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on Microeconomics |
| By: | Anton Kolotilin (School of Economics, UNSW); Alexander Wolitzky (Department of Economics, MIT) |
| Abstract: | We study the problem of a partisan gerrymanderer who assigns voters to equipopulous districts to maximize his party’s expected seat share. The designer faces both aggregate, district-level uncertainty (how many votes his party will receive) and idiosyncratic, voter-level uncertainty (which voters will vote for his party). Segregate-pair districting, where weaker districts contain one type of voter, while stronger districts contain two, is optimal for the gerrymanderer. The optimal form of segregate-pair districting depends on the designer’s popularity and the relative amounts of aggregate and idiosyncratic uncertainty. When idiosyncratic uncertainty dominates, a designer with majority support pairs all voters, while a designer with minority support segregates opposing voters and pairs more favorable voters; these plans resemble uniform districting and “packing-and-cracking, ” respectively. When aggregate uncertainty dominates, the designer segregates moderate voters and pairs extreme voters; this “matching slices” plan has received some attention in the literature. Estimating the model using precinct-level returns from recent US House elections shows that, in practice, idiosyncratic uncertainty dominates. We discuss implications for redistricting reform, political polarization, and detecting gerrymandering. Methodologically, we exploit a formal connection between gerrymandering—partitioning voters into districts—and information design—partitioning states of the world into signals. |
| Keywords: | Gerrymandering, pack-and-crack, segregate-pair, information design |
| JEL: | C78 D72 D82 |
| Date: | 2024–10 |
| URL: | https://d.repec.org/n?u=RePEc:swe:wpaper:2024-06 |
| By: | Axel Niemeyer; Justus Preusser |
| Abstract: | We study allocation problems without monetary transfers where agents hold private information about one another, modeled as a general form of correlated information. Such peer information is relevant in a number of settings, including science funding, allocation of targeted aid, or intra-firm allocation. We characterize optimal dominant-strategy incentive-compatible (DIC) mechanisms using techniques from the theory of perfect graphs. Optimal DIC mechanisms tend to be complex and involve allocation lotteries that cannot be purified without upsetting incentives. In rich type spaces, nearly all extreme points of the set of DIC mechanisms are stochastic. Finding an optimal deterministic DIC mechanism is NP-hard. We propose the simple class of ranking-based mechanisms and show that they are approximately optimal when agents are informationally small. These mechanisms allocate to agents ranked highly by their peers but strategically deny the allocation to agents suspected of having evaluated their peers dishonestly. |
| Date: | 2024–10 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2410.08954 |
| By: | Federica Carannante (Princeton University); Marco Pagnozzi (Università di Napoli Federico II and CSEF); Elia Sartori (CSEF) |
| Abstract: | We study the interim seller’s revenue — the expected revenue conditional on the valuation of one bidder — in a class of sealed-bid auctions that are ex-ante equivalent by the Revenue Equivalence Theorem. Interim revenue differences across auction formats depend on the expected transfer of a generic bidder conditional on a competitor’s valuation. The first-price auction yields higher (lower) interim revenue than the second-price auction if the valuation is below (above) a threshold. At the lowest possible valuation, the first-price auction also yields the highest interim revenue among all standard auctions. By contrast, at high valuations the first-price auction yields the lowest interim revenue, while the last-pay auction — an atypical mechanism where only the lowest bidder pays — allows the seller to extract arbitrarily large revenues. |
| Date: | 2024–07–01 |
| URL: | https://d.repec.org/n?u=RePEc:sef:csefwp:728 |
| By: | Joseph Feffer |
| Abstract: | This paper studies a simplicity notion in a mechanism design setting in which agents do not necessarily share a common prior. I develop a model in which agents participate in a prior-free game of (coarse) information acquisition followed by an auction. After acquiring information, the agents have uncertainty about the environment in which they play and about their opponents' higher-order beliefs. A mechanism admits a coarse beliefs equilibrium if agents can play best responses even with this uncertainty. Focusing on multidimensional scoring auctions, I fully characterize a property that allows an auction format to admit coarse beliefs equilibria. The main result classifies auctions into two sets: those in which agents learn relatively little about their setting versus those in which they must fully learn a type distribution to form equilibrium strategies. I then find a simple, primitive condition on the auction's rules to distinguish between these two classes. I then use the condition to categorize real-world scoring auctions by their strategic simplicity. |
| Date: | 2024–10 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2410.06150 |
| By: | Tao Lin; Ce Li |
| Abstract: | Classical information design models (e.g., Bayesian persuasion and cheap talk) require players to have perfect knowledge of the prior distribution of the state of the world. Our paper studies repeated persuasion problems in which the information designer does not know the prior. The information designer learns to design signaling schemes from repeated interactions with the receiver. We design learning algorithms for the information designer to achieve no regret compared to using the optimal signaling scheme with known prior, under two models of the receiver's decision-making. (1) The first model assumes that the receiver knows the prior and can perform posterior update and best respond to signals. In this model, we design a learning algorithm for the information designer with $O(\log T)$ regret in the general case, and another algorithm with $\Theta(\log \log T)$ regret in the case where the receiver has only two actions. (2) The second model assumes that the receiver does not know the prior and employs a no-regret learning algorithm to take actions. We show that the information designer can achieve regret $O(\sqrt{\mathrm{rReg}(T) T})$, where $\mathrm{rReg}(T)=o(T)$ is an upper bound on the receiver's learning regret. Our work thus provides a learning foundation for the problem of information design with unknown prior. |
| Date: | 2024–10 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2410.05533 |
| By: | Emir Kamenica (University of Chicago); Xiao Lin (University of Pennsylvania) |
| Abstract: | When does a Sender, in a Sender-Receiver game, strictly value commitment? In a setting with finite actions and finite states, we establish that, generically, Sender values commitment if and only if he values randomization. In other words, commitment has no value if and only if a partitional experiment is optimal under commitment. Moreover, if Sender’s preferred cheap-talk equilibrium necessarily involves randomization, then Sender values commitment. We also ask: how often (i.e., for what share of preference profiles) does commitment have no value? For any prior, any independent, atomless distribution of preferences, and any state space: if there are |A| actions, the likelihood that commitment has no value is at least 1 |A||A| . As the number of states grows large, this likelihood converges precisely to 1 |A||A| . |
| Keywords: | Bayesian persuasion; cheap talk |
| JEL: | D80 D83 |
| Date: | 2024–10–01 |
| URL: | https://d.repec.org/n?u=RePEc:pen:papers:24-033 |
| By: | Alessandro Lizzeri (Princeton University and NBER); Eran Shmaya (State University of New York at Stony Brook); Leeat Yariv (Princeton University, CEPR, and NBER) |
| Abstract: | Starting from Robbins (1952), the literature on experimentation via multi-armed bandits has wed exploration and exploitation. Nonetheless, in many applications, agents’ exploration and exploitation need not be intertwined: a policymaker may assess new policies different than the status quo; an investor may evaluate projects outside her portfolio. We characterize the optimal experimentation policy when exploration and exploitation are disentangled in the case of Poisson bandits, allowing for general news structures. The optimal policy features complete learning asymptotically, exhibits lots of persistence, but cannot be identified by an index à la Gittins. Disentanglement is particularly valuable for intermediate parameter values. |
| Keywords: | Exploration and Exploitation, Poisson Bandits |
| JEL: | C73 D81 D83 O35 |
| Date: | 2024–04 |
| URL: | https://d.repec.org/n?u=RePEc:pri:cepsud:334 |
| By: | Xiaoyu Cheng; Peter Klibanoff; Sujoy Mukerji; Ludovic Renou |
| Abstract: | This paper explores whether and to what extent ambiguous communication can be beneficial to the sender in a persuasion problem, when the receiver (and possibly the sender) is ambiguity averse. We provide a concavification-like characterization of the sender's optimal ambiguous communication. The characterization highlights the necessity of using a collection of experiments that form a splitting of an obedient experiment, that is, whose recommendations are incentive compatible for the receiver. At least some of the experiments in the collection must be Pareto-ranked in the sense that both the sender and receiver agree on their payoff ranking. The existence of a binary such Pareto-ranked splitting is necessary for ambiguous communication to benefit the sender, and, if an optimal Bayesian persuasion experiment can be split in this way, this is sufficient for an ambiguity-neutral sender as well as the receiver to benefit. We show such gains are impossible when the receiver has only two actions available. Such gains persist even when the sender is ambiguity averse, as long as not too much more so than the receiver and not infinitely averse. |
| Date: | 2024–10 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2410.05504 |
| By: | Sanxi Li; Jun Yu; Mingsheng Zhang |
| Abstract: | Search prominence may have a detrimental impact on a firm's profits in the presence of costly product returns. We analyze the impact of search prominence on firm profitability in a duopoly search model, considering the presence of costly product returns. Consumer match values are assumed to be independently and identically distributed across the two products. Our results show that the non-prominent firm benefits from facing consumers with relatively low match values for the prominent firm's products, thus avoiding costly returns. When return costs are sufficiently high, the prominent firm may earn lower profits than its non-prominent competitor. This outcome holds under both price exogeneity and price competition. Furthermore, the profitability advantage of prominence diminishes as return costs increase. Platforms that maximize ad revenue should consider retaining positive return cost for consumers rather than fully passing it on to firms. For e-commerce platforms, it is crucial to align product return policies with broader management objectives to optimize firm profitability. |
| Date: | 2024–10 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2410.06791 |
| By: | Reimer, Julia |
| JEL: | L42 D42 D43 D82 |
| Date: | 2024 |
| URL: | https://d.repec.org/n?u=RePEc:zbw:vfsc24:302444 |
| By: | Meisner, Vincent; Pillath, Pascal |
| JEL: | D82 |
| Date: | 2024 |
| URL: | https://d.repec.org/n?u=RePEc:zbw:vfsc24:302417 |
| By: | Cuimin Ba (University of Pittsburgh); J. Aislinn Bohren (University of Pennsylvania); Alex Imas (University of Chicago) |
| Abstract: | This paper explores how cognitive constraints—namely, attention and processing capacity—interact with properties of the learning environment to determine how people react to information. In our model, people form a simplified mental representation of the environment via salience-channeled attention, then process information with cognitive imprecision. The model predicts overreaction to information when environments are complex, signals are noisy, information is surprising, or priors are concentrated on less salient states; it predicts underreaction when environments are simple, signals are precise, information is expected, or priors are concentrated on salient states. Results from a series of pre-registered experiments provide support for these predictions and direct evidence for the proposed cognitive mechanisms. We show that the two psychological mechanisms act as cognitive complements: their interaction is critical for explaining belief data and together they yield a highly complete model in terms of capturing explainable variation in belief-updating. Our theoretical and empirical results connect disparate findings in prior work: underreaction is typically found in laboratory studies, which feature simple learning settings, while overreaction is more prevalent in financial markets which feature greater complexity. |
| Keywords: | overreaction, underreaction, beliefs, noisy cognition, representativeness, bounded rationality, attention, mental representation, completeness, restrictiveness, behavioral economics, learning, forecasting, inference |
| Date: | 2024–08–29 |
| URL: | https://d.repec.org/n?u=RePEc:pen:papers:24-030 |