
on Microeconomics 
By:  Francesc Dilmé 
Abstract:  This paper studies bargaining between a seller and a buyer with binary private valuation. Because the setting is more tractable than the case of general valuation distributions (studied in Gul et al., 1986), we are able to explicitly construct the full set of equilibria via induction. This lets us provide a simple proof of the Coase conjecture and obtain new results: The seller extracts all surplus as she becomes more patient, and the equilibrium outcome converges to the perfectinformation outcome as private information vanishes. We also fully characterize the case where there is a deadline: We establish that if the probability that the buyer’s valuation is high is large enough, then the seller charges a high price at all times, there are trade bursts at the outset and the deadline, and trade occurs at a constant rate in between. 
Keywords:  Bargaining, private information, onesided offers. 
JEL:  C78 D82 
Date:  2024–03 
URL:  http://d.repec.org/n?u=RePEc:bon:boncrc:crctr224_2024_515&r=mic 
By:  Dino Gerardi (Collegio Carlo Alberto/University of Turin); Lucas Maestri (FGV EPGE  Escola Brasileira de Economia e Finanças); Ignacio Monzón (Collegio Carlo Alberto/University of Turin) 
Abstract:  We present a model of delegation with moral hazard. A principal delegates a decision to an agent, who affects the distribution of the state of the world by exerting costly and unobservable effort. The principal faces a tradeoff between (i) granting the agent discretion, so he can adapt the decision to the state and (ii) limiting the agent’s discretion, to induce him to exert effort. Our model is flexible on how effort affects the state distribution, thus capturing several distinct economic environments. Optimal delegation takes one of four simple forms, all commonly used in practice: floors, ceilings, floorceilings or gaps. 
Keywords:  delegation, moral hazard, endogenous state, floors, ceilings, caps, gaps 
JEL:  C70 C78 D82 
Date:  2024–03 
URL:  http://d.repec.org/n?u=RePEc:aoz:wpaper:309&r=mic 
By:  Rumen Kostadinov 
Abstract:  I study a dynamic model of durablegood monopoly where the seller cannot commit to future prices and is uncertain about the buyer’s value. I adopt a priorfree approach where the seller minimises lifetime regret against the worstcase type of the buyer. In the unique equilibrium the seller’s worstcase regret against types who purchase at any given time equals the worstcase regret against types who purchase at any other time. The seller cannot profitably deviate even if he could commit to his deviation. Despite this, the equilibrium does not match the commitment outcome. This is because the seller’s objective is endogenously determined by his optimal counterfactual behaviour against each type, which is timeinconsistent. The Coase conjecture holds: in the frequentoffer limit the good is sold immediately at a price equal to the lowest value. 
Keywords:  durablegood monopoly; Coase conjecture; regret 
JEL:  C73 D81 
Date:  2024–03 
URL:  http://d.repec.org/n?u=RePEc:mcm:deptwp:202402&r=mic 
By:  Sumit Goel; Wade HannCaruthers 
Abstract:  We study a contract design problem between a principal and multiple agents. Each agent participates in an independent task with binary outcomes (success or failure), in which it may exert costly effort towards improving its probability of success, and the principal has a fixed budget which it can use to provide outcomedependent rewards to the agents. Crucially, we assume the principal cares only about maximizing the agents' probabilities of success, not how much of the budget it expends. We first show that a contract is optimal for some objective if and only if it is a successfulgeteverything contract. An immediate consequence of this result is that piecerate contracts and bonuspool contracts are never optimal in this setting. We then show that for any objective, there is an optimal prioritybased weighted contract, which assigns positive weights and priority levels to the agents, and splits the budget among the highestpriority successful agents, with each such agent receiving a fraction of the budget proportional to her weight. This result provides a significant reduction in the dimensionality of the principal's optimal contract design problem and gives an interpretable and easily implementable optimal contract. Finally, we discuss an application of our results to the design of optimal contracts with two agents and quadratic costs. In this context, we find that the optimal contract assigns a higher weight to the agent whose success it values more, irrespective of the heterogeneity in the agents' cost parameters. This suggests that the structure of the optimal contract depends primarily on the bias in the principal's objective and is, to some extent, robust to the heterogeneity in the agents' cost functions. 
Date:  2024–02 
URL:  http://d.repec.org/n?u=RePEc:arx:papers:2402.15890&r=mic 
By:  Burkhard C. Schipper 
Abstract:  We consider a decision maker who is unaware of objects to be sampled and thus cannot form beliefs about the occurrence of particular objects. Ex ante she can form beliefs about the occurrence of novelty and the frequencies of yet to be known objects. Conditional on any sampled objects, she can also form beliefs about the next object being novel or being one of the previously sampled objects. We characterize behaviorally such beliefs under subjective expected utility. In doing so, we relate "reverse" Bayesianism, a central property in the literature on decision making under growing awareness, with exchangeable random partitions, the central property in the literature on the discovery of species problem and mutations in statistics, combinatorial probability theory, and population genetics. Partition exchangeable beliefs do not necessarily satisfy "reverse" Bayesianism. Yet, the most prominent models of exchangeable random partitions, the model by De Morgan (1838), the one parameter model of Ewens (1972), and the two parameter model of Pitman (1995) and Zabell (1997), do satisfy "reverse" Bayesianism. 
Date:  2024–03 
URL:  http://d.repec.org/n?u=RePEc:arx:papers:2403.01421&r=mic 
By:  Luca Di Corato (Department of Economics, Ca Foscari University of Venice); Michele Moretto (Department of Economics and Management, University of Padova, Fondazione Eni Enrico Mattei and Centro Studi LeviCase) 
Abstract:  We consider a longterm contractual relationship in which a buyer procures a fixed quantity of a product from a supplier and then sells it on the market. The production cost is private information and evolves randomly over time. The solution to this dynamic principalagent problem involves a periodic twopart payment. The fixed part of the payment depends on the initial supplier’s cost type while the other is contingent on the current cost type. A notable feature is that, by using the information about the initial cost type, the buyer can reduce the burden of information rents paid for the revelation of the future cost type. We show that the distortion, resulting from information asymmetry, remains constant over time and decreases with the initial type. Lastly, we show that our analysis immediately applies also when input prices are private information and evolve randomly over time. 
Keywords:  Dynamic PrincipalAgent model, Supply contracting, Continuous time, Twopart payment 
JEL:  C61 D82 D86 
Date:  2024–02 
URL:  http://d.repec.org/n?u=RePEc:fem:femwpa:2024.04&r=mic 
By:  Rupayan Pal (Indira Gandhi Institute of Development Research); Emmanuel Petrakis (Departamento de Econom¡a, Universidad Carlos III de Madrid) 
Abstract:  This paper shows that in a duopoly a firm has no incentives to divest its passive shares in its rival when firms' strategies are strategic complements. This holds independently whether goods are substitutes or complements and whether firms engage in simultaneous or sequential move product market competition. However, if firms' strategies are strategic substitutes and are engaged in simultaneous move competition, it is optimal for both firms to fully divest their shares in their rivals under a private placement mechanism via independent intermediaries or under competitive bidding. Yet, in the sequential move game only the follower has such incentives. Notably, under a private placement mechanism via a common intermediary, there are circumstances under which there are partial or no firms' divestment incentives, highlighting that the divestment mechanism employed by firms may have a crucial role on their divestment incentives. 
Keywords:  Crossownership, passive shares, strategic substitutes and complements, divestment incentives, market competition 
JEL:  L13 L41 L2 D43 
Date:  2024–02 
URL:  http://d.repec.org/n?u=RePEc:ind:igiwpp:2024003&r=mic 
By:  David Dillenberger (University of Pennsylvania); Uzi Segal (Boston College) 
Abstract:  Consider an economy with equal amounts of N types of goods, to be allocated to agents with strict quasiconvex preferences over lotteries. We show that exante, all feasible and Pareto efficient al locations give almost all agents a binary lottery. Therefore, even if all preferences are the same, some identical agents necessarily receive different lotteries. Our results imply that many of the popular alloca tion mechanisms used in practice are not exante efficient. Assuming the reduction of compound lotteries axiom, social welfare deteriorates by first randomizing over these binary lotteries. Full exante equality can be achieved if agents satisfy the compound independence axiom. 
Keywords:  Allocation Problem, Binary Lotteries, ExAnte Efficiency, Matching, NoEnvy, NonExpected Utility, QuasiConvex Preferences. 
JEL:  C78 D61 D81 
Date:  2024–03–03 
URL:  http://d.repec.org/n?u=RePEc:boc:bocoec:1065&r=mic 
By:  Stergios Athanasoglou; Somouaoga Bonkoungou 
Abstract:  We consider a group of voters that needs to decide between two candidates. We propose a novel family of neutral and strategyproof rules, which we call sequential unanimity rules. By demonstrating their formal equivalence to the Mwinning coalition rules of Moulin (1983), we show that sequential unanimity rules are characterized by neutrality and strategyproofness. We establish our results by developing algorithms that transform a given Mwinning coalition rule into an equivalent sequential unanimity rule and vice versa. The analysis can be extended to accommodate the full preference domain in which voters may be indifferent between candidates. 
Date:  2024–02 
URL:  http://d.repec.org/n?u=RePEc:arx:papers:2402.13009&r=mic 
By:  Francesco De Sinopoli; Leo Ferraris; Claudia Meroni 
Abstract:  In a coordination game with multiple Pareto ordered equilibria and population uncertainty, we show that group size helps select a unique equilibrium, for reasons reminiscent of the global games literature. A critical mass phenomenon emerges at equilibrium. Group size has an emboldening effect on participants. 
Keywords:  Poisson Games, Coordination Games, Equilibrium Selection, Global Games 
JEL:  C72 D82 
Date:  2024–03 
URL:  http://d.repec.org/n?u=RePEc:mib:wpaper:533&r=mic 
By:  Christian Ewerhart; Stanisław Kaźmierowski 
Abstract:  Colonel Blotto games with discrete strategy spaces effectively illustrate the intricate nature of multidimensional strategic reasoning. This paper studies the equilibrium set of such games where, in line with prior experimental work, the tiebreaking rule is allowed to be flexible. We begin by pointing out that equilibrium constructions known from the literature extend to our class of games. However, we also note that, irrespective of the tiebreaking rule, the equilibrium set is excessively large. Specifically, any pure strategy that allocates at most twice the fair share to each battlefield is used with positive probability in some equilibrium. Furthermore, refinements based on the elimination of weakly dominated strategies prove ineffective. To derive specific predictions amid this multiplicity, we compute strategies resulting from longrun adaptive learning. 
Keywords:  Colonel Blotto games, multidimensional strategic reasoning, tiebreaking rules, Nash equilibrium, dominated strategies, adaptive learning 
JEL:  C72 C91 D74 
Date:  2024–03 
URL:  http://d.repec.org/n?u=RePEc:zur:econwp:443&r=mic 
By:  Alfred Galichon; Antoine Jacquet 
Abstract:  Matching problems with linearly transferable utility (LTU) generalize the wellstudied transferable utility (TU) case by relaxing the assumption that utility is transferred oneforone within matched pairs. We show that LTU matching problems can be reframed as nonzerosum games between two players, thus generalizing a result from von Neumann. The underlying linear programming structure of TU matching problems, however, is lost when moving to LTU. These results draw a new bridge between nonTU matching problems and the theory of bimatrix games, with consequences notably regarding the computation of stable outcomes. 
Date:  2024–02 
URL:  http://d.repec.org/n?u=RePEc:arx:papers:2402.12200&r=mic 
By:  Sara Fish; Yannai A. Gonczarowski; Sergiu Hart 
Abstract:  We study a matching problem between agents and public goods, in settings without monetary transfers. Since goods are public, they have no capacity constraints. There is no exogenously defined budget of goods to be provided. Rather, each provided good must justify its cost, leading to strong complementarities in the "preferences" of goods. Furthermore, goods that are in high demand given other alreadyprovided goods must also be provided. The question of the existence of a stable solution (a menu of public goods to be provided) exhibits a rich combinatorial structure. We uncover sufficient conditions and necessary conditions for guaranteeing the existence of a stable solution, and derive both positive and negative results for strategyproof stable matching. 
Date:  2024–02 
URL:  http://d.repec.org/n?u=RePEc:arx:papers:2402.11370&r=mic 