|
on Economic Design |
| By: | Liran Einav; Amy Finkelstein; Pietro Tebaldi |
| Abstract: | Health insurance is increasingly provided through managed competition, in which subsidies for consumers and risk adjustment for insurers are key market design instruments. We illustrate that subsidies offer two advantages over risk adjustment in markets with adverse selection. They provide greater flexibility in tailoring premiums to heterogeneous buyers, and they produce equilibria with lower markups and greater enrollment. We assess these effects using demand and cost estimates from the California Affordable Care Act marketplace. Holding government spending fixed, we estimate that subsidies can increase enrollment by 16 percentage points (76%) over risk adjustment, while all consumers are weakly better off. |
| JEL: | G22 G28 H51 I13 |
| Date: | 2024–06 |
| URL: | https://d.repec.org/n?u=RePEc:nbr:nberwo:32586&r= |
| By: | Anna Bogomolnaia; Herv\'e Moulin |
| Abstract: | In a general fair division model with transferable utilities we discuss endogenous lower and upper guarantees on individual shares of benefits or costs. Like the more familiar exogenous bounds on individual shares described by an outside option or a stand alone utility, these guarantees depend on my type but not on others' types, only on their number and the range of types. Keeping the range from worst share to best share as narrow as permitted by the physical constraints of the model still leaves a large menu of tight guarantee functions. We describe in detail these design options in several iconic problems where each tight pair of guarantees has a clear normative meaning: the allocation of indivisible goods or costly chores, cost sharing of a public facility and the exploitation of a commons with substitute or complementary inputs. The corresponding benefit or cost functions are all sub- or super-modular, and for this class we characterise the set of minimal upper and maximal lower guarantees in all two agent problems. |
| Date: | 2024–06 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2406.14198&r= |
| By: | Federica Carannante (Princeton University); Marco Pagnozzi (Università di Napoli Federico II and CSEF); Elia Sartori (CSEF) |
| Abstract: | We analyze how the seller adjusts the reserve price in infinitely repeated auctions using the information conveyed by past bids. Bidders are myopic and have constant valuations; losers are replaced by new bidders, and winners leave with an exogenous probability. Our model is a stylized description of the market for online display advertisements, where publishers sell impressions through real-time first- or second-price auctions. The optimal reserve price is either equal to the value of the last winner, or lower than it when the winner’s value is sufficiently high. In this second case, the reserve price decreases in the winner’s value in a first-price auction, while it is independent of it in a second-price auction. Because past winners who are outbid substitute for the reserve price in a second-price auction, the seller often sets a lower reserve price and obtains a higher revenue than in a first-price auction. Long-run trade may be non-monotonic in the probability that winners leave. |
| Date: | 2024–06–20 |
| URL: | https://d.repec.org/n?u=RePEc:sef:csefwp:720&r= |
| By: | Mridu Prabal Goswami |
| Abstract: | We consider one buyer and one seller. For a bundle $(t, q)\in [0, \infty[\times [0, 1]=\mathbb{Z}$, $q$ either refers to the wining probability of an object or a share of a good, and $t$ denotes the payment that the buyer makes. We define classical and restricted classical preferences of the buyer on $\mathbb{Z}$; they incorporate quasilinear, non-quasilinear, risk averse preferences with multidimensional pay-off relevant parameters. We define rich single-crossing subsets of the two classes, and characterize strategy-proof mechanisms by using monotonicity of the mechanisms and continuity of the indirect preference correspondences. We also provide a computationally tractable optimization program to compute the optimal mechanism. We do not use revenue equivalence and virtual valuations as tools in our proofs. Our proof techniques bring out the geometric interaction between the single-crossing property and the positions of bundles $(t, q)$s. Our proofs are simple and provide computationally tractable optimization program to compute the optimal mechanism. The extension of the optimization program to the $n-$ buyer environment is immediate. |
| Date: | 2024–06 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2406.12279&r= |
| By: | Bo Peng; Zhihao Gavin Tang |
| Abstract: | We consider the robust contract design problem when the principal only has limited information about the actions the agent can take. The principal evaluates a contract according to its worst-case performance caused by the uncertain action space. Carroll (AER 2015) showed that a linear contract is optimal among deterministic contracts. Recently, Kambhampati (JET 2023) showed that the principal's payoff can be strictly increased via randomization over linear contracts. In this paper, we characterize the optimal randomized contract, which remains linear and admits a closed form of its cumulative density function. The advantage of randomized contracts over deterministic contracts can be arbitrarily large even when the principal knows only one non-trivial action of the agent. Furthermore, our result generalizes to the model of contracting with teams, by Dai and Toikka (Econometrica 2022). |
| Date: | 2024–06 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2406.11528&r= |
| By: | Igor Sadoune; Marcelin Joanis; Andrea Lodi |
| Abstract: | This paper introduces the Minimum Price Markov Game (MPMG), a dynamic variant of the Prisoner's Dilemma. The MPMG serves as a theoretical model and reasonable approximation of real-world first-price sealed-bid public auctions that follow the minimum price rule. The goal is to provide researchers and practitioners with a framework to study market fairness and regulation in both digitized and non-digitized public procurement processes, amidst growing concerns about algorithmic collusion in online markets. We demonstrate, using multi-agent reinforcement learning-driven artificial agents, that algorithmic tacit coordination is difficult to achieve in the MPMG when cooperation is not explicitly engineered. Paradoxically, our results highlight the robustness of the minimum price rule in an auction environment, but also show that it is not impervious to full-scale algorithmic collusion. These findings contribute to the ongoing debates about algorithmic pricing and its implications. |
| Date: | 2024–07 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2407.03521&r= |
| By: | Luofeng Liao; Christian Kroer |
| Abstract: | We initiate the study of statistical inference and A/B testing for two market equilibrium models: linear Fisher market (LFM) equilibrium and first-price pacing equilibrium (FPPE). LFM arises from fair resource allocation systems such as allocation of food to food banks and notification opportunities to different types of notifications. For LFM, we assume that the data observed is captured by the classical finite-dimensional Fisher market equilibrium, and its steady-state behavior is modeled by a continuous limit Fisher market. The second type of equilibrium we study, FPPE, arises from internet advertising where advertisers are constrained by budgets and advertising opportunities are sold via first-price auctions. For platforms that use pacing-based methods to smooth out the spending of advertisers, FPPE provides a hindsight-optimal configuration of the pacing method. We propose a statistical framework for the FPPE model, in which a continuous limit FPPE models the steady-state behavior of the auction platform, and a finite FPPE provides the data to estimate primitives of the limit FPPE. Both LFM and FPPE have an Eisenberg-Gale convex program characterization, the pillar upon which we derive our statistical theory. We start by deriving basic convergence results for the finite market to the limit market. We then derive asymptotic distributions, and construct confidence intervals. Furthermore, we establish the asymptotic local minimax optimality of estimation based on finite markets. We then show that the theory can be used for conducting statistically valid A/B testing on auction platforms. Synthetic and semi-synthetic experiments verify the validity and practicality of our theory. |
| Date: | 2024–06 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2406.15522&r= |
| By: | Jiadong Gu |
| Abstract: | This paper studies optimal mechanisms for collecting and trading data. Consumers benefit from revealing information about their tastes to a service provider because this improves the service. However, the information is also valuable to a third party as it may extract more revenue from the consumer in another market called the product market. The paper characterizes the constrained optimal mechanism for the service provider subject to incentive feasibility. It is shown that the service provider sometimes sells no information or only partial information in order to preserve profits in the service market. In a general setup, the service provision distortion and no-price discrimination in the product market are exclusive. Moreover, a ban on data trade may reduce social welfare because it makes it harder to price discriminate in the product market. |
| Date: | 2024–06 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2406.12457&r= |
| By: | Victor Augias; Alexis Ghersengorin; Daniel M. A. Barreto |
| Abstract: | Consumer data can be used to sort consumers into different market segments, allowing a monopolist to charge different prices at each segment. We study consumer-optimal segmentations with redistributive concerns, i.e., that prioritize poorer consumers. Such segmentations are efficient but may grant additional profits to the monopolist, compared to consumer-optimal segmentations with no redistributive concerns. We characterize the markets for which this is the case and provide a procedure for constructing optimal segmentations given a strong redistributive motive. For the remaining markets, we show that the optimal segmentation is surprisingly simple: it generates one segment with a discount price and one segment with the same price that would be charged if there were no segmentation. We also show that a regulator willing to implement the redistributive-optimal segmentation does not need to observe precisely the composition and the frequency of each market segment, the aggregate distribution over prices suffices. |
| Date: | 2024–06 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2406.14174&r= |