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on Microeconomics |
| By: | Martimort, David; Poudou, Jean-Christophe; Thomas, Lionel |
| Abstract: | A buyer (the principal) procures a good or service from a risk-neutral seller (the agent). The seller, protected by limited liability, has private information on his marginal cost of production (adverse selection), and exerts a non-verifiable effort that increases surplus (moral hazard). Even when the effort and production technologies are separable, the optimal contract always mixes features that are found separately under with pure moral hazard or pure screening. Screening distortions are mitigated in comparison with the pure screening scenario with the possibility of bunching for the least efficient types even in contexts where full separation would be obtained with pure screening. Effort distortions are also used as a screening device. In comparison with a pure moral hazard scenario, those distortions may be lessened for the most efficient types, up to the point of possibly allowing implementation of the first-best effort, while they are worsened for the worst types. Although our analysis is cast in a simple procurement setting, we illustrate our findings in other economic environments of general interest including economic and environmental regulation, financial contracting, provision of quality in services, and price discrimination. |
| Keywords: | Adverse selection; moral hazard; contract theory |
| JEL: | D82 |
| Date: | 2025–03–11 |
| URL: | https://d.repec.org/n?u=RePEc:tse:wpaper:130428 |
| By: | Kym Pram; Burkhard C. Schipper (Department of Economics, University of California Davis) |
| Abstract: | We study the design of efficient mechanisms under asymmetric awareness and information. Unawareness refers to the lack of conception rather than the lack of information. Assuming quasi-linear utilities and private values, we show that we can implement in conditional dominant strategies a social choice function that is utilitarian ex-post efficient when pooling all awareness of all agents without the need of the social planner being fully aware ex-ante. To this end, we develop novel dynamic versions of Vickrey-Clarke-Groves mechanisms in which types are revealed and subsequently elaborated at endogenous higher awareness levels. We explore how asymmetric awareness affects budget balance and participation constraints. We show that ex-ante unforeseen contingencies are no excuse for deficits. Finally, we propose a modified reverse second price auction for efficient procurement of complex incompletely specified projects. |
| Keywords: | dynamic mechanism design, VCG mechanisms, auctions versus negotiations, unknown unknowns, complex projects |
| JEL: | D83 |
| Date: | 2025–04–05 |
| URL: | https://d.repec.org/n?u=RePEc:cda:wpaper:372 |
| By: | Narvin Kartik; Andreas Kleiner |
| Abstract: | For multidimensional Euclidean type spaces, we study convex choice: from any choice set, the set of types that make the same choice is convex. We establish that, in a suitable sense, this property characterizes the sufficiency of local incentive constraints. Convex choice is also of interest more broadly, e.g., in cheaptalk games. We tie convex choice to a notion of directional single-crossing differences (DSCD). For an expected-utility agent choosing among lotteries, DSCD implies that preferences are either one-dimensional or must take the affine form that has been tractable in multidimensional mechanism design. |
| Keywords: | single crossing; incentive compatibility; mechanism design; cheap talk |
| JEL: | D82 |
| Date: | 2025–03 |
| URL: | https://d.repec.org/n?u=RePEc:bon:boncrc:crctr224_2025_676 |
| By: | Alfonso Maselli (University of Pennsylvania) |
| Abstract: | We study a decision maker who approaches an uncertain decision problem by formulating a set of plausible probabilistic models of the environment but is aware that these models are only stylized and incomplete approximations. The agent is effectively facing two layers of uncertainty. Not only is the decision maker uncertain regarding what model in this set has the best fit (model ambiguity), but she is also concerned that the best-fit model itself might be a poor description of the environment (model misspecification). We develop an axiomatic foundation for a general class of preferences that capture concern toward these two layers of uncertainty and allow us to compare individuals’ degrees of aversion to model misspecification and model ambiguity independently of each other. |
| Date: | 2025–04–04 |
| URL: | https://d.repec.org/n?u=RePEc:pen:papers:25-010 |
| By: | Takeshi Murooka; Yuichi Yamamoto |
| Abstract: | This paper considers Bayesian learning when players are biased about the data-generating process, and are biased about the opponent’s bias about the data-generating process. Specifically, we assume that each player’s bias about others takes the form of interpersonal projection, which is a tendency to overestimate the extent to which others share the player’s own view. We show that even an arbitrarily small amount of bias can destroy correct learning of an unknown state, i.e., there is zero probability of the posterior belief staying in a neighborhood of the true state. |
| Date: | 2025–04 |
| URL: | https://d.repec.org/n?u=RePEc:dpr:wpaper:1284 |
| By: | Kentaro Asai (Kyoto University); Bruce Grundy (Australian National University); Ryuichiro Izumi (Department of Economics, Wesleyan University) |
| Abstract: | Should banks be transparent during a bail-in? Banks suffering losses may bail-in creditors to optimally allocate resources between early and late withdrawers. However, if losses are private information, then bail-ins may signal asset quality. In the absence of signaling, banks can sell assets at a pooled price, effectively insuring creditors against asset risks. However, when bail-ins signal quality, banks may delay bail-ins and sell assets at higher prices, but this incentive to delay can trigger inefficient bank runs. To prevent such runs, banks should choose to be either fully transparent or entirely opaque, ensuring asset quality is not private information. |
| Keywords: | Bank Runs, Swing Pricing, Bail-ins, Signaling, Asymmetric Information, Opacity |
| JEL: | E44 G21 G23 G28 D82 D84 D86 |
| Date: | 2025–04 |
| URL: | https://d.repec.org/n?u=RePEc:wes:weswpa:2025-003 |
| By: | Caprice, Stéphane; Shekhar, Shiva |
| Abstract: | In this paper, we study supplier encroachment in competition with multi-product retailers and its effects on retail profits under endoge-nous consumer shopping behavior. We find that supplier encroach-ment (weakly) increases both supplier and retailer profits, as the re-tailer benefits from better consumer segmentation and price discrim-ination despite (weakly) higher wholesale prices. The effect of en-croachment on consumers is more nuanced: when the competitive product’s value is high, consumers benefit. Instead, when the value of the competitive product is low, consumers buying exclusively from the multi-product retailer are worse off while consumers who mix and match across stores are better off. Overall, supplier encroachment can improve market outcomes if the value of the supplier’s product offering is sufficiently high. |
| Keywords: | Encroachment; Vertical Contracting; Downstream Competition and Consumer Shopping Costs. |
| JEL: | L13 L22 L42 L81 |
| Date: | 2025–03 |
| URL: | https://d.repec.org/n?u=RePEc:tse:wpaper:130442 |
| By: | Christian Ewerhart |
| Abstract: | This paper examines the definition and continuity of expected payoffs in compact games with continuous payoff functions. There are three main results. First, we confirm that Glicksberg’s (1952) original definition of expected payoffs as an iterated integral is mathematically sound under general conditions. Second, we show that the now more common definition as a single integral is both rigorous and equivalent to the original when strategy spaces are either Hausdorff or second countable. Third, we offer an alternative proof of the continuity of expected payoffs without imposing the Hausdorff separation axiom. Together, these results lead to a strengthening of Glicksberg’s theorem on equilibrium existence in compact Hausdorff games with continuous payoff functions. |
| Keywords: | Compact games, expected payoffs, weak* topology, measurability, continuity |
| JEL: | C72 |
| Date: | 2025–03 |
| URL: | https://d.repec.org/n?u=RePEc:zur:econwp:467 |
| By: | Nicolas Schutz; Anton Sobolev |
| Abstract: | We study the competitive effects of dual pricing, a vertical restraint that involves charging a distributor a different price for units intended to be resold online than for units intended to be resold offline. We develop a model in which a manufacturer contracts with hybrid retailers, which sell the manufacturer’s product both in their brick-and-mortar stores and through an online channel. We find that dual pricing allows the manufacturer to induce the industry monopoly outcome whereas uniform pricing does not. Yet, dual pricing does not necessarily harm consumers or society at large, as the market outcome is distorted by market power regardless of whether dual or uniform pricing is used. Indeed, we find that consumer surplus and aggregate surplus tend to be higher under dual pricing if the online market is small, if the search costs faced by offline consumers are high, and if the pass-through rate of cost increases is high. |
| Keywords: | dual pricing, price dispersion, search, vertical restraints |
| JEL: | L13 L42 D43 D83 |
| Date: | 2025–03 |
| URL: | https://d.repec.org/n?u=RePEc:bon:boncrc:crctr224_2025_678 |
| By: | Srihari Govindan (Department of Economics, University of Rochester, Rochester, USA); Rida Laraki (Morrocan Center for Game Theory, UM6P, Rabat, Morocco); Lucas Pahl (School of Economics, University of Sheffield, Sheffield S1 4DT, UK) |
| Abstract: | We present the following analog of O’Neill’s Theorem (Theorem 5.2 in [17]) for finite games. Let C1, . . . , Ck be the components of Nash equilibria of a finite normal-form game G. For each i, let ci be the index of Ci. For each ε > 0, there exist pairwise disjoint neighborhoods V1, ..., Vk of the components such that for any choice of finitely many distinct completely mixed strategy profiles {σij}ij, σij ∈ Vi for each i = 1, . . . , k and numbers rij ∈ {−1, 1} such that j rij = ci, there exists a normal-form game G¯ obtained from G by adding duplicate strategies and an ε-perturbation G¯ε of G¯ such that the set of equilibria of G¯ε is {σ¯ij}ij , where for each i, j:(1) σ¯ij is equivalent to the profile σij; (2) the index σ¯ij equals rij. |
| Keywords: | Game Theory, Index Theory, Fixed Point Theory |
| JEL: | C72 |
| Date: | 2025–01 |
| URL: | https://d.repec.org/n?u=RePEc:shf:wpaper:2025002 |
| By: | Bernhardt, Dan (University of Illinois and University of Warwick); Boulatov, Alex (International College of Economics and Finance, Moscow,) |
| Abstract: | We analyze speculation by an informed trader who can commit to her trading strategy in a Kyle-style dealership market. Market makers observe the exact parametric form of the speculator’s trading strategy but not her private information and then price competitively given the net (informed plus noise trade) order flow. We derive necessary and suffcient conditions for the speculator not to profit from commitment. This imposes conditions on model primitives satisfied by Normally-distributed uncertainty that give rise to linear equilibria, but are generically not satisfied. With commitment the speculator may trade less aggressively after some signals, but more aggressively after others. |
| Date: | 2025 |
| URL: | https://d.repec.org/n?u=RePEc:wrk:warwec:1553 |
| By: | Christian Ewerhart |
| Abstract: | This paper identifies a central role of the topological separation axiom T1 in the definition of mixed strategies in noncooperative games with arbitrary pure strategy spaces. Our main result says that a pure strategy space is topologically T1 if and only if (i) all singleton strategy sets are Borel, (ii) all Dirac measures are regular, and (iii) the canonical mapping from pure strategies to Dirac measures is one-to-one. The analysis therefore suggests that the T1 separation axiom is a minimum requirement on the topology of a pure strategy space when randomization is allowed for. Using an example, we show that the T1 assumption is indeed missing from the minimax theorem of Mertens (1986). |
| Keywords: | Mixed strategies, Hausdorff spaces, T1 separation axiom, minimax theorem |
| JEL: | C72 |
| Date: | 2025–04 |
| URL: | https://d.repec.org/n?u=RePEc:zur:econwp:468 |
| By: | Heifetz, Aviad; Peña, Jorge |
| Abstract: | In the standard continuous-time choice-taking gradient dynamics in smooth two-player games, each player implicitly assumes that their opponent momentarily main-tains their last choice. Contrastingly, in the utility-taking gradient dynamics each player implicitly assumes that their opponent momentarily maintains their utility level, by marginally adjusting their choice to that effect. Somewhat surprisingly, employing a transversality argument we find that, in an open and dense set of smooth games, this dynamics is undefined at Nash equilibria. This occurs because, at a Nash equilibrium, the opponent’s indifference curve is not locally a function of one’s own strategy, mak-ing it impossible to specify an opponent’s adjustment that would maintain their utility in response to one’s own marginal deviation from Nash behavior. Furthermore, when approaching a Nash equilibrium of such a generic game, the utility-taking gradient dy-namics either accelerates without bound towards the equilibrium or diverges away from it with unbounded speed. |
| Keywords: | gradient dynamics |
| Date: | 2025–03 |
| URL: | https://d.repec.org/n?u=RePEc:tse:wpaper:130433 |
| By: | Moav, Omer (University of Warwick & Reichman University); Pascali, Luigi (UPF & LUISS); Pauzner, Ady (Tel Aviv University & Reichman University) |
| Abstract: | Cooperation in joint ventures is widespread, despite its vulnerability to defection. It can emerge when the interaction is repeated and agents are patient enough to prefer the benefits of future cooperation over the short-term gains from defection. Thus, if a large fraction of the population consists of impatient exploiters who always defect and agents are randomly paired to play a repeated prisoner dilemma game, patient agents defect as well, and society is in a no-cooperation trap. We show that the existence of an outside option can break this trap even if the fraction of patient agents is arbitrarily small. Impatient agents self-select out of the game, allowing patient agents to cooperate. Patience thus has an evolutionary advantage, leading to widespread cooperation. |
| Date: | 2025 |
| URL: | https://d.repec.org/n?u=RePEc:wrk:warwec:1554 |
| By: | Kinda Hachem; Martin Kuncl |
| Abstract: | Several countries now require banks or money market funds to impose state-contingent costs on short-term creditors to absorb financial stress. We study these requirements as part of the broader prudential toolkit in a model with five key ingredients: banks may face an aggregate stress state with high withdrawals; a fire-sale externality motivates a mix of non-contingent and state-contingent regulation; banks may use shadow technologies to circumvent regulation; parameters of the shadow technologies may be private information; and bailouts may occur. We characterize the optimal policy for various combinations of these ingredients and demonstrate that the threat of shadow activities constrains state-contingent regulation more than noncontingent regulation, especially when imperfect information and limited commitment coexist. The planner triggers shadow activities with positive probability under imperfect information, and shadow activities that deplete resources in the stress state elicit larger bailouts under limited commitment, rendering the requirement of state-contingent costs a weak instrument. |
| Keywords: | pecuniary externality; bailout; Bail-in; shadow banking; optimal regulation |
| JEL: | D62 E61 G01 G21 G28 |
| Date: | 2025–03–01 |
| URL: | https://d.repec.org/n?u=RePEc:fip:fednsr:99645 |
| By: | Aase, Knut K. (Dept. of Business and Management Science, Norwegian School of Economics) |
| Abstract: | We consider Pareto optimal risk sharing between a buyer and a seller of insurance contracts, as well as consumption substitution and saving in a two-period context. The separation of the time periods allows us to consider the substitution effect. We show that the classical result of Pareto optimal risk sharing between a customer and an insurer is robust, and remains so also with recursive utility. For both expected utility and recursive utility we obtain precautionary savings with prudence. With recursive utility we identify the connection between the coefficient of elasticity of substitution in consumption and optimal saving, both under certainty and uncertainty. The separation of consumption substitution from risk aversion is shown to be partial. |
| Keywords: | Pareto optimal risk sharing; two-period models; recursive utility; consumption substitution; separation; precautionary savings |
| JEL: | G00 G22 |
| Date: | 2025–02–25 |
| URL: | https://d.repec.org/n?u=RePEc:hhs:nhhfms:2025_007 |
| By: | Andreas Hefti; Peiyao Shen |
| Abstract: | Understanding disparities in contest success is central to explaining how competition shapes the distribution of rewards, influence, or market shares. We introduce the Proportional Play Equilibrium (PPE), a boundedly rational alternative to Nash Equilibrium (NE) grounded in the Illusion of Proportionality, and show that it results in more unequal outcomes by exaggerating the success chances of stronger contestants. Laboratory evidence strongly supports PPE’s predictions for success dispersion while rejecting those of NE. Our results highlight how equilibrium analysis under full rationality may mischaracterize the inequality-generating effects of competition, with further implications for understanding inequality in markets or political contests. |
| Keywords: | Illusion of proportionality, bounded rationality, contest success, market share and inequality, behavioral contest theory |
| JEL: | D01 D91 D72 C72 |
| Date: | 2025–03 |
| URL: | https://d.repec.org/n?u=RePEc:zur:econwp:466 |
| By: | Lucas Pahl (School of Economics, University of Sheffield, Sheffield S1 4DT, UK); Carlos Pimienta (School Of Economics, The University of New South Wales, Sydney, Australia) |
| Abstract: | We prove the 2-player, generic extensive-form case of the conjecture of Govindan and Wilson (1997a, b) and Hauk and Hurkens (2002) stating that an equilibrium component is essential in every equivalent game if and only if the index of the component is nonzero. This provides an index-theoretic characterization of the concept of hyperstable components of equilibria in generic extensive-form games, first formulated by Kohlberg and Mertens (1986). We also illustrate how to compute hyperstable equilibria in multiple economically relevant examples and show how the predictions of hyperstability compare with other solution concepts. |
| Keywords: | Game Theory, Robustness of Equilibria, Fixed Point Theory, Index Theory |
| JEL: | C72 |
| Date: | 2025–01 |
| URL: | https://d.repec.org/n?u=RePEc:shf:wpaper:2025001 |
| By: | Aase, Knut K. (Dept. of Business and Management Science, Norwegian School of Economics) |
| Abstract: | We analyze optimal risk sharing between a customer and an in surer, and present alternative explanations for the prevalence of kinks in Pareto optimal contracts, like deductibles and upper bounds as in XL-contracts. Linear indemnity functions have primarily been considered in the literature. We focus on nonlinear contracts, which can be explained on the basic of different preferences held by the parties involved. In this setting we derive Pareto optimal contracts with ”near” deductibles and ”near’ caps, which we illustrate by examples. Lastly we consider a model based on non-verifiability where the insurer is risk-neutral. We change to a setting where both the cedent and the reinsurer are strictly risk averse. This rationalizes both an endogenous upper cap and a deductible, retaining compensations for risk bearing. |
| Keywords: | Pareto optimal risk sharing; nonlinear contracts; XL-contracts; non-verifiability |
| JEL: | G00 G22 |
| Date: | 2025–02–26 |
| URL: | https://d.repec.org/n?u=RePEc:hhs:nhhfms:2025_008 |
| By: | Franz Dietrich (Centre d'Economie de la Sorbonne, Université Paris 1 Panthéon-Sorbonne, Paris School of Economics, CNRS) |
| Abstract: | Ever since the Harsanyi-Sen debate, it is controversial whether someone's welfare should be measured by her von-Neumann-Morgenstern (VNM) utility, for instance when analysing welfare intensity, social welfare, interpersonal welfare comparisons, or welfare inequality. We prove that natural working hypotheses lead to a di¤erent welfare measure. It addresses familiar concerns about VNM utility, by faithfully capturing non-ordinal welfare features such as welfare intensity, despite resting on purely ordinal evidence such as revealed preferences or self-reported welfare comparisons. Using this welfare measure instead of VNM utility alters social welfare analysis for instance, Harsanyi's 'utilitarian theorem' now effectively supports prioritarianism. VNM utility is shown to be a hybrid object, determined by an interplay of two factors: welfare and attitude to intrinsic risk, i.e., to risk in welfare rather than outcomes |
| Keywords: | welfare; utility; social welfare; utilitarianism; Harsanyi-Sen debate |
| JEL: | D00 D60 D63 D69 D70 D80 |
| Date: | 2025–01 |
| URL: | https://d.repec.org/n?u=RePEc:mse:cesdoc:25003 |