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on Economic Design |
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Issue of 2023‒04‒17
twelve papers chosen by Guillaume Haeringer, Baruch College and Alex Teytelboym, University of Oxford |
| By: | Felix Brandt; Matthias Greger; Ren\'e Romen |
| Abstract: | Random serial dictatorship (RSD) is a randomized assignment rule that - given a set of $n$ agents with strict preferences over $n$ houses - satisfies equal treatment of equals, ex post efficiency, and strategyproofness. For $n \le 3$, Bogomolnaia and Moulin (2001) have shown that RSD is characterized by these three axioms. Using best first search in combination with quadratic programming, we extend this characterization to $n \le 5$, getting closer to answering the long-standing open question whether the characterization holds for arbitrary $n$. On the way, we describe weakenings of ex post efficiency and strategyproofness that are sufficient for our characterization and identify problems when making statements for larger $n$. |
| Date: | 2023–03 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2303.11976&r=des |
| By: | Anna Bogomolnaia (HSE St Petersburg - Higher School of Economics - St Petersburg, University of Glasgow, CES - Centre d'économie de la Sorbonne - UP1 - Université Paris 1 Panthéon-Sorbonne - CNRS - Centre National de la Recherche Scientifique); Hervé Moulin (University of Glasgow, HSE St Petersburg - Higher School of Economics - St Petersburg, CES - Centre d'économie de la Sorbonne - UP1 - Université Paris 1 Panthéon-Sorbonne - CNRS - Centre National de la Recherche Scientifique) |
| Abstract: | When dividing a "manna" Ω of private items (commodities, workloads, land, time slots) between n agents, the individual guarantee is the welfare each agent can secure in the worst case of other agents' preferences and actions. If the manna is nonatomic and utilities are continuous (not necessarily monotone or convex) the minmax utility, that of our agent's best share in the agent's worst partition of the manna, is guaranteed by Kuhn's generalization of divide and choose. The larger maxmin utility—of the agent's worst share in the agent's best partition—cannot be guaranteed even for two agents. If, for all agents, more manna is better than less (or less is better than more), the new bid and choose rules offer guarantees between minmax and maxmin by letting agents bid for the smallest (or largest) size of a share they find acceptable. |
| Keywords: | fair division, divide and choose, guarantees, nonatomic utilities |
| Date: | 2022–04–08 |
| URL: | http://d.repec.org/n?u=RePEc:hal:cesptp:hal-03886828&r=des |
| By: | Jorge Alcalde-Unzu; Oihane Gallo; Marc Vorsatz |
| Abstract: | We analyze the problem of locating a public facility in a domain of single-peaked and single-dipped preferences when the social planner knows the type of preference (single-peaked or single-dipped) of each agent. Our main result characterizes all strategy-proof rules and shows that they can be decomposed into two steps. In the first step, the agents with single-peaked preferences are asked about their peaks and, for each profile of reported peaks, at most two alternatives are preselected. In the second step, the agents with single-dipped preferences are asked to reveal their dips to complete the decision between the preselected alternatives. Our result generalizes the findings of Moulin (1980) and Barber\`a and Jackson (1994) for single-peaked and of Manjunath (2014) for single-dipped preferences. Finally, we show that all strategy-proof rules are also group strategy-proof and analyze the implications of Pareto efficiency. |
| Date: | 2023–03 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2303.05781&r=des |
| By: | Shurojit Chatterji; Huaxia Zeng |
| Abstract: | We introduce the notion of a multidimensional hybrid preference domain on a (finite) set of alternatives that is a Cartesian product of finitely many components. We study strategy-proof rules on this domain and show that every such rule can be decomposed into component-wise strategy proof rules. More importantly, we show that under a suitable ``richness'' condition, every domain of preferences that reconciles decomposability of rules with strategy-proofness must be a multidimensional hybrid domain. We finally identify an intuitive weakening of separability that explains how a multidimensional hybrid domain may arise in a public goods provision model. |
| Date: | 2023–03 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2303.10889&r=des |
| By: | Victor Augias; Eduardo Perez-Richet |
| Abstract: | We study how to optimally design selection mechanisms, accounting for agents' investment incentives. A principal wishes to allocate a resource of homogeneous quality to a heterogeneous population of agents. The principal commits to a possibly random selection rule that depends on a one-dimensional characteristic of the agents she intrinsically values. Agents have a strict preference for being selected by the principal and may undertake a costly investment to improve their characteristic before it is revealed to the principal. We show that even if random selection rules foster agents' investments, especially at the top of the characteristic distribution, deterministic "pass-fail" selection rules are in fact optimal. |
| Date: | 2023–03 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2303.11805&r=des |
| By: | Bednay, Dezső; Fleiner, Balázs; Tasnádi, Attila |
| Abstract: | Social choice rules (SCRs) aggregate individual preferences to social preferences. By Arrow's (1951) impossibility theorem there does not exist a non-dictatorial SCR satisfying three desirable properties. Considering this negative axiomatic result, in this paper we determine distances of SCRs from the dictatorial rules to rank common SCRs. In particular, we apply the Kendall tau, the Spearman rank correlation and the Spearman footrule metrics. We find that from the investigated SCRs the Borda, the Copeland and the Kemény-Young SCRs stand out. Furthermore, we show that anonymous SCRs approach the constant rule when the number of alternatives is fixed and the number of voters tends to infinity. |
| Keywords: | Simulation, Asymptotic behavior, Dictatorship, Kendall tau, Spearman rank correlation, Spearman footrule |
| JEL: | D71 |
| Date: | 2023–03–30 |
| URL: | http://d.repec.org/n?u=RePEc:cvh:coecwp:2023/03&r=des |
| By: | Kyle Greenberg; Parag A. Pathak; Tayfun S\"onmez |
| Abstract: | We present the proof-of-concept for minimalist market design (S\"{o}nmez, 2023) as an effective methodology to enhance an institution based on the desiderata of stakeholders with minimal interference. Four objectives-respecting merit, increasing retention, aligning talent, and enhancing trust-guided reforms to US Army's centralized branching process of cadets to military specialties since 2006. USMA's mechanism for the Class of 2020 exacerbated challenges implementing these objectives. Formulating the Army's desiderata as rigorous axioms, we analyze their implications. Under our minimalist approach to institution redesign, the Army's objectives uniquely identify a branching mechanism. Our design is now adopted at USMA and ROTC. |
| Date: | 2023–03 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2303.06564&r=des |
| By: | Pallavi Pal |
| Abstract: | In this paper, I derive a new method to identify the distribution of the advertiser’s ad-value in the sponsored search auction, explicitly looking at weighted Generalized Second Price auction (GSPw henceforth). Compared to previous literature, this method incorporates a weaker and more realistic assumption of ‘incomplete information’ on advertisers’ private information. Additionally, I evaluate how much the advertisers shade their bid below their value, defined as bid shading amount. The results show that the bid shading is very small; the 50th percentile of the bid shading upper bound is below by 0.2% of their value. The low amount of bid shading is due to high competition intensity in the online ad market as the number of competing bids in the online ad market is very large. The bid shading calculation can also shed light on how the change of ad auction will impact the ad revenue. |
| Date: | 2023 |
| URL: | http://d.repec.org/n?u=RePEc:ces:ceswps:_10299&r=des |
| By: | Semin Kim (Yonsei University) |
| Abstract: | Barbera and Jackson (2004) define a constitution as a pair of voting rules (f, F), where f is employed for ordinary decisions, and F is employed to choose between f and a proposed voting rule. While they study the stability of constitutions at the ex-ante stage, where agents’ preferences over final outcomes are uncertain, we focus on the ex-post stage, where agents’ preferences are known. We present a characterization of ex-post stable constitutions. Furthermore, we examine the robustness of this characterization to the changes in the voting environment and the relationship between ex-post stability and ex-ante stability of constitutions. |
| Keywords: | Constitutions, Ex-post stability, Voting rules. |
| JEL: | D02 D71 D72 |
| Date: | 2023–03 |
| URL: | http://d.repec.org/n?u=RePEc:yon:wpaper:2023rwp-212&r=des |
| By: | Jason Milionis; Ciamac C. Moallemi; Tim Roughgarden |
| Abstract: | In decentralized finance ("DeFi"), automated market makers (AMMs) enable traders to programmatically exchange one asset for another. Such trades are enabled by the assets deposited by liquidity providers (LPs). The goal of this paper is to characterize and interpret the optimal (i.e., profit-maximizing) strategy of a monopolist liquidity provider, as a function of that LP's beliefs about asset prices and trader behavior. We introduce a general framework for reasoning about AMMs. In this model, the market maker (i.e., LP) chooses a demand curve that specifies the quantity of a risky asset (such as BTC or ETH) to be held at each dollar price. Traders arrive sequentially and submit a price bid that can be interpreted as their estimate of the risky asset price; the AMM responds to this submitted bid with an allocation of the risky asset to the trader, a payment that the trader must pay, and a revised internal estimate for the true asset price. We define an incentive-compatible (IC) AMM as one in which a trader's optimal strategy is to submit its true estimate of the asset price, and characterize the IC AMMs as those with downward-sloping demand curves and payments defined by a formula familiar from Myerson's optimal auction theory. We characterize the profit-maximizing IC AMM via a generalization of Myerson's virtual values. The optimal demand curve generally has a jump that can be interpreted as a "bid-ask spread, " which we show is caused by a combination of adverse selection risk (dominant when the degree of information asymmetry is large) and monopoly pricing (dominant when asymmetry is small). |
| Date: | 2023–02 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2303.00208&r=des |
| By: | Furkan Sezer; Ceyhun Eksin |
| Abstract: | Information design in an incomplete information game includes a designer with the goal of influencing players' actions through signals generated from a designed probability distribution so that its objective function is optimized. If the players have quadratic payoffs that depend on the players' actions and an unknown payoff-relevant state, and signals on the state that follow a Gaussian distribution conditional on the state realization, then the information design problem under quadratic design objectives is a semidefinite program (SDP). We consider a setting in which the designer has partial knowledge on agents' utilities. We address the uncertainty about players' preferences by formulating a robust information design problem. Specifically, we consider ellipsoid perturbations over payoff matrices in linear-quadratic-Gaussian (LQG) games. We show that this leads to a tractable robust SDP formulation. Using the robust SDP formulation, we obtain analytical conditions for the optimality of no information and full information disclosure. The robust convex program is also extended to interval and general convex cone uncertainty sets on the payoff matrices. Numerical studies are carried out to identify the relation between the perturbation levels and the optimal information structures. |
| Date: | 2023–03 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2303.05489&r=des |
| By: | Fallou Niakh |
| Abstract: | Risk-sharing is one way to pool risks without the need for a third party. To ensure the attractiveness of such a system, the rule should be accepted and understood by all participants. A desirable risk-sharing rule should fulfill actuarial fairness and Pareto optimality while being easy to compute. This paper establishes a one-to-one correspondence between an actuarially fair Pareto optimal (AFPO) risk-sharing rule and a fixed point of a specific function. A fast numerical method for computing these risk-sharing rules is also derived. As a result, we are able to compute AFPO risk-sharing rules for a large number of heterogeneous participants in this framework. |
| Date: | 2023–03 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2303.05421&r=des |