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on Microeconomics |
| By: | Philippe Jehiel; Aviman Satpathy |
| Abstract: | We introduce the Coarse Payoff-Assessment Learning (CPAL) model, which captures reinforcement learning by boundedly rational decision-makers who focus on the aggregate outcomes of choosing among exogenously defined clusters of alternatives (similarity classes), rather than evaluating each alternative individually. Analyzing a smooth approximation of the model, we show that the learning dynamics exhibit steady-states corresponding to smooth Valuation Equilibria (Jehiel and Samet, 2007). We demonstrate the existence of multiple equilibria in decision trees with generic payoffs and establish the local asymptotic stability of pure equilibria when they occur. Conversely, when trivial choices featuring alternatives within the same similarity class yield sufficiently high payoffs, a unique mixed equilibrium emerges, characterized by indifferences between similarity classes, even under acute sensitivity to payoff differences. Finally, we prove that this unique mixed equilibrium is globally asymptotically stable under the CPAL dynamics. |
| Date: | 2024–12 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2412.09321 |
| By: | Marie Laclau (HEC Paris - Ecole des Hautes Etudes Commerciales, CNRS - Centre National de la Recherche Scientifique); Ludovic Renou (QMUL - Queen Mary University of London); Xavier Venel (LUISS - Libera Università Internazionale degli Studi Sociali Guido Carli [Roma]) |
| Abstract: | We consider sender-receiver games, where the sender and the receiver are two distant nodes in a communication network. We show that if the network has two disjoint paths of communication between the sender and the receiver, then we can replicate all equilibrium outcomes not only of the direct communication game (i.e., when the sender and the receiver communicate directly with each other) but also of the mediated game (i.e., when the sender and the receiver communicate with the help of a mediator). |
| Keywords: | Cheap talk, direct, mediated, communication, protocol, network |
| Date: | 2024–04 |
| URL: | https://d.repec.org/n?u=RePEc:hal:journl:hal-04836057 |
| By: | Joshua S. Gans |
| Abstract: | This is a paper in the ``economists ruin everything'' field. It considers whether Catch-22 situations can persist as an equilibrium phenomenon. Rather than being an arbitrary rule or a set of self-serving beliefs, the focus is on the preferences of Gatekeepers who choose to create such situations in the first place. The base game-theoretic model is of a Catch-22 situation inspired by Heller's famous paradox. We consider a Requester who may be Sane or Insane and a Gatekeeper who must decide whether to grant the Requester's desired outcome or force them into a less desirable one. This is modelled as a game in which the Requester chooses whether to send a request signal before the Gatekeeper decides. We solve for the conditions under which a Catch-22 situation persists as an equilibrium and its efficiency properties. It is demonstrated that Catch-22 situations can arise, but they reflect an efficient response on the part of a Gatekeeper facing asymmetric information. An application to labour markets is also considered |
| JEL: | C72 D82 |
| Date: | 2024–12 |
| URL: | https://d.repec.org/n?u=RePEc:nbr:nberwo:33304 |
| By: | Stefano Colombo; Paolo G. Garella; Noriaki Matsushima |
| Abstract: | We analyze behavior-based price discrimination (BBPD) where consumers choose between being identified (e.g., by opting in) or remaining anonymous, as opposed to mandatory opt-in. Opting in provides consumers with benefits but also enables firms to apply history-dependent pricing. Under voluntary opt-in, market segmentation becomes more fragmented compared to standard BBPD. Consumer surplus and social welfare are higher with voluntary opt-in, while firm profits increase under mandatory opt-in. However, if consumers heavily discount the future and firms are forward-looking, these results may reverse entirely. Our result implies that policymakers can ensure that consumers retain control over their data along with encouraging them to adopt a more forward-looking perspective. |
| Date: | 2023–11 |
| URL: | https://d.repec.org/n?u=RePEc:dpr:wpaper:1219r |
| By: | Dirk Bergemann; Marek Bojko; Paul D\"utting; Renato Paes Leme; Haifeng Xu; Song Zuo |
| Abstract: | We study mechanism design when agents hold private information about both their preferences and a common payoff-relevant state. We show that standard message-driven mechanisms cannot implement socially efficient allocations when agents have multidimensional types, even under favorable conditions. To overcome this limitation, we propose data-driven mechanisms that leverage additional post-allocation information, modeled as an estimator of the payoff-relevant state. Our data-driven mechanisms extend the classic Vickrey-Clarke-Groves class. We show that they achieve exact implementation in posterior equilibrium when the state is either fully revealed or the utility is linear in an unbiased estimator. We also show that they achieve approximate implementation with a consistent estimator, converging to exact implementation as the estimator converges, and present bounds on the convergence rate. We demonstrate applications to digital advertising auctions and large language model (LLM)-based mechanisms, where user engagement naturally reveals relevant information. |
| Date: | 2024–12 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2412.16132 |
| By: | Felix Brandt; Patrick Lederer |
| Abstract: | An important -- but very demanding -- property in collective decision-making is strategyproofness, which requires that voters cannot benefit from submitting insincere preferences. Gibbard (1977) has shown that only rather unattractive rules are strategyproof, even when allowing for randomization. However, Gibbard's theorem is based on a rather strong interpretation of strategyproofness, which deems a manipulation successful if it increases the voter's expected utility for at least one utility function consistent with his ordinal preferences. In this paper, we study weak strategyproofness, which deems a manipulation successful if it increases the voter's expected utility for all utility functions consistent with his ordinal preferences. We show how to systematically design attractive, weakly strategyproof social decision schemes (SDSs) and explore their limitations for both strict and weak preferences. In particular, for strict preferences, we show that there are weakly strategyproof SDSs that are either ex post efficient or Condorcet-consistent, while neither even-chance SDSs nor pairwise SDSs satisfy both properties and weak strategyproofness at the same time. By contrast, for the case of weak preferences, we discuss two sweeping impossibility results that preclude the existence of appealing weakly strategyproof SDSs. |
| Date: | 2024–12 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2412.11977 |
| By: | Yingni Guo; Hao Li; Xianwen Shi |
| Abstract: | A seller of an indivisible good designs a selling mechanism for a buyer whose private information (his type) is the distribution of his value for the good. A selling mechanism includes both a menu of sequential pricing, and a menu of information disclosure about the realized value that the buyer is allowed to learn privately. In a model of two types with an increasing likelihood ratio, we show that under some regularity conditions the disclosure policy in an optimal mechanism has a nested interval structure: the high type is allowed to learn whether his value is greater than the seller's cost, while the low type is allowed to learn whether his value is in an interval above the cost. The interval of the low type may exclude values at the top of the distribution to reduce the information rent of the high type. Information discrimination is in general necessary in an optimal mechanism. |
| Keywords: | Sequential Screening, Dynamic Mechanism Design, Disclosure, Information Design |
| JEL: | D83 D82 |
| Date: | 2025–01–16 |
| URL: | https://d.repec.org/n?u=RePEc:tor:tecipa:tecipa-792 |
| By: | Ying Xue Li; Burkhard C. Schipper |
| Abstract: | When bidders bid on complex objects, they might be unaware of characteristics effecting their valuations. We assume that each buyer's valuation is a sum of independent random variables, one for each characteristic. When a bidder is unaware of a characteristic, he omits the random variable from the sum. We study the seller's decision to raise bidders' awareness of characteristics before a second-price auction with entry fees. Optimal entry fees capture an additional unawareness rent due to unaware bidders misperceiving their probability of winning and the price to be paid upon winning. When raising a bidder's individual awareness of a characteristic with positive expected value, the seller faces a trade-off between positive effects on the expected first order statistic and unawareness rents of remaining unaware bidders on one hand and the loss of the unawareness rent from the newly aware bidder on the other. We present characterization results on raising public awareness together with no versus full information. We discuss the winner's curse due to unawareness of characteristics. |
| Date: | 2024–12 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2412.12676 |
| By: | Alexei Parakhonyak; Andrew Rhodes |
| Abstract: | We consider a model in which consumers wish to buy a product repeatedly over time, but need to engage in costly search to learn prices and find a product that matches them well. The optimal search rule has two reservation values, one for newly-searched products, and another for products that were searched in the past. Depending on the search cost, firms either keep price steady over time, or gradually raise price to take advantage of a growing pool of high-valuation repeat customers. The model generates rich search and purchase dynamics, as consumers may optimally “stagger” search over time, initially trying different products, settling on one and buying it for a while, before choosing to search again for something better. We also show that consumers may be better off when firms can offer personalized prices based on their search history. |
| Date: | 2024–12–20 |
| URL: | https://d.repec.org/n?u=RePEc:oxf:wpaper:1066 |
| By: | Yanlin Chen; Xianwen Shi; Jun Zhang |
| Abstract: | We study the welfare effects of price discrimination in a duopoly market with both captive and contested consumers. Using a unified information design approach, we characterize the best and worst market segmentations for producer surplus, consumer surplus, and social surplus. The firm-optimal segmentation, which divides the market into two nested segments, consistently harms consumers compared to uniform pricing. The consumer-optimal segmentation, which divides the market into a symmetric segment and a nested segment, sometimes leads to a Pareto improvement. Social surplus, if monotone in firm profit, is often maximized either by the firm-optimal or consumer-optimal segmentation. |
| Keywords: | Information Design, Market Segmentation, Firm-optimal Segmentation, Consumer-optimal Segmentation |
| JEL: | D43 D82 |
| Date: | 2025–01–16 |
| URL: | https://d.repec.org/n?u=RePEc:tor:tecipa:tecipa-790 |
| By: | Anton Kolotilin; Hongyi Li; Andriy Zapechelnyuk |
| Abstract: | We study monotone persuasion in the linear case, where posterior distributions over states are summarized by their mean. We solve the two leading cases where optimal unrestricted signals can be nonmonotone. First, if the objective is s-shaped and the state is discrete, then optimal monotone signals are upper censorship, whereas optimal unrestricted signals may require randomization. Second, if the objective is m-shaped and the state is continuous, then optimal monotone signals are interval disclosure, whereas optimal unrestricted signals may require nonmonotone pooling. We illustrate our results with an application to media censorship. |
| Date: | 2024–12 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2412.14400 |
| By: | Jean-Michel Benkert; Ludmila Matyskova; Egor Starkov |
| Abstract: | A researcher allocates a budget of informative tests across multiple unknown attributes to influence a decision-maker. We derive the researcher's equilibrium learning strategy by solving an auxiliary single-player problem. The attribute weights in this problem depend on how much the researcher and the decision-maker disagree. If the researcher expects an excessive response to new information, she forgoes learning altogether. In an organizational context, we show that a manager favors more diverse analysts as the hierarchical distance grows. In another application, we show how an appropriately opposed advisor can constrain a discriminatory politician, and identify the welfare-inequality Pareto frontier of researchers. |
| Date: | 2024–12 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2412.10024 |
| By: | Mridu Prabal Goswami |
| Abstract: | We consider an economic environment with one buyer and one seller. For a bundle $(t, q)\in [0, \infty[\times [0, 1]=\mathbb{Z}$, $q$ refers to the winning probability of an object, and $t$ denotes the payment that the buyer makes. We consider continuous and monotone preferences on $\mathbb{Z}$ as the primitives of the buyer. These preferences can incorporate both quasilinear and non-quasilinear preferences, and multidimensional pay-off relevant parameters. We define rich single-crossing subsets of this class 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 for mechanisms with finite range. 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 in the space $\mathbb{Z}$. We also provide an extension of our analysis to an $n-$buyer environment, and to the situation where $q$ is a qualitative variable. |
| Date: | 2024–12 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2412.11113 |
| By: | Mikhail Drugov; Dmitry Ryvkin; Jun Zhang |
| Abstract: | We study tournaments where winning a rank-dependent prize requires passing a minimum performance standard. We show that, for any prize allocation, the optimal standard is always at a mode of performance that is weakly higher than the global mode and identify a necessary and sufficient condition for it to be at the global mode. When the prize scheme can be designed as well, the winner-take-all prize scheme is optimal for noise distributions with an increasing failure rate; and awarding equal prizes to all qualifying agents is optimal for noise distributions with a decreasing failure rate. For distributions with monotone likelihood ratios -- log-concave and log-convex, respectively -- these pay schemes are also optimal in a larger class of anonymous, monotone contracts that may depend on cardinal performance. |
| Date: | 2024–12 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2412.01139 |
| By: | Wade Hann-Caruthers; Minghao Pan; Omer Tamuz |
| Abstract: | We consider a group of agents who can each take an irreversible costly action whose payoff depends on an unknown state. Agents learn about the state from private signals, as well as from past actions of their social network neighbors, which creates an incentive to postpone taking the action. We show that outcomes depend on network structure: on networks with a linear structure patient agents do not converge to the first-best action, while on regular directed tree networks they do. |
| Date: | 2024–12 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2412.07061 |
| By: | Itai Arieli; Yakov Babichenko; Dima Shaiderman; Xianwen Shi |
| Abstract: | We propose a dynamic persuasion model of product adoption, where an impatient, long-lived sender commits to a dynamic disclosure policy to persuade a sequence of short-lived receivers to adopt a new product. The sender privately observes a sequence of signals, one per period, about the product quality, and therefore the sequence of her posteriors forms a discrete-time martingale. The disclosure policy specifies ex ante how the sender's information will be revealed to the receivers in each period. We introduce a new concept called ``Blackwell-preserving kernels'' and show that if the sender's belief martingale possesses these kernels, the family of optimal strategies for the sender takes an interval form; namely, in every period, the set of martingale realizations in which adoption occurs is an interval. Utilizing this, we prove that if the sender is sufficiently impatient, then under a random walk martingale, the optimal policy is fully transparent up to the moment of adoption; namely, the sender reveals all the information she privately holds in every period. |
| Keywords: | Dynamic Information Design, Bayesian Persuasion, Learning |
| JEL: | D83 D82 |
| Date: | 2025–01–16 |
| URL: | https://d.repec.org/n?u=RePEc:tor:tecipa:tecipa-791 |
| By: | Wesley H. Holliday |
| Abstract: | We propose a model of unawareness that remains close to the paradigm of Aumann's model for knowledge [R. J. Aumann, International Journal of Game Theory 28 (1999) 263-300]: just as Aumann uses a correspondence on a state space to define an agent's knowledge operator on events, we use a correspondence on a state space to define an agent's awareness operator on events. This is made possible by three ideas. First, like the model of [A. Heifetz, M. Meier, and B. Schipper, Journal of Economic Theory 130 (2006) 78-94], ours is based on a space of partial specifications of the world, partially ordered by a relation of further specification or refinement, and the idea that agents may be aware of some coarser-grained specifications while unaware of some finer-grained specifications; however, our model is based on a different implementation of this idea, related to forcing in set theory. Second, we depart from a tradition in the literature, initiated by [S. Modica and A. Rustichini, Theory and Decision 37 (1994) 107-124] and adopted by Heifetz et al. and [J. Li, Journal of Economic Theory 144 (2009) 977-993], of taking awareness to be definable in terms of knowledge. Third, we show that the negative conclusion of a well-known impossibility theorem concerning unawareness in [Dekel, Lipman, and Rustichini, Econometrica 66 (1998) 159-173] can be escaped by a slight weakening of a key axiom. Together these points demonstrate that a correspondence on a partial-state space is sufficient to model unawareness of events. Indeed, we prove a representation theorem showing that any abstract Boolean algebra equipped with awareness, knowledge, and belief operators satisfying some plausible axioms is representable as the algebra of events arising from a partial-state space with awareness, knowledge, and belief correspondences. |
| Date: | 2024–12 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2412.00897 |
| By: | Hao Li; Xianwen Shi |
| Abstract: | We study when and how randomization can help improve the seller's revenue in the sequential screening setting. In a model with discrete ex ante types and a continuum of ex post valuations, the standard approach based on solving a relaxed problem that keeps only local downward incentive compatibility constraints often fails. Under a strengthening of first-order stochastic dominance ordering on the valuation distribution functions of ex ante types, we introduce and solve a modified relaxed problem by retaining all local incentive compatibility constraints, provide necessary and sufficient conditions for optimal mechanisms to be stochastic, and characterize optimal stochastic contracts. Our analysis mostly focuses on the case of three ex ante types, but our methodology of solving the modified problem, as well as the necessary and sufficient conditions for randomization to be optimal, can be extended to any finite number of ex ante types. |
| Keywords: | Sequential Screening, Stochastic Mechanism |
| JEL: | D83 D82 |
| Date: | 2025–01–16 |
| URL: | https://d.repec.org/n?u=RePEc:tor:tecipa:tecipa-793 |