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on Economic Design |
| By: | Roberto Pinheiro |
| Abstract: | In this paper, we present a model of repeated first-price private value auctions in which the bidders have access to a cheap talk communication mechanism. In this framework, messages allow bidders to transmit their preference rankings over the goods to be auctioned, similar to Pesendorfer (2000). We show that collusion through this static mechanism not only dominates the static bid rotation mechanism presented by McAfee and McMillan (1992), but it is also not strictly dominated by the dynamic bid rotation mechanism presented by Aoyagi (2003). However, we show that asymptotic efficiency of collusion through increasing the number of ordered goods, presented by Pesendorfer (2000), demands patience rates to asymptotically approach one, making collusion increasingly more difficult to sustain. Finally, we study mechanisms through which the auctioneer may try to break bidders' collusion. |
| Keywords: | collusion; auctions; cheap talk communication; repeated games |
| JEL: | D44 C72 L41 |
| Date: | 2024–10–07 |
| URL: | https://d.repec.org/n?u=RePEc:fip:fedcwq:98920 |
| By: | Shenghao Gao; Peyman Khezr; Armin Pourkhanali |
| Abstract: | This study explores the performance of auctions in China's seasoned equity offering (SEO) market, both theoretically and empirically. In these auctions, issuers must commit to a pre-announced revenue target and a maximum number of shares available for auction. We use a common value framework to analyze this auction mechanism, detailing its operation, share allocation, and pricing. The theoretical findings suggest that when buyers bid truthfully, the seller's optimal strategy is to set the total share quantity equal to the target revenue divided by the reserve price. We demonstrate that committing to a target revenue results in a higher level of truthful bidding compared to a standard uniform-price auction without any revenue commitment. We empirically test our theoretical findings using data from China's SEO markets. First, we assess the impact of various issuer strategies on firm-level SEO discounts, categorizing scenarios based on share availability and target revenue. We find that the scenario where the reserve price times the share quantity matches the target revenue is the most optimal for sellers. Second, we examine bidding behavior and auction performance, showing that China's SEO uniform price auction performs exceptionally well. Specifically, the actual issue prices are only 0.029 below the truthful case prices, indicating that the revenue raised is still close to what would have been achieved with truthful bids. |
| Date: | 2024–09 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2410.00063 |
| By: | Lirong Xia |
| Abstract: | How to design fair and (computationally) efficient voting rules is a central challenge in Computational Social Choice. In this paper, we aim at designing efficient algorithms for computing most equitable rules for large classes of preferences and decisions, which optimally satisfy two fundamental fairness/equity axioms: anonymity (every voter being treated equally) and neutrality (every alternative being treated equally). By revealing a natural connection to the graph isomorphism problem and leveraging recent breakthroughs by Babai [2019], we design quasipolynomial-time algorithms that compute most equitable rules with verifications, which also compute verifications about whether anonymity and neutrality are satisfied at the input profile. Further extending this approach, we propose the canonical-labeling tie-breaking, which runs in quasipolynomial-time and optimally breaks ties to preserve anonymity and neutrality. As for the complexity lower bound, we prove that even computing verifications for most equitable rules is GI-complete (i.e., as hard as the graph isomorphism problem), and sometimes GA-complete (i.e., as hard as the graph automorphism problem), for many commonly studied combinations of preferences and decisions. To the best of our knowledge, these are the first problems in computational social choice that are known to be complete in the class GI or GA. |
| Date: | 2024–10 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2410.04179 |
| By: | Vincent Meisner; Pascal Pillath |
| Abstract: | We design the profit-maximizing mechanism to sell an excludable and non-rival good with network effects. Buyers have heterogeneous private values that depend on how many others also consume the good. In optimum, an endogenous number of the highest types shares consumption, and we provide an algorithm that implements this allocation in dominant strategies. We apply our insights to digital content creation, and we are able to rationalize features seen in monetization schemes in this industry such as voluntary contributions, community subsidies, and exclusivity bids. |
| Keywords: | Mechanism design, non-rival goods, club goods, network effects, digital content, creator economy |
| JEL: | D82 |
| Date: | 2024–09–20 |
| URL: | https://d.repec.org/n?u=RePEc:bdp:dpaper:0049 |
| By: | Oihane Gallo |
| Abstract: | We analyze the problem of locating a public facility on a line in a society where agents have either single-peaked or single-dipped preferences. We consider the domain analyzed in Alcalde-Unzu et al. (2024), where the type of preference of each agent is public information, but the location of her peak/dip as well as the rest of the preference are unknown. We characterize all strategy-proof and type-anonymous rules on this domain. Building on existing results, we provide a two-step characterization": first, the median between the peaks and a collection of fixed values is computed (Moulin, 1980), resulting in either a single alternative or a pair of contiguous alternatives. If the outcome of the median is a pair, we apply a double-quota majority method" in the second step to choose between the two alternatives in the pair (Moulin, 1983). We also show the additional conditions that type-anonymity imposes on the strategy-proof rules characterized by Alcalde-Unzu et al. (2024). Finally, we show the equivalence between the two characterizations. |
| Date: | 2024–10 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2410.03387 |
| By: | Benjamin Balzer; Benjamin Young |
| Abstract: | We provide a model of endogenous perception of private information in single-agent screening problems. The agent's evaluation of their type is determined by their cognitive state: either sophisticated (i.e., they correctly perceive their type) or naive (i.e., they misperceive their type). The cognitive state depends on the mechanism's incentive structure via costly investment in cognition. Specifically, the agent is sophisticated only if their value of sophistication (i.e., the expected payoff difference between sophisticated and naive behavior) exceeds some cognitive cost. We impose no restrictions on the form of misperception when naive, allowing for both unbiased perceptions (i.e., information) as well as those generated in a biased manner. We derive a general representation of the value of sophistication, show how it varies with the mechanism's allocation rule, and use it to define a notion of accuracy in perception. In applications we showcase how perception both shapes and is shaped by the design of mechanisms. |
| Date: | 2024–09 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2409.19853 |
| By: | Javier Cembrano; Max Klimm; Arturo Merino |
| Abstract: | Impartial selection problems are concerned with the selection of one or more agents from a set based on mutual nominations from within the set. To avoid strategic nominations of the agents, the axiom of impartiality requires that the selection of each agent is independent of the nominations cast by that agent. This paper initiates the study of impartial selection problems where the nominations are weighted and the set of agents that can be selected is restricted by a combinatorial constraint. We call a selection mechanism $\alpha$-optimal if, for every instance, the ratio between the total sum of weighted nominations of the selected set and that of the best feasible set of agents is at least $\alpha$. We show that a natural extension of a mechanism studied for the selection of a single agent remains impartial and $\frac{1}{4}$-optimal for general independence systems, and we generalize upper bounds from the selection of multiple agents by parameterizing them by the girth of the independence system. We then focus on independence systems defined by knapsack and matroid constraints, giving impartial mechanisms that exploit a greedy order of the agents and achieve approximation ratios of $\frac{1}{3}$ and $\frac{1}{2}$, respectively, when agents cast a single nomination. For graphic matroids, we further devise an impartial and $\frac{1}{3}$-optimal mechanism for an arbitrary number of unweighted nominations. |
| Date: | 2024–09 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2409.20477 |
| By: | Andrzej Baranski; Sumit Goel |
| Abstract: | We study the classical contest design problem of allocating a budget across different prizes to maximize effort in a finite type-space environment. For any contest, we characterize the unique symmetric equilibrium. In this equilibrium, different agent types mix over contiguous intervals so that more efficient agents always exert greater effort than less efficient agents. We then solve for the expected equilibrium effort, and identify conditions under which the effect of increasing competition under linear costs is informative about the effect of such a transformation under general costs. As a result, we find that the winner-takes-all contest is optimal under linear and concave costs. Lastly, we obtain an equilibrium convergence result for the continuum type-space, and since the finite type-space encompasses the complete information environment as a special case, our analysis offers a unified approach to studying contests in these classical environments. |
| Date: | 2024–10 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2410.04970 |
| By: | Thành Nguyen (Purdue University); Rakesh Vohra (University of Pennsylvania) |
| Abstract: | Any mapping from states to signals induces a distribution over possible posteriors. For decision-making purposes, one is interested in parameters of those posteriors, such as their quartiles or whether they first-order stochastically dominate some given distribution. We show that a generalization of Gale’s demand theorem can be used to characterize which distributions over possible posteriors with the requisite properties can be generated by some mapping from states to signals. |
| Keywords: | Bayesian Persuasion, Information Design, Polymatroids |
| Date: | 2024–08–01 |
| URL: | https://d.repec.org/n?u=RePEc:pen:papers:24-025 |
| By: | Ryan Y. Lin; Siddhartha Ojha; Kevin Cai; Maxwell F. Chen |
| Abstract: | Machine-learning technologies are seeing increased deployment in real-world market scenarios. In this work, we explore the strategic behaviors of large language models (LLMs) when deployed as autonomous agents in multi-commodity markets, specifically within Cournot competition frameworks. We examine whether LLMs can independently engage in anti-competitive practices such as collusion or, more specifically, market division. Our findings demonstrate that LLMs can effectively monopolize specific commodities by dynamically adjusting their pricing and resource allocation strategies, thereby maximizing profitability without direct human input or explicit collusion commands. These results pose unique challenges and opportunities for businesses looking to integrate AI into strategic roles and for regulatory bodies tasked with maintaining fair and competitive markets. The study provides a foundation for further exploration into the ramifications of deferring high-stakes decisions to LLM-based agents. |
| Date: | 2024–09 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2410.00031 |
| By: | Javier Cembrano; Jos\'e Correa; Gonzalo D\'iaz; Victor Verdugo |
| Abstract: | How to elect the representatives in legislative bodies is a question that every modern democracy has to answer. This design task has to consider various elements so as to fulfill the citizens' expectations and contribute to the maintenance of a healthy democracy. The notion of proportionality, in that the support of a given idea in the house should be nearly proportional to its support in the general public, lies at the core of this design task. In the last decades, demographic aspects beyond political support have been incorporated by requiring that they are also fairly represented in the body, giving rise to a multidimensional version of the apportionment problem. In this work, we provide an axiomatic justification for a recently proposed notion of multidimensional proportionality and extend it to encompass two relevant constraints often used in electoral systems: a threshold on the number of votes that a list needs in order to be eligible and the election of the most-voted candidate in each district. We then build upon these results to design methods based on multidimensional proportionality. We use the Chilean Constitutional Convention election (May 15-16, 2021) results as a testing ground -- where the dimensions are given by political lists, districts, and genders -- and compare the apportionment obtained under each method according to three criteria: proportionality, representativeness, and voting power. While local and global methods exhibit a natural trade-off between local and global proportionality, including the election of most-voted candidates on top of methods based on 3-dimensional proportionality allows us to incorporate both notions while ensuring higher levels of representativeness and a balanced voting power. |
| Date: | 2024–10 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2410.03304 |
| By: | Marco LiCalzi (Dept. of Management, Venice School of Management, Università Ca' Foscari Venice); M. Alperen Yasar (Dept. of Economics, Università Ca' Foscari Venice and Panthéon-Sorbonne University) |
| Abstract: | A vocabulary is a list of words designating subsets of points from a grand set X. We model a vocabulary as a partition of X and study the aggregation of individual vocabularies into a collective one. We characterize aggregation rules when X is linearly ordered and each partition is formed by order intervals. Notably, we allow for individual vocabularies to differ both in the number and in the extension of their words. Under a suitable restriction on agents’ preferences, we show that our aggregation rules are strategy-proof. |
| Keywords: | collective judgement, ordinal scale of measurement, extended medians. |
| JEL: | D70 D83 Z13 |
| Date: | 2024–07 |
| URL: | https://d.repec.org/n?u=RePEc:vnm:wpdman:215 |
| By: | Esben Scrivers Andersen |
| Abstract: | We derive a system of fixed-point equations for the equilibrium transfers in a class of one-to-one matching models with linear transferable utility. We then show that, when the degree of substitution between alternatives is bounded from above, the derived system of equations constitutes a contraction mapping. As a result, fixed-point iterations are guaranteed to converge to the unique distribution of equilibrium transfers. |
| Date: | 2024–09 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2409.05518 |
| By: | Corgnet, Brice; DeSantis, Mark; Siemroth, Christoph |
| JEL: | C92 D61 G12 G14 G41 |
| Date: | 2024 |
| URL: | https://d.repec.org/n?u=RePEc:zbw:vfsc24:302411 |
| By: | Melo, Vitor; Rocha, Hugo Vaca Pereira; Sigaud, Liam; Warren, Patrick L.; Gaddis, S. Michael (NWEA) |
| Abstract: | We examine the extent and mechanisms by which race affects the college admissions process. We provide evidence from a field experiment where fictitious applicants request application fee waivers from all university admissions counselors in the United States. White applicants are much more likely to receive a waiver, be informed that the application is free, or receive a request for more information than Black or Asian applicants. Our results contrast sharply with previous evidence from acceptance decisions showing bias in favor of Black applicants. We introduce a model of university pricing and use information from counselors' LinkedIn and university profiles, along with university characteristics, to test predictions. We find evidence consistent with agent-taste-based discrimination, where biases stem from counselors' preferences, and profit-maximizing statistical discrimination. Discrimination in university admissions can vary substantially based on the context in which decisions are made. |
| Date: | 2024–10–04 |
| URL: | https://d.repec.org/n?u=RePEc:osf:socarx:5ctms |
| By: | Yang Sun; Wei Zhao; Junjie Zhou |
| Abstract: | We study dynamic network formation from a centralized perspective. In each period, the social planner builds a single link to connect previously unlinked pairs. The social planner is forward-looking, with instantaneous utility monotonic in the aggregate number of walks of various lengths. We show that, forming a nested split graph at each period is optimal, regardless of the discount function. When the social planner is sufficiently myopic, it is optimal to form a quasi-complete graph at each period, which is unique up to permutation. This finding provides a micro-foundation for the quasi-complete graph, as it is formed under a greedy policy. We also investigate the robustness of these findings under non-linear best response functions and weighted networks. |
| Date: | 2024–09 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2409.14136 |