
on Microeconomics 
By:  Pierpaolo Battigalli; Emiliano Catonini 
Abstract:  We study strategic reasoning in a signaling game where players have common belief in an outcome distribution and in the event that the receiver believes that the sender's firstorder beliefs are independent of her payofftype. We characterize the behavioral implications of these epistemic hypotheses through a rationalizability procedure with secondorder belief restrictions. Our solution concept is related to, but weaker than Divine Equilibrium (Banks and Sobel, 1987). First, we do not obtain sequential equilibrium, but just Perfect Bayesian Equilibrium with heterogeneous offpath beliefs (Fudenberg and He, 2018). Second, when we model how the receiver may rationalize a particular deviation, we take into account that some types could have preferred a different deviation, and we show this is natural and relevant via an economic example. 
Date:  2022 
URL:  http://d.repec.org/n?u=RePEc:igi:igierp:681&r=mic 
By:  Sophie Bade; Joseph Root 
Abstract:  We study the set of incentive compatible and efficient twosided matching mechanisms. We classify all such mechanisms under an additional assumption  "genderneutrality"  which guarantees that the two sides be treated symmetrically. All group strategyproof, efficient and genderneutral mechanisms are recursive and the outcome is decided in a sequence of rounds. In each round, two agents are selected, one from each side. These agents are either "matchedbydefault" or "unmatchedbydefault." In the former case either of the selected agents can unilaterally force the other to match with them while in the latter case they may only match together if both agree. In either case, if this pair of agents is not matched together, each gets their top choice among the set of remaining agents. As an important step in the characterization, we first show that in onesided matching all group strategyproof and efficient mechanisms are sequential dictatorships. An immediate corollary is that there are no individually rational, group strategyproof and efficient onesided matching mechanisms. 
Date:  2023–01 
URL:  http://d.repec.org/n?u=RePEc:arx:papers:2301.13037&r=mic 
By:  Taylor, Greg 
Abstract:  We study the profitability of bundling by an upstream firm who licenses complementary technologies to downstream competitors, and who faces a superior competitor for one of its technologies. In an otherwise standard “Chicagostyle” model, we show that the existence of downstream competition can make inefficient bundling profitable. Forcing downstream firms to use a less efficient technology can soften competition, thus allowing the upstream firm to extract more profit through the licensing of its monopolized technology. Bundling is more likely to be profitable if downstream competition is intense and if technologies are strongly complementary. The mechanism requires a public commitment to bundling (e.g. technical bundling) and the unobservability of the contracts offered to downstream firms. A similar logic can make it profitable for the upstream firm to degrade the interoperability between its technologies and those of its rivals, even without foreclosing competition. 
Date:  2023–01–31 
URL:  http://d.repec.org/n?u=RePEc:tse:wpaper:21904&r=mic 
By:  Schmitz, Patrick W. 
Abstract:  A principal wants an agent to exert unobservable research effort. Ruling out negative payments implies that (i) the principal cannot punish bad outcomes and (ii) she cannot extract rents. We disentangle these two effects by allowing the principal to place verifiable teaching duties on the agent. In the first scenario, the principal can punish the agent with completely unproductive teaching duties conditional on bad research outcomes. In the second scenario, the agent is forced to teach regardless of research outcomes, though his teaching disutility is larger than the principal's benefit. Each of the two scenarios may involve higher research efforts. 
Keywords:  moral hazard; limited liability; hidden action; incentive contracts; job design 
JEL:  D86 
Date:  2023 
URL:  http://d.repec.org/n?u=RePEc:pra:mprapa:116220&r=mic 
By:  Francesco Caruso (Università di Napoli Federico II); Maria Carmela Ceparano (Università di Napoli Federico II); Jacqueline Morgan (Università di Napoli Federico II and CSEF) 
Abstract:  The study on how equilibria behave when perturbations occur in the data of a game is a fundamental theme, since actions and payoffs of the players may be affected by uncertainty or trembles. In this paper we investigate the asymptotic behavior of the subgame perfect Nash equilibrium (SPNE) in oneleader onefollower Stackelberg games under perturbations both of the action sets and of the payoff functions. To pursue this aim, we consider a general sequence of perturbed Stackelberg games and a set of assumptions that fit the usual types of perturbations. We study if the limit of SPNEs of the perturbed games is an SPNE of the original game and if the limit of SPNE outcomes of perturbed games is an SPNE outcome of the original game. We fully positively answer when the follower’s best reply correspondence is single valued. When the follower’s best reply correspondence is not single valued, the answer is positive only for the SPNEs outcomes; whereas the answer for SPNEs may be negative, even if the perturbation does not affect the sets and affects only one payoff function. However, we show that under suitable nonrestrictive assumptions it is possible to obtain an SPNE starting from the limit of SPNEs of perturbed games, possibly modifying the limit at just one point. 
Keywords:  Subgame perfect Nash equilibrium twoplayer Stackelberg game; action and/or payoff perturbation; convergence; asymptotic behavior; variational stability. 
URL:  http://d.repec.org/n?u=RePEc:sef:csefwp:661&r=mic 
By:  MengJhang Fong; PoHsuan Lin; Thomas R. Palfrey 
Abstract:  This paper develops a framework to extend the strategic form analysis of cursed equilibrium (CE) developed by Eyster and Rabin (2005) to multistage games. The approach uses behavioral strategies rather than normal form mixed strategies, and imposes sequential rationality. We define cursed sequential equilibrium (CSE) and compare it to sequential equilibrium and standard normalform CE. We provide a general characterization of CSE and establish its properties. We apply CSE to five applications in economics and political science. These applications illustrate a wide range of differences between CSE and Bayesian Nash equilibrium or CE: in signaling games; games with preplay communication; reputation building; sequential voting; and the dirty faces game where higher order beliefs play a key role. A common theme in several of these applications is showing how and why CSE implies systematically different behavior than Bayesian Nash equilibrium in dynamic games of incomplete information with private values, while CE coincides with Bayesian Nash equilibrium for such games. 
Date:  2023–01 
URL:  http://d.repec.org/n?u=RePEc:arx:papers:2301.11971&r=mic 
By:  Lorenzo Stanca 
Abstract:  A major concern with Bayesian decision making under uncertainty is the use of a single probability measure to quantify all relevant uncertainty. This paper studies prior robustness as a form of continuity of the value of a decision problem. It is shown that this notion of robustness is characterized by a form of stable choice over a sequence of perturbed decision problems, in which the available acts are perturbed in a precise fashion. Subsequently, a choicebased measure of prior robustness is introduced and applied to portfolio choice and climate mitigation. 
Keywords:  Risk, Uncertainty, Robustness, Ambiguity, Robust statistics, Prior selection. 
Date:  2023 
URL:  http://d.repec.org/n?u=RePEc:cca:wpaper:690&r=mic 
By:  David Spector (PSE  Paris School of Economics  UP1  Université Paris 1 PanthéonSorbonne  ENSPSL  École normale supérieure  Paris  PSL  Université Paris sciences et lettres  EHESS  École des hautes études en sciences sociales  ENPC  École des Ponts ParisTech  CNRS  Centre National de la Recherche Scientifique  INRAE  Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement, PJSE  Paris Jourdan Sciences Economiques  UP1  Université Paris 1 PanthéonSorbonne  ENSPSL  École normale supérieure  Paris  PSL  Université Paris sciences et lettres  EHESS  École des hautes études en sciences sociales  ENPC  École des Ponts ParisTech  CNRS  Centre National de la Recherche Scientifique  INRAE  Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement) 
Abstract:  Many collusive agreements involve the exchange of selfreported sales data between competitors, which use them to monitor compliance with a target market share allocation. Such communication may facilitate collusion even if it is unverifiable cheap talk and the underlying information becomes publicly available with a delay. The exchange of sales information may allow firms to implement incentivecompatible market share reallocation mechanisms after unexpected swings, limiting the recourse to price wars. Such communication may allow firms to earn profits that could not be earned in any collusive, symmetric purestrategy equilibrium without communication. 
Date:  2022–03 
URL:  http://d.repec.org/n?u=RePEc:hal:journl:halshs03760756&r=mic 
By:  Ingela Alger (TSER  Toulouse School of Economics  UT1  Université Toulouse 1 Capitole  Université Fédérale Toulouse MidiPyrénées  EHESS  École des hautes études en sciences sociales  CNRS  Centre National de la Recherche Scientifique  INRAE  Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement); JeanFrançois Laslier (Unknown) 
Abstract:  This paper revisits two classical problems in the theory of voting—viz. the divided majority problem and the strategic revelation of information—in the light of evolutionarily founded partial Kantian morality. It is shown that, compared to electorates consisting of purely selfinterested voters, such Kantian morality helps voters solve coordination problems and improves the information aggregation properties of equilibria, even for modest levels of morality. 
Date:  2022–04 
URL:  http://d.repec.org/n?u=RePEc:hal:journl:hal03682814&r=mic 
By:  Andrea Attar (TSER  Toulouse School of Economics  UT1  Université Toulouse 1 Capitole  Université Fédérale Toulouse MidiPyrénées  EHESS  École des hautes études en sciences sociales  CNRS  Centre National de la Recherche Scientifique  INRAE  Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement); Thomas Mariotti (TSE  Unité de recherche Transformation des Systèmes d'Élevage  INRAE  Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement); François Salanié (TSE  Unité de recherche Transformation des Systèmes d'Élevage  INRAE  Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement) 
Abstract:  We study insurance markets in which privately informed consumers can purchase coverage from several firms whose pricing strategies are subject to an antidumping regulation. The resulting regulated game supports a single allocation in which each layer of coverage is fairly priced given the consumer types who purchase it. This competitive allocation cannot be Paretoimproved by a social planner who can neither observe consumer types nor monitor their trades with firms. Accordingly, we argue that public intervention under multiple contracting and adverse selection should penalize firms that crosssubsidize between contracts, while leaving consumers free to choose their preferred amount of coverage. 
Keywords:  Insurance Markets, Regulation, Multiple Contracting, Adverse Selection., Insurance Markets Regulation Multiple Contracting Adverse Selection. JEL Classification: D43 D82 D86, Adverse Selection. JEL Classification: D43, D82, D86 
Date:  2022–08 
URL:  http://d.repec.org/n?u=RePEc:hal:journl:hal03796415&r=mic 
By:  Andreas Haupt; Zoe Hitzig 
Abstract:  Firms have access to abundant data on market participants. They use these data to target contracts to agents with specific characteristics, and describe these contracts in opaque terms. In response to such practices, recent proposed regulations aim to increase transparency, especially in digital markets. In order to understand when opacity arises in contracting and the potential effects of proposed regulations, we study a moral hazard model in which a riskneutral principal faces a continuum of weakly riskaverse agents. The agents differ in an observable characteristic that affects the payoff of the principal. In a described contract, the principal sorts the agents into groups, and to each group communicates a distribution of outputcontingent payments. Within each group, the realized distribution of payments must be consistent with the communicated contract. A described contract is transparent if the principal communicates the realized contract to the agent exante, and otherwise it is opaque. We provide a geometric characterization of the principal's optimal described contract as well as conditions under which the optimal described mechanism is transparent and opaque. We apply our results to the design and description of driver payment schemes on ridehailing platforms. 
Date:  2023–01 
URL:  http://d.repec.org/n?u=RePEc:arx:papers:2301.13404&r=mic 
By:  Dirk Bergemann (Yale University); Tibor Heumann (Yale University); Stephen Morris (Cowles Foundation, Yale University) 
Abstract:  We consider a nonlinear pricing environment with private information. We provide profit guarantees (and associated mechanisms) that the seller can achieve across all possible distributions of willingness to pay of the buyers. With a constant elasticity cost function, constant markup pricing provides the optimal revenue guarantee across all possible distributions of willingness to pay and the lower bound is attained under a Pareto distribution. We characterize how profits and consumer surplus vary with the distribution of values and show that Pareto distributions are extremal. We also provide a revenue guarantee for general cost functions. We establish equivalent results for optimal procurement policies that support maximal surplus guarantees for the buyer given all possible cost distributions of the sellers. 
Date:  2023–01 
URL:  http://d.repec.org/n?u=RePEc:cwl:cwldpp:2353&r=mic 
By:  Yeganeh Alimohammadi; Aranyak Mehta; Andres Perlroth 
Abstract:  Autobidding has recently become a popular feature in ad auctions. This feature enables advertisers to simply provide highlevel constraints and goals to an automated agent, which optimizes their auction bids on their behalf. In this paper, we examine the effect of different auctions on the incentives of advertisers to report their constraints to the autobidder intermediaries. More precisely, we study whether canonical auctions such as first price auction (FPA) and second price auction (SPA) are autobidding incentive compatible (AIC): whether an advertiser can gain by misreporting their constraints to the autobidder. We consider valuemaximizing advertisers in two important settings: when they have a budget constraint and when they have a target costperacquisition constraint. The main result of our work is that for both settings, FPA and SPA are not AIC. This contrasts with FPA being AIC when autobidders are constrained to bid using a (suboptimal) uniform bidding policy. We further extend our main result and show that any (possibly randomized) auction that is truthful (in the classic profitmaximizing sense), scalar invariant and symmetric is not AIC. Finally, to complement our findings, we provide sufficient market conditions for FPA and SPA to become AIC for two advertisers. These conditions require advertisers' valuations to be wellaligned. This suggests that when the competition is intense for all queries, advertisers have less incentive to misreport their constraints. From a methodological standpoint, we develop a novel continuous model of queries. This model provides tractability to study equilibrium with autobidders, which contrasts with the standard discrete query model, which is known to be hard. Through the analysis of this model, we uncover a surprising result: in autobidding with two advertisers, FPA and SPA are auction equivalent. 
Date:  2023–01 
URL:  http://d.repec.org/n?u=RePEc:arx:papers:2301.13414&r=mic 
By:  Andrea Canidio 
Abstract:  I study mechanism design with blockchainbased tokens, that is, tokens that can be used within a mechanism but can also be saved and traded outside of the mechanism. I do so by considering a repeated, privatevalue auction, in which the auctioneer accepts payments in a blockchainbased token he creates and initially owns. I show that the presentdiscounted value of the expected revenues is the same as in a standard auction with dollars, but these revenues accrue earlier and are less variable. I then introduce noncontractible effort and the possibility of misappropriating revenues. I compare the auction with tokens to an auction with dollars in which the auctioneer can also issue financial securities. An auction with tokens is preferred when there are sufficiently severe contracting frictions, while the opposite is true when contracting frictions are low. 
Date:  2023–01 
URL:  http://d.repec.org/n?u=RePEc:arx:papers:2301.13794&r=mic 
By:  Andreas A. Haupt; Nicole Immorlica; Brendan Lucier 
Abstract:  Motivated by applications such as voluntary carbon markets and educational testing, we consider a market for goods with varying but hidden levels of quality in the presence of a thirdparty certifier. The certifier can provide informative signals about the quality of products, and can charge for this service. Sellers choose both the quality of the product they produce and a certification. Prices are then determined in a competitive market. Under a singlecrossing condition, we show that the levels of certification chosen by producers are uniquely determined at equilibrium. We then show how to reduce a revenuemaximizing certifier's problem to a monopolistic pricing problem with nonlinear valuations, and design an FPTAS for computing the optimal slate of certificates and their prices. In general, both the welfareoptimal and revenueoptimal slate of certificates can be arbitrarily large. 
Date:  2023–01 
URL:  http://d.repec.org/n?u=RePEc:arx:papers:2301.13449&r=mic 
By:  Robert J. McCann; Kelvin Shuangjian Zhang 
Abstract:  Adverse selection is a version of the principalagent problem that includes monopolist nonlinear pricing, where a monopolist with known costs seeks a profitmaximizing price menu facing a population of potential consumers whose preferences are known only in the aggregate. For multidimensional spaces of agents and products, Rochet and Chon\'e (1998) reformulated this problem to a concave maximization over the set of convex functions, by assuming agent preferences combine bilinearity in the product and agent parameters with a quasilinear sensitivity to prices. We characterize solutions to this problem by identifying a dual minimization problem. This duality allows us to reduce the solution of the square example of RochetChon\'e to a novel free boundary problem, giving the first analytical description of an overlooked market segment. 
Date:  2023–01 
URL:  http://d.repec.org/n?u=RePEc:arx:papers:2301.07660&r=mic 
By:  Chiara Fumagalli; Massimo Motta; Emanuele Tarantino 
Abstract:  A startup and an incumbent negotiate over an acquisition price under asymmetric information about the startup’s ability to succeed in the market. The acquisition may result in the shelving of the startup’s project or the development of a project that would otherwise never reach the market because of financial constraints. Despite this possible procompetitive effect, the optimal merger policy commits to standards of review that prohibit highprice takeovers, even if they may be welfarebeneficial ex post. Ex ante this pushes the incumbent to acquire startups lacking the financial resources to develop independently, and increases expected welfare. Keywords: Optimal merger policy, selection effect, nascent competitors. JEL Classification: L41, L13, K21 
Date:  2022 
URL:  http://d.repec.org/n?u=RePEc:igi:igierp:680&r=mic 
By:  Flavio M. Menezes (Australian Institute for Business and Economics, University of Queensland, Brisbane, Australia); John Quiggin (School of Economics, University of Queensland, Brisbane, Australia) 
Abstract:  This paper reconciles the concepts of ex ante and ex post supply function equilibria of, respectively, Klemperer and Meyer (1989) and Menezes and Quiggin (2020) with the conjectural variations equilibrium of Bowley (1924) and Bresnahan (1981). We show that under appropriate conditions, the ex ante and ex post equilibrium supply curves coincide with each other and with the consistent conjectural equilibrium solution. Further, this is a dominant strategy equilibrium for both ex ante and ex post games, and represents the case in which players are indifferent regarding move order. We explore the implications of our results for empirical work. 
Keywords:  Imperfect competition, games in supply functions, conjectural variations 
JEL:  D43 L13 
Date:  2023–02–04 
URL:  http://d.repec.org/n?u=RePEc:qld:uqaibe:1&r=mic 
By:  Anna Bogomolnaia; Herve Moulin 
Abstract:  We propose a fair and efficient solution for assigning agents to m posts subject to congestion, when agents care about both their post and its congestion. Examples include assigning jobs to busy servers, students to crowded schools or crowded classes, commuters to congested routes, workers to crowded office spaces or to team projects etc... Congestion is anonymous (it only depends on the number n of agents in a given post). A canonical interpretation of ex ante fairness allows each agent to choose m postspecific caps on the congestion they tolerate: these requests are mutually feasible if and only if the sum of the caps is n. For ex post fairness we impose a competitive requirement close to envy freeness: taking the congestion profile as given each agent is assigned to one of her best posts. If a competitive assignment exists, it delivers unique congestion and welfare profiles and is also efficient and ex ante fair. In a fractional (randomised or time sharing) version of our model, a unique competitive congestion profile always exists. It is approximately implemented by a mixture of ex post deterministic assignments: with an approxination factor equal to the largest utility loss from one more unit of congestion, the latter deliver identical welfare profiles and are weakly efficient. Our approach to ex ante fairness generalises to the model where each agent's congestion is weighted. Now the caps on posts depend only upon own weight and total congestion, not on the number of other agents contributing to it. Remarkably in both models these caps are feasible if and only if they give to each agent the right to veto all but (1/m) of their feasible allocations. 
Date:  2023–01 
URL:  http://d.repec.org/n?u=RePEc:arx:papers:2301.12163&r=mic 
By:  de Cornière, Alexandre; Taylor, Greg 
Abstract:  Does enhanced access to data foster or hinder competition among firms? Using a competitioninutility framework that encompasses many situations where firms use data, we model data as a revenueshifter and identify two opposite effects: a markup effect according to which data induces firms to compete harder, and a surplusextraction effect. We provide conditions for data to be pro or anticompetitive, requiring neither knowledge of demand nor computation of equilibrium. We apply our results to situations where data is used to recommend products, monitor insuree behavior, pricediscriminate, or target advertising. We also revisit the issue of data and market structure. 
JEL:  L1 L4 L5 
Date:  2023–01–31 
URL:  http://d.repec.org/n?u=RePEc:tse:wpaper:32535&r=mic 