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on Microeconomics |
| By: | Dirk Bergemann (Cowles Foundation, Yale University); Tibor Heumann (Pontificia Universidad Catolica de Chile); Stephen Morris (Dept. of Economics, MIT) |
| Abstract: | We analyze a nonlinear pricing model where the seller controls both product pricing (screening) and buyer information about their own values (persuasion). We prove that the optimal mechanism always consists of finitely many signals and items, even with a continuum of buyer values. The seller optimally pools buyer values and reduces product variety to minimize\ informational rents. We show that value pooling is optimal even for finite value distributions if their entropy exceeds a critical threshold. We also provide sufficient conditions under which the optimal menu restricts offering to a single item. |
| Keywords: | Nonlinear Pricing, Screening, Bayesian Persuasion, Finite Menu, Second-Degree Price Discrimination, Recommender System |
| JEL: | D44 D47 D83 D84 |
| Date: | 2025–03–06 |
| URL: | https://d.repec.org/n?u=RePEc:cwl:cwldpp:2338r3 |
| By: | Arkarup Basu Mallik (ISI Kolkata); Mihir Bhattacharya (Ashoka University) |
| Abstract: | We consider a model of preference aggregation when a single public good has to be chosen. We do not impose any restrictions on the preferences. We show the impossibility of contraction consistent (CC), anonymous and Pareto efficient social choice functions. We provide a characterization of the priority based social choice function (Priority Rule) which satisfies a weaker version of consistency called Efficient Dominance (ED). ED is a Weak Axiom of Revealed Preference (WARP) type of consistency criterion over the set of Pareto efficient alternatives. We show that the Priority Rule is the only social choice function that satisfies Pareto efficiency and Efficient Dominance. |
| Date: | 2025–03–06 |
| URL: | https://d.repec.org/n?u=RePEc:ash:wpaper:142 |
| By: | Dirk Bergemann (Yale University); Marek Bojko (Yale University); Paul DŸtting (Google Research); Renato Paes Leme (Google Research); Haifeng Xu (University of Chicago and Google Research); Song Zuo (Google Research) |
| Abstract: | We study mechanism design when agents have private preferences and private information about 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 affine 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: | 2025–03–17 |
| URL: | https://d.repec.org/n?u=RePEc:cwl:cwldpp:2418r1 |
| By: | Satyam Kumar Rai (Ashoka University); Suraj Shekhar (Ashoka University) |
| Abstract: | We model a society with two ethnic groups in which the state of the world is uncertain. Without new information, ethnic conflict is inevitable. If there is an informed agent who knows the state of the world and can communicate via private cheap talk messages, can she prevent conflict? We find that while a peace-loving informed agent is unable to prevent conflict as she cannot communicate credibly with either ethnicity, a more aggressive informed agent can communicate information to her own ethnicity, and therefore prevent conflict with positive probability. Furthermore, we show that if each ethnicity has their own informed agent, then both ethnic groups receive information but, under some conditions, there is an informative equilibrium in the environment with one informed agent which generates a higher probability of peace than any informative equilibrium with two informed agents. |
| Date: | 2025–03–11 |
| URL: | https://d.repec.org/n?u=RePEc:ash:wpaper:143 |
| By: | Aggey Simons (Department of Economics, University of Ottawa, Canada) |
| Abstract: | This paper characterizes optimal contract structures under adverse selection when the principal faces a general class of mixed (involving allocation and transfer) constraints. We establish conditions for the existence and the continuity of the optimal allocation. We show that under regularity conditions, the optimal continuous contract features at most three distinct regions: segments where the constraint is slack and the allocation follows a modified Baron-Myerson path, alternating with segments where the constraint binds. Assuming non-generic cases are excluded, the binding constraint forces a constant allocation (bunching) over a range of agent types. This framework encompasses a wide range of applications, including enforcement limits, budget constraints, and quality regulations. Our analysis demonstrates how bunching can arise endogenously from optimal design under smooth constraints, distinct from exogenously induced behavioural responses documented empirically. |
| Keywords: | Adverse Selection, Optimal Contracts, Mixed Constraints, Endogenous Bunching, Continuity, Allocation Dynamics |
| JEL: | C61 D82 D86 H21 L51 |
| Date: | 2025 |
| URL: | https://d.repec.org/n?u=RePEc:ott:wpaper:2502e |
| By: | Hiroshi Kitamura; Noriaki Matsushima; Misato Sato; Wataru Tamura |
| Abstract: | This study constructs a model of exclusive-offer competition between two existing upstream firms. Under exclusive-offer competition, the upstream firm's profit depends on the rival's exclusive offer. If the rival makes an exclusive offer acceptable for the downstream firm, the upstream firm is excluded unless it succeeds in exclusion. Consequently, the upper bound of exclusive offers becomes higher than when one of the upstream firms is a potential entrant that cannot make any exclusive offer. Thus, the exclusion of the existing upstream firm can be an equilibrium outcome even in the case where the potential entrant is never excluded. |
| Date: | 2025–03 |
| URL: | https://d.repec.org/n?u=RePEc:dpr:wpaper:1280 |
| By: | Arkarup Basu Mallik (ISI Kolkata); Mihir Bhattacharya (Ashoka University); Anuj Bhowmik (ISI Kolkata) |
| Abstract: | We provide a model of individual choice in which the decision maker is constrained and chooses from a subset of the available alternatives given a set of attributes. We introduce an attribute competition filter which provides conditions under which an alternative continues to be considered from a subset of alternatives and a subset of attributes. We use two axioms to characterize a rational choice function from the consideration sets, Single Reversal in Attributes (SRA) and Contraction Consistency with Fixed Attributes (CCFA). The former only allows for a single reversal in choice from a subset of the attributes, while the latter requires choices to be contraction consistent. We show that a choice function from consideration sets under attributes is rationalizable if and only if the choice function satisfies SRA and CCFA. In another section, we consider the dual problem: The alternatives considered are exogenously visible i.e. all the alternatives are considered and limited attention is paid to the attributes available while the preference relation is over the set of alternatives via individual attributes. JEL classification: D00, D01 |
| Keywords: | limited attention, attributes, choice reversals |
| Date: | 2024–11–27 |
| URL: | https://d.repec.org/n?u=RePEc:ash:wpaper:135 |
| By: | Müller, Lars (Center for Mathematical Economics, Bielefeld University); Karos, Dominik (Center for Mathematical Economics, Bielefeld University) |
| Abstract: | This paper analyzes the welfare effects of private and unilateral disclosure of sensi- tive information in a sequential bargaining context. We consider a model where two sellers each propose a take-it-or-leave-it price for a homogeneous good to a single buyer. The buyer accepts or rejects the first seller’s offer before the second seller proposes her price. Crucially, the second seller might learn the first seller’s price and whether it was accepted, allowing her to update her belief about the buyer’s willingness to pay and optimize her pricing strategy. The welfare effects caused by this information exchange are evaluated under general conditions. We show that it benefits the buyer if a rejection is revealed but might harm him if an acceptance is revealed. Additionally, the information exchange improves the societal welfare by reducing inefficiencies and promoting additional trade. This paper strengthens the theoretical framework for assessing the welfare effects of information exchanges by offering new insights and providing tools to assess causality for alleged damages. |
| Keywords: | Information Exchange, Collusion, Unawareness |
| Date: | 2025–04–16 |
| URL: | https://d.repec.org/n?u=RePEc:bie:wpaper:703 |
| By: | Sanyyam Khurana (Ashoka University) |
| Abstract: | In this paper, we consider resale in efficient auctions. The potential gains from trade arise from a delay in resale which reduces the bidders’ values. We consider two information states during resale: (a) complete information where all the bids are revealed and (b) incomplete information where no bids are revealed. Under complete information, we establish revenue equivalence between the first- and second-price auction for a family of trade rules where the market power is distributed between the reseller and buyer. We also show that, if all the market power lies with the reseller (resp., buyer), it is optimal (resp., not) to reveal information. |
| Keywords: | efficiency; information revelation; private value; resale; symmetry; time delay |
| Date: | 2024–10–14 |
| URL: | https://d.repec.org/n?u=RePEc:ash:wpaper:128 |
| By: | Matt Van Essen (Department of Economics, University of Tennessee); Ivan Anich (Department of Economics, University of Tennessee) |
| Abstract: | The classic Lindahl allocation in a public good economy is both Pareto efficient and individually rational. However, it is easy to generate examples where the Lindahl outcome violates our intuition about economic justice. We explore how a suitable generalization of Lindahl taxation can lead to fair outcomes. We alter Lindahl’s equilibrium approach so that consumers are given personalized price schedules for the public good (as opposed to simply personalized prices). The result is a special case of Mas-Colell and Silvestre’s cost share equilibrium. We show that any outcome on the individually rational Pareto frontier can be achieved by some generalized Lindahl equilibrium. We next set up an optimization problem to search for a “just” Lindahl equilibrium. A social welfare function is first used to select an outcome on the individually rational Pareto frontier. We then provide an algorithm to construct the price functions that induce the precise generalized Lindahl equilibrium that obtains this outcome. Finally, we present a mechanism that Nash implements the set of generalized Lindahl equilibria for our environment. |
| JEL: | C72 H21 H41 |
| URL: | https://d.repec.org/n?u=RePEc:ten:wpaper:2025-01 |
| By: | Brianna Alderman (Harvard University); Roger Blair (University of Florida); Javier Donna (University of Miami) |
| Abstract: | We study the Microsoft-Activision acquisition through the lens of a complementary-product merger. When two complementary good producers consolidate, the merger is not horizontal because the two firms do not produce substitutable goods. Nor is the merger vertical, as neither firm supplies the other. We develop an economic model to study these types of mergers that allows for the possibility of rivals exiting the market. Three main conclusions flow from our analysis. (1) The welfare effects of the Microsoft-Activision acquisition are ambiguous; they depend on several industry factors. (2) One will not obtain the correct welfare effects using an incorrect vertical structure; harm to consumers will typically be larger in a complementary-product merger relative to a vertical one. (3) Consumer harm associated with rivals’ exit due to the merger might substantially reduce welfare even if it is a welfare-enhancing merger absent exit. Our analysis provides an analytical roadmap for the antitrust enforcement authorities regarding the theories of harm in complementary-good mergers. |
| Keywords: | Antitrust, Competition Policy, Regulation, Complementary Mergers, Vertical Mergers, Merger Identification. |
| JEL: | K21 K41 L13 L42 L44 L52 |
| Date: | 2025–04 |
| URL: | https://d.repec.org/n?u=RePEc:aoz:wpaper:359 |
| By: | Dirk Bergemann (Yale University); Alessandro Bonatti (Massachusetts Institute of Technology); Nicholas Wu (Yale University) |
| Abstract: | In digital advertising, the allocation of sponsored search, sponsored product, or display advertisements is mediated by auctions. The generation of bids in these auctions for attention is increasingly supported by auto-bidding algorithms and platform-provided data. We analyze the equilibrium properties of a sequence of increasingly sophisticated auto-bidding algorithms. First, we consider the equilibrium bidding behavior of an individual advertiser who controls the auto bidding algorithm through the choice of their budget. Second, we examine the interaction when all bidders use budget-controlled bidding algorithms. Finally, we derive the bidding algorithm that maximizes the platformÕs revenue while ensuring all advertisers continue to participate. |
| Date: | 2025–03–02 |
| URL: | https://d.repec.org/n?u=RePEc:cwl:cwldpp:2429 |
| By: | Adriana Alventosa (ERI-CES, Universitat de València); José Manuel Ordóñez-de-Haro (Departamento de Teoría e Historia Económica. Universidad de Málaga.); Javier Rodero Cosano (Smart Decision Lab, Departamento de Teoría e Historia Económica. Universidad de Málaga.) |
| Abstract: | This paper develops a dynamic discrete-time model of collusive behaviour in which firms can apply for leniency to reduce fines. We propose a sequential-move game inspired by the centipede game, capturing firms' incentives to be the first to self-report a cartel. The model examines cartel formation, stability, and recidivism, assuming that fines apply to the undiscovered record of collusion, not just current conduct. We find that when collusion is attractive but the leniency programme is not sufficiently generous, firms form a single cartel without self-reporting. However, when collusion is highly attractive and the leniency programme sufficiently generous, it can destabilize cartels but also foster recidivism: firms use leniency to ``clean the slate'' and restart collusion at a lower expected cost. This equilibrium behaviour may help explain the empirically observed prevalence of short-lived cartels and repeat offenders under existing leniency regimes. |
| Keywords: | Antitrust; Cartels; Recidivism; Leniency; Dynamic Games |
| JEL: | D43 K21 K42 L40 |
| Date: | 2025–04 |
| URL: | https://d.repec.org/n?u=RePEc:mal:wpaper:2025-2 |
| By: | Arkarup Basu Mallik (ISI, Kolkata); Mihir Bhattacharya (Ashoka University); Anuj Bhowmik (ISI, Kolkata) |
| Abstract: | We consider an attribute-based model of stochastic choice with variable attention to different attributes. We characterize stochastic choice rules with attributes and limited attention (SCRALA). Under SCRALA, the probability with which an alternative (say, x) is chosen is the product of the probabilities with which attention is drawn by the attributes where x is ranked highest and the (weighted) probability with which attention is not drawn by the attributes under which x is not the highest ranked. Our results are characterized by axioms defined on observable choice data and all the attention parameters are uniquely identified. |
| Keywords: | attributes; limited attention; stochastic choice |
| Date: | 2024–08–23 |
| URL: | https://d.repec.org/n?u=RePEc:ash:wpaper:120 |
| By: | Chevalier-Roignant, Benoît; Villeneuve, Stéphane; Delpech, Fabien; Grapotte, May-Line |
| Abstract: | There are many business situations in which investments by a supplier and a producer (“coinvest-ments") are both necessary for either of them to grasp a business opportunity. For instance, better quality tanks are needed to manufacture reliable hydrogen-powered vehicles. One of these two firms, typically the one facing a lower cost, may be more willing to invest, but the cautionary attitude of the other delays the coinvestment. We model supply-chain interactions in a classical tractable way to derive the firms’ net present values (NPVs) upon coinvestment and determine their Nash equilibrium investment (timing) strategies. Firms coinvest when the real options of the weaker firm is ‘deep in the money.’ These business situations are likely to be affected by evolving market circumstances, in particular due to changes in the demand dynamics or endogenous decision (by, say, the supplier) to conduct research and development (R&D). We investigate related model extensions, which confirm the robustness of our key result. |
| Date: | 2025–04–09 |
| URL: | https://d.repec.org/n?u=RePEc:tse:wpaper:130510 |
| By: | Arthur Campbell (Department of Economics, Monash University, Australia); Geoffrey Go (Commonwealth Treasury, Australia); Chengsi Wang (Department of Economics, Monash University, Australia) |
| Abstract: | Content creators produce original work, while digital platforms share secondary versions to generate ad revenue, often without compensating them. This imbalance may reduce incentives for creating high-quality content, leading to government interventions aiming to re-balance the bargaining strengths. This paper examines how enhancing content creators' bargaining strength affects investments in primary and secondary content and subscription prices. While it directly boosts secondary content quality, the intervention's impact on primary content is ambiguous due to the opposite awareness and pricing effects. Cannibalization between primary and secondary contents may contribute to or impede quality improvement. These dynamics hold across subscription and advertising-based models and the analysis extends to two-sided investments. |
| Keywords: | advertising, online platforms, content sharing, journalism. |
| JEL: | L52 L82 |
| Date: | 2025–04 |
| URL: | https://d.repec.org/n?u=RePEc:mos:moswps:2025-04 |
| By: | Shinsuke Ikeda; Takeshi Ojima |
| Abstract: | Consumers often exhibit behavioral cycles with alternating abstinence and indulgence over time. In the framework of tempting good consumption under limited willpower, we develop a simple model of the self-control cycles. To do so, based on the empirically relevant property of self-control, we incorporate two countervailing effects that self-control behaviors have on willpower with different delays. First, exercising self-control as of restraining tempting consumption depletes willpower in the next instant, and thereby reduces mental capital available for self-control thereafter. Second, as the self-control experience is accumulated, the consumer's willpower is gradually enhanced. The resulting predator-prey type dynamics in consumers' cognitive mechanics lead to cycles in tempting good consumption. The self-control cycles occur when (i) the self-control cost reducing effect of willpower and (ii) the willpower enhancing effect of self-control are both sufficiently strong. |
| Date: | 2025–03 |
| URL: | https://d.repec.org/n?u=RePEc:dpr:wpaper:1277 |
| By: | Van-Quy Nguyen (Faculty of Mathematical Economics, National Economics University, Hanoi, Vietnam); Jean-Marc Bonnisseau (Université Paris 1 Panthéon-Sorbonne, Centre d'Economie de la Sorbonne, Paris School of Economics); Elena L. Del Mercato (Université Paris 1 Panthéon-Sorbonne, Centre d'Economie de la Sorbonne, Paris School of Economics) |
| Abstract: | We consider a pure exchange economy with consumption externalities in preferences. We study commodity taxes and lump-sum transfers schemes, which lead to equilibrium allocations where all individuals are strictly better off. We extend the result of Geanakoplos and Polemarchakis (2008) on the generic existence of Pareto im- proving policies with uniform taxes and equal transfers to general non-separable preferences, when the number of individuals is strictly smaller than the number of commodities. We overcome this limitation by considering either uniform taxes with personalized lump-sum transfers, or personalized taxes with uniform lump-sum transfers. As in Geanakoplos and Polemarchakis (2008), we mainly use utility perturbations. We also provide the existence of Pareto improving policies for Bergson-Samuelson utilities and two-individual economies, without perturbing utilities |
| Keywords: | Consumption externalities; commodity taxes; lump-sum transfers; Pareto improvement |
| JEL: | D50 D60 D62 |
| Date: | 2024–06 |
| URL: | https://d.repec.org/n?u=RePEc:mse:cesdoc:24007r |