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on Economic Design |
| By: | Frank Yang; Kai Hao Yang |
| Abstract: | We characterize the extreme points of multidimensional monotone functions from $[0, 1]^n$ to $[0, 1]$, as well as the extreme points of the set of one-dimensional marginals of these functions. These characterizations lead to new results in various mechanism design and information design problems, including public good provision with interdependent values; interim efficient bilateral trade mechanisms; asymmetric reduced form auctions; and optimal private private information structure. As another application, we also present a mechanism anti-equivalence theorem for two-agent, two-alternative social choice problems: A mechanism is payoff-equivalent to a deterministic DIC mechanism if and only if they are ex-post equivalent. |
| Date: | 2025–02 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2502.18876 |
| By: | Tohya Sugano |
| Abstract: | In this paper we address the design of matching mechanisms that are strategy-proof and simultaneously as stable as possible. Building on the impossibility result by \cite{Roth1982-cl} for one-to-one matching problems, we formulate an optimization problem that maximizes stability under the constraint of strategy-proofness. In our model the objective is to minimize the degree of instability measured as the sum (or worst-case maximum) of stability violations over all preference profiles. We further introduce the socially important properties of anonymity and symmetry into the formulation. Our computational results show that, for small markets, our optimization approach leads to mechanisms with substantially lower stability violations than RSD. In particular, the optimal mechanism under our formulation exhibits roughly one-third the stability violation of RSD. For deterministic mechanisms in the three-agent case, we also find that any strategy-proof mechanism hvae at least two blocking pairs at the worst case, and we propose an algorithm that attains this lower bound. Finally, we discuss extensions to larger markets and present simulation evidence that our mechanism yields a reduction of approximately $0.25$ blocking pairs on average compared to SD mechanism. |
| Date: | 2025–02 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2502.12431 |
| By: | Haris Aziz; Md. Shahidul Islam; Szilvia P\'apai |
| Abstract: | We consider a two-sided matching problem in which the agents on one side have dichotomous preferences and the other side representing institutions has strict preferences (priorities). It captures several important applications in matching market design in which the agents are only interested in getting matched to an acceptable institution. These include centralized daycare assignment and healthcare rationing. We present a compelling new mechanism that satisfies many prominent and desirable properties including individual rationality, maximum size, fairness, Pareto-efficiency on both sides, strategyproofness on both sides, non-bossiness and having polynomial time running time. As a result, we answer an open problem whether there exists a mechanism that is agent-strategyproof, maximum, fair and non-bossy. |
| Date: | 2025–02 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2502.09962 |
| By: | Rachitesh Kumar; Omar Mouchtaki |
| Abstract: | First-price auctions are one of the most popular mechanisms for selling goods and services, with applications ranging from display advertising to timber sales. Unlike their close cousin, the second-price auction, first-price auctions do not admit a dominant strategy. Instead, each buyer must design a bidding strategy that maps values to bids -- a task that is often challenging due to the lack of prior knowledge about competing bids. To address this challenge, we conduct a principled analysis of prior-independent bidding strategies for first-price auctions using worst-case regret as the performance measure. First, we develop a technique to evaluate the worst-case regret for (almost) any given value distribution and bidding strategy, reducing the complex task of ascertaining the worst-case competing-bid distribution to a simple line search. Next, building on our evaluation technique, we minimize worst-case regret and characterize a minimax-optimal bidding strategy for every value distribution. We achieve it by explicitly constructing a bidding strategy as a solution to an ordinary differential equation, and by proving its optimality for the intricate infinite-dimensional minimax problem underlying worst-case regret minimization. Our construction provides a systematic and computationally-tractable procedure for deriving minimax-optimal bidding strategies. When the value distribution is continuous, it yields a deterministic strategy that maps each value to a single bid. We also show that our minimax strategy significantly outperforms the uniform-bid-shading strategies advanced by prior work. Our result allows us to precisely quantify, through minimax regret, the performance loss due to a lack of knowledge about competing bids. We leverage this to analyze the impact of the value distribution on the performance loss, and find that it decreases as the buyer's values become more dispersed. |
| Date: | 2025–02 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2502.09907 |
| By: | Agustin G. Bonifacio |
| Abstract: | In the problem of fully allocating a social endowment of perfectly divisible commodities among a group of agents with multidimensional single-peaked preferences, we study strategy-proof rules that are not Pareto-dominated by other strategy-proof rules. Specifically, we: (i) establish a sufficient condition for a rule to be Pareto-undominated strategy-proof; (ii) introduce a broad class of rules satisfying this property by extending the family of "sequential allotment rules" to the multidimensional setting; and (iii) provide a new characterization of the "multidimensional uniform rule" involving Pareto-undominated strategy-proofness. Results (i) and (iii) generalize previous findings that were only applicable to the two-agent case. |
| Date: | 2025–02 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2502.17682 |
| By: | Kento Hashimoto; Keita Kuwahara; Reo Nonaka |
| Abstract: | Finding the optimal (revenue-maximizing) mechanism to sell multiple items has been a prominent and notoriously difficult open problem. Existing work has mainly focused on deriving analytical results tailored to a particular class of problems (for example, Giannakopoulos (2015) and Yang (2023)). The present paper explores the possibility of a generally applicable methodology of the Automated Mechanism Design (AMD). We first employ the deep learning algorithm developed by D\"utting et al. (2023) to numerically solve small-sized problems, and the results are then generalized by educated guesswork and finally rigorously verified through duality. By focusing on a single buyer who can consume one item, our approach leads to two key contributions: establishing a much simpler way to verify the optimality of a wide range of problems and discovering a completely new result about the optimality of grand bundling. First, we show that selling each item at an identical price (or equivalently, selling the grand bundle of all items) is optimal for any number of items when the value distributions belong to a class that includes the uniform distribution as a special case. Different items are allowed to have different distributions. Second, for each number of items, we established necessary and sufficient conditions that $c$ must satisfy for grand bundling to be optimal when the value distribution is uniform over an interval $[c, c + 1]$. This latter model does not satisfy the previously known sufficient conditions for the optimality of grand bundling Haghpanah and Hartline (2021). Our results are in contrast to the only known results for $n$ items (for any $n$), Giannakopoulos (2015) and Daskalakis et al. (2017), which consider a single buyer with additive preferences, where the values of items are narrowly restricted to i.i.d. according to a uniform or exponential distribution. |
| Date: | 2025–02 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2502.10086 |
| By: | Robert Day; Benjamin Lubin |
| Abstract: | We use valid inequalities (cuts) of the binary integer program for winner determination in a combinatorial auction (CA) as "artificial items" that can be interpreted intuitively and priced to generate Artificial Walrasian Equilibria. While the lack of an integer programming gap is sufficient to guarantee a Walrasian equilibrium, we show that it does not guarantee a "price-match equilibrium" (PME), a refinement that we introduce, in which prices are justified by an iso-revenue outcome for any hypothetical removal of a single bidder. We prove the existence of PME for any CA and characterize their economic properties and computation. We implement minimally artificial PME rules and compare them with other prominent CA payment rules in the literature. |
| Date: | 2025–02 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2502.15893 |
| By: | Jack Hirsch; Eric Tang |
| Abstract: | We study the effect of providing information to agents who queue before a scarce good is distributed at a fixed time. When agents have quasi-linear utility in time spent waiting, they choose entry times as they would bids in a descending auction. An information designer can influence their behavior by providing updates about the length of the queue. Many natural information policies release "sudden bad news, " which occurs when agents learn that the queue is longer than previously believed. We show that sudden bad news can cause assortative inefficiency by prompting a mass of agents to simultaneously attempt to join the queue. As a result, if the value distribution has an increasing (decreasing) hazard rate, information policies that release sudden bad news increase (decrease) total surplus, relative to releasing no information. When agents face entry costs to join the queue and the value distribution has a decreasing hazard rate, an information designer maximizes total surplus by announcing only when the queue is full. |
| Date: | 2025–02 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2502.19553 |
| By: | Ruofei Ma; Wenpin Tang; David Yao |
| Abstract: | In this paper, we consider the impact of the order flow auction (OFA) in the context of the proposer-builder separation (PBS) mechanism through a game-theoretic perspective. The OFA is designed to improve user welfare by redistributing maximal extractable value (MEV) to the users, in which two auctions take place: the order flow auction and the block-building auction. We formulate the OFA as a multiplayer game, and focus our analyses on the case of two competing players (builders). We prove the existence and uniqueness of a Nash equilibrium for the two-player game, and derive a closed-form solution by solving a quartic equation. Our result shows that the builder with a competitive advantage pays a relatively lower cost, leading to centralization in the builder space. In contrast, the proposer's shares evolve as a martingale process, which implies decentralization in the proposer (or, validator) space. Our analyses rely on various tools from stochastic processes, convex optimization, and polynomial equations. We also conduct numerical studies to corroborate our findings, and explore other features of the OFA under the PBS mechanism. |
| Date: | 2025–02 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2502.12026 |
| By: | Keita Kuwahara |
| Abstract: | We propose an $O(n^2)$-time algorithm to determine whether a given matching is efficient in the roommates problem. |
| Date: | 2025–02 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2502.16960 |
| By: | Xiaoyun Qiu; Liren Shan |
| Abstract: | How should one jointly design tests and the arrangement of agencies to administer these tests (testing procedure)? To answer this question, we analyze a model where a principal must use multiple tests to screen an agent with a multi-dimensional type, knowing that the agent can change his type at a cost. We identify a new tradeoff between setting difficult tests and using a difficult testing procedure. We compare two settings: (1) the agent only misrepresents his type (manipulation) and (2) the agent improves his actual type (investment). Examples include interviews, regulations, and data classification. We show that in the manipulation setting, stringent tests combined with an easy procedure, i.e., offering tests sequentially in a fixed order, is optimal. In contrast, in the investment setting, non-stringent tests with a difficult procedure, i.e., offering tests simultaneously, is optimal; however, under mild conditions offering them sequentially in a random order may be as good. Our results suggest that whether the agent manipulates or invests in his type determines which arrangement of agencies is optimal. |
| Date: | 2025–02 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2502.12264 |
| By: | Siddarth Srinivasan; Ezra Karger; Michiel Bakker; Yiling Chen |
| Abstract: | Common sense suggests that when individuals explain why they believe something, we can arrive at more accurate conclusions than when they simply state what they believe. Yet, there is no known mechanism that provides incentives to elicit explanations for beliefs from agents. This likely stems from the fact that standard Bayesian models make assumptions (like conditional independence of signals) that preempt the need for explanations, in order to show efficient information aggregation. A natural justification for the value of explanations is that agents' beliefs tend to be drawn from overlapping sources of information, so agents' belief reports do not reveal all that needs to be known. Indeed, this work argues that rationales-explanations of an agent's private information-lead to more efficient aggregation by allowing agents to efficiently identify what information they share and what information is new. Building on this model of rationales, we present a novel 'deliberation mechanism' to elicit rationales from agents in which truthful reporting of beliefs and rationales is a perfect Bayesian equilibrium. |
| Date: | 2025–02 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2502.13410 |