nep-mic New Economics Papers
on Microeconomics
Issue of 2021‒12‒13
seven papers chosen by
Jing-Yuan Chiou
National Taipei University

  1. The Optimality of Upgrade Pricing By Dirk Bergemann; Alessandro Bonatti; Andreas Haupt; Alex Smolin
  2. Belief Convergence under Misspecified Learning: A Martingale Approach By Mira Frick; Ryota Iijima; Yuhta Ishii
  3. Imprecise Information and Second-Order Beliefs By Norio Takeoka; Takashi Ui
  4. Arrovian Efficiency and Auditability in Discrete Mechanism Design By Marek Pycia; M. Utku Ünver
  5. Social rationalizability with mediation By Herings, P. Jean-Jacques; Mauleon, Ana; Vannetelbosch, Vincent
  6. Aggregation of Models, Choices, Beliefs, and Preferences By Hamed Hamze Bajgiran; Houman Owhadi
  7. Profit-Sharing vs Price-Fixing Collusion with Heterogeneous Firms By Hattori, Keisuke

  1. By: Dirk Bergemann (Cowles Foundation, Yale University); Alessandro Bonatti (MIT); Andreas Haupt (Institute for Data, Systems, and Society, MIT); Alex Smolin (Dept. of Economics, Yale University)
    Abstract: We consider a multiproduct monopoly pricing model. We provide sufficient conditions under which the optimal mechanism can be implemented via upgrade pricing—a menu of product bundles that are nested in the strong set order. Our approach exploits duality methods to identify conditions on the distribution of consumer types under which (a) each product is purchased by the same set of buyers as under separate monopoly pricing (though the transfers can be different), and (b) these sets are nested. We exhibit two distinct sets of sufficient conditions. The ï¬ rst set of conditions weakens the monotonicity requirement of types and virtual values but maintains a regularity assumption, i.e., that the product-by-product revenue curves are single-peaked. The second set of conditions establishes the optimality of upgrade pricing for type spaces with monotone marginal rates of substitution (MRS)—the relative preference ratios for any two products are monotone across types. The monotone MRS condition allows us to relax the earlier regularity assumption. Under both sets of conditions, we fully characterize the product bundles and prices that form the optimal upgrade pricing menu. Finally, we show that, if the consumer’s types are monotone, the seller can equivalently post a vector of single-item prices: upgrade pricing and separate pricing are equivalent.
    Keywords: Revenue Maximization, Mechanism design, Strong duality, Upgrade pricing
    JEL: D42 D82
    Date: 2021–07
  2. By: Mira Frick (Cowles Foundation, Yale University); Ryota Iijima (Cowles Foundation, Yale University); Yuhta Ishii (Department of Economics at Pennsylvania State University)
    Abstract: We present an approach to analyze learning outcomes in a broad class of misspecified environments, spanning both single-agent and social learning. We introduce a novel "prediction accuracy" order over subjective models, and observe that this makes it possible to partially restore standard martingale convergence arguments that apply under correctly specified learning. Based on this, we derive general conditions to determine when beliefs in a given environment converge to some long-run belief either locally or globally (i.e., from some or all initial beliefs). We show that these conditions can be applied, first, to unify and generalize various convergence results in previously studied settings. Second, they enable us to analyze environments where learning is "slow," such as costly information acquisition and sequential social learning. In such environments, we illustrate that even if agents learn the truth when they are correctly specified, vanishingly small amounts of misspecification can generate extreme failures of learning.
    Keywords: Misspecified learning, Stability, Robustness, Berk-Nash equilibrium
    Date: 2020–05
  3. By: Norio Takeoka (Department of Economics, Hitotsubashi University); Takashi Ui (Department of Economics, Hitotsubashi University)
    Abstract: A decision problem under uncertainty is often given with a piece of objective but imprecise information about the states of the world such as in the Ellsberg urn. By incorporating such information into the smooth ambiguity model of Seo (2009), we characterize a class of smooth ambiguity representations whose second-order beliefs are consistent with the objective information. As a corollary, we provide an axiomatization for the second-order expected utility, which has been studied by Nau (2001), Neilson (2009), Grant, Polak, and Strzalecki (2009), Strzalecki (2011), and Ghirardato and Pennesi (2019). In our model, attitude toward uncertainty can be disentangled from a perception about uncertainty and connected with attitude toward reduction of compound lotteries.
    Date: 2021–12
  4. By: Marek Pycia (University of Zurich); M. Utku Ünver (Boston College)
    Abstract: We study mechanism design and preference aggregation in environments in which the space of social alternatives is discrete and the preference domain is rich, as in standard models of social choice and so-called allocation without transfers. We show that a mechanism (or aggregation rule) selects the best outcome with respect to some resolute Arrovian social welfare function if, and only if, it is Pareto efficient and auditable. We further show that auditability implies non-bossiness and is implied by the conjunction of non-bossiness and individual strategy-proofness, and that the later conjunction is equivalent to group strategy-proofness as well as to Maskin monotonicity. As applications, we derive new characterizations in voting and allocation domains.
    Keywords: Strategy-proofness, Pareto efficiency, Arrovian preference aggregation, auditability, non-bossiness, voting, house allocation
    JEL: C78 D78
    Date: 2021–11–15
  5. By: Herings, P. Jean-Jacques (RS: GSBE Theme Data-Driven Decision-Making, RS: GSBE Theme Conflict & Cooperation, Microeconomics & Public Economics); Mauleon, Ana; Vannetelbosch, Vincent
    Abstract: We propose a solution concept for social environments called social rationalizability with mediation that identifies the consequences of common knowledge of rationality and farsightedness. In a social environment several coalitions may and could be willing to move at the same time. Individuals not only hold conjectures about the behaviors of other individuals but also about how a mediator is going to solve conflicts of interest. The set of socially rationalizable outcomes with mediation is shown to be non-empty for all social environments and it can be computed by an iterative reduction procedure. We show that social rationalizability with mediation does not necessarily satisfy coalitional rationality when the number of coalition members is greater than two.
    JEL: C70 C72 C78
    Date: 2021–12–02
  6. By: Hamed Hamze Bajgiran; Houman Owhadi
    Abstract: A natural notion of rationality/consistency for aggregating models is that, for all (possibly aggregated) models $A$ and $B$, if the output of model $A$ is $f(A)$ and if the output model $B$ is $f(B)$, then the output of the model obtained by aggregating $A$ and $B$ must be a weighted average of $f(A)$ and $f(B)$. Similarly, a natural notion of rationality for aggregating preferences of ensembles of experts is that, for all (possibly aggregated) experts $A$ and $B$, and all possible choices $x$ and $y$, if both $A$ and $B$ prefer $x$ over $y$, then the expert obtained by aggregating $A$ and $B$ must also prefer $x$ over $y$. Rational aggregation is an important element of uncertainty quantification, and it lies behind many seemingly different results in economic theory: spanning social choice, belief formation, and individual decision making. Three examples of rational aggregation rules are as follows. (1) Give each individual model (expert) a weight (a score) and use weighted averaging to aggregate individual or finite ensembles of models (experts). (2) Order/rank individual model (expert) and let the aggregation of a finite ensemble of individual models (experts) be the highest-ranked individual model (expert) in that ensemble. (3) Give each individual model (expert) a weight, introduce a weak order/ranking over the set of models/experts, aggregate $A$ and $B$ as the weighted average of the highest-ranked models (experts) in $A$ or $B$. Note that (1) and (2) are particular cases of (3). In this paper, we show that all rational aggregation rules are of the form (3). This result unifies aggregation procedures across different economic environments. Following the main representation, we show applications and extensions of our representation in various separated economics topics such as belief formation, choice theory, and social welfare economics.
    Date: 2021–11
  7. By: Hattori, Keisuke
    Abstract: This paper compares the profitability and sustainability between profit-sharing collusion with side payments and price-fixing collusion without side payments in a two-firm repeated Bertrand game when firms differ in both cost and discount factor. Although profit-sharing collusion yields larger joint profits, bargaining over collusive agreements makes heterogeneous firms prefer different types of collusion: a low-cost (high cost) firm is more likely to adhere to profit-sharing (price-fixing) collusion. If both firms have the same discount factor, profit-sharing collusion is more sustainable. However, price-fixing collusion can be the only sustainable collusion if the efficient firm is more patient than the inefficient firm. Furthermore, we extend profit-sharing collusion by incorporating side payments with different enforcement procedures (i.e., different timing of side payments) and different purposes: to reach agreement and to make the agreement sustainable. Our results provide a theoretical rationale for why firms fail or succeed at reaching and sustaining some forms of collusion.
    Keywords: Collusion; Asymmetric costs; Asymmetric discount factors; Side payments; Repeated game
    JEL: C73 C78 L13 L41
    Date: 2021–11–23

This nep-mic issue is ©2021 by Jing-Yuan Chiou. It is provided as is without any express or implied warranty. It may be freely redistributed in whole or in part for any purpose. If distributed in part, please include this notice.
General information on the NEP project can be found at For comments please write to the director of NEP, Marco Novarese at <>. Put “NEP” in the subject, otherwise your mail may be rejected.
NEP’s infrastructure is sponsored by the School of Economics and Finance of Massey University in New Zealand.