distance from home increases. Our findings indicate the importance of school quality in relation to proximity to the students residence. This conclusion is supported by a parental survey conducted after admissions, in which 80% of respondents indicated that proximity was the most important factor in their school choice. These results have considerable implications for the design of effective educational information interventions. |
| JEL: | A20 D12 I24 C93 H75 |
| Date: | 2024–10 |
| URL: | https://d.repec.org/n?u=RePEc:idb:brikps:13836 |
| By: | Bergh, Andreas (Department of Economics, Lund University, and); Wernberg, Joakim (Department of Technology and Society, Lund University, and) |
| Abstract: | Quasi-markets in the provision of public services are increasingly common but also highly contested. We formulate a conceptual framework based on economic theory to describe how quasi-markets differ from traditional markets in five aspects: 1) revenues, costs, and profits; 2) the matching of supply and demand; 3) competition; 4) structural change; and 5) rent-seeking. Using the assumption of profit-maximizing actors, we provide a stress test of quasi-market design and highlight how these differences affect incentives and expected outcomes. Applying the framework to the Swedish school voucher system, we show how design decisions have generated unintended consequences that are detrimental to service quality and run counter to policy goals. |
| Keywords: | Quasi-Markets; School vouchers; Market structure; Public administration |
| JEL: | D47 H52 H83 |
| Date: | 2024–11–15 |
| URL: | https://d.repec.org/n?u=RePEc:hhs:iuiwop:1505 |